[ { "image_filename": "designv11_29_0001271_analsci.27.1-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001271_analsci.27.1-Figure3-1.png", "caption": "Fig. 3 (a) Flow electrolysis cell with porous PTFE resin tube, FECRIT, proposed for precise coulometry.10\u201312,15 (b) Sectional view of the PTFE tube equipped with a metal wire. (c) Vessel made by utilizing 5 mL volumetric flask to collect the W effused from the PTFE resin tube. (d) Configuration of two-step FECRIT system with sample injection part. 1, Porous PTFE resin tube; 2, metal wire; 3, platinum wire; 4, reference electrode in O; 5, W-path; 6, W|DCE interface; 7, narrow opening (about 100 \u03bcm width) to leak air; W, aqueous sample solution; O, organic solution.", "texts": [ " It = I0exp(\u2013\u03bbt) (1) The \u03bb is the function of A (cm2), V (cm3) of W or O where the ion of interest exists, the diffusion coefficient of the ion, D (cm2 s\u20131), and the thickness of the diffusion layer at the interface, \u03b4 (cm).19 \u03bb = AD/V\u03b4 (2) According to Eqs. (1) and (2), the rapid electrolysis is attained when the ratio of A/V is large and \u03b4 is small. The electrolysis with the direct stirring of the W | O interface and that with the micro-flow cell with a hydrophobic membrane-stabilized W | O interface described above are ideas to enlarge the W | O interface, though they were not evaluated as the accurate and precise coulometric methods. The present authors and colleagues developed flow cells (see Fig. 3) for the rapid and coulometric ion transfer at the W | O interface10\u201312,15 by utilizing a porous poly(tetrafluoroethylene), PTFE, tube (1.0 mm inner diameter) with a metal wire (0.8 mm diameter) inserted into the tube. The tube was immersed in O, and the W containing a species of interest was forced to flow through the narrow gap (called the W-path, hereafter) between the tube and the metal wire. The electrolysis was performed by applying E between W and O. The cell was named as the Flow Electrolysis Cell for Rapid Ion Transfer, and abbreviated as FECRIT", "21 2\u00b72\u00b72 Flow cell composed of a porous PTFE resin tube Though the cells of Figs. 1 and 2 were proposed for total electrolyses based on interfacial ion transfer reactions, the precisions and accuracies attained by these cells were not sufficient compared with those obtained by the ordinary coulometry based on redox reactions (i.e., accuracy better than 99% and precision better than \u00b10.1% level). Another difficulty with the cell of Fig. 2 is that the structure of the cell is rather complicated and hence its fabrication is not easy. The FECRIT of Fig. 3 was developed by the group of present authors as a new cell that could overcome the above difficulties.10\u201312,15 The fabrication of FECRIT, the procedure for the electrolysis with FECRIT and some applications of FECRIT will be described in detail in Sects. 3 and 4. 2\u00b72\u00b73 Flow cell composed of porous polypropylene tube doped with reagents for the polymeric ion-selective electrode Since the FECRIT system requires a large volume of volatile organic solvent and rather high quantities of special chemicals such as ionophores, the group of Bakker proposed a liquid membrane based coulometric ion detector with membrane components typically used in polymeric ion-selective electrodes in order to escape from the restrictions of FECRIT", " However, the relative standard deviations of coulomb numbers observed were reported to be very good as 0.11 and 0.70% for three repeated measurements (n = 3) of 10\u20135 and 10\u20134 M Ca2+, respectively. The result indicates that the cell of Fig. 4, in which no volatile organic solvent exists will also be promising for coulometric analysis, though it is difficult to utilize the merits of a flow system such as FECRIT (see Sects. 3 and 4) since the electrolysis is carried out after stopping the flow of the sample solution. Determinations\u2014 As illustrated in Fig. 3, the FECRIT consisted of a porous PTFE resin tube (1) (1 mm inner diameter, 2 mm outer diameter, 50 cm length (unless otherwise stated), 1 \u03bcm pore size and 60% pore density; PoreflonTM tube, TB-0201; a product of Sumitomo Electric Fine Polymer Inc.), a metal wire (2) (0.8 mm diameter (unless otherwise stated)) inserted into the tube, a platinum wire (3) placed outside and parallel to the tube and a tetraphenylborate ion selective electrode, TPhBE, or a tetraethylammonium ion selective electrode, TEAE, which was the RE in O (4)", "25 In another method of electrolysis which will hereafter be called the \u201cflow injection method\u201d, a definite volume of the sample solution was introduced into the stream of a carrier solution containing only SE by using an injector for liquid chromatography placed in front of the FECRIT. In the measurements performed by both the homogeneous solution flow method and the flow injection method, W was forced to flow through the FECRIT at f of 0.1 mL min\u20131 unless otherwise described. In order to remove the interference from diverse ions, the two-step FECRIT system was developed12 by connecting 2 FECRITs in series (see Fig. 3(d)). In this system, the 1st step FECRIT was used for the removal of the diverse ions, and the 2nd one for the coulometric determination of the ionic species of interest. The characteristics of the FECRIT were investigated based on the current\u2013potential difference, I\u2013E, relation observed at the W | O interface in the FECRIT. In this investigation, the transfer of K+ from W to DCE facilitated by dibenzo-18-crown-6 (see Fig. 5), DB18C6, was taken as an example, and the I\u2013E curve was recorded by forcing W containing 5 \u00d7 10\u20134 M KCl to flow at f of 0", " Therefore, TODGA was considered to facilitate the transfer of Ca2+ selectively differentiating from Na+, K+, H+ and Mg2+. However, the facilitation by TODGA was not selective enough to avoid the interference from Na+ of c about 50 times larger than cCa2+,28 as indicated by the I\u2013E curve (curve 2 in Fig. 8) observed by forcing W containing 0.01 M NaCl and 5 \u00d7 10\u20133 M MgCl2 (SE) to flow through the Ag/AgCl-FECRIT system with DCE containing 0.01 M TODGA. The interference from Na+ could be removed by using the two-step FECRIT system (see Fig. 3(d)). In the system, the 1st step FECRIT was used for the removal of Na+, and the 2nd one for the coulometric determination of Ca2+. The transfer of Na+ was facilitated by adding 0.01 M bis[(12-crown-4)methyl]-2dodecyl-2-methylmalonate, bis(12-crown-4), (see Fig. 5) to DCE in the 1st step FECRIT, and Na+ in W was removed selectively leaving Ca2+ in W by applying E available for the Il such as +0.21 V versus TEAE. In this connection, the positive current wave for the transfer of Na+ facilitated by bis(12-crown-4) showed reversible characteristics, and E1/2 of the wave was at 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001691_iccci.2013.6466123-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001691_iccci.2013.6466123-Figure3-1.png", "caption": "Fig. 3 Kinematic coordinate system assignments", "texts": [ " Part II: the validity of the coordinates based motion control algorithm, and the sub goal based algorithm with GLVD building is tested. Once the frontier regions are defined, the closest region from the robot is chosen as the sub-goal. Here, we use the motion control algorithm with GLVD for a rescue operation in a congested building side where some fellows get injured. The robot by its sensors used to scan the whole area step by step using GVD, even in odd areas where no one can think of reach also, considering the safest path towards the destination. Part III: From the figure 3, 4, 5, 6 it can be concluded that, the robot is covering the whole area for finding out the victims in a specified time. The robot is scanning the inner lane and is finding out the entities in the lane. The sensor used here is the ultrasonic sensor and from the sensor data it can absolutely find out that where the victims are. The robot sensor angle should be suitably adjusted so that it can scan the innermost surface of the specified map also the heading of the robot should be held in a definite position" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000459_la901812k-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000459_la901812k-Figure2-1.png", "caption": "Figure 2. Viscous friction forces acting on myosin V. Figure 3. Forces emulating conformational changes and external forces.", "texts": [ " The unit of mass, the attogram (ag) is chosen so that the mass values are on the order 100, and the length and time units, the nanometer (nm) and millisecond (ms), are chosen for similar reasons.Thesemasses and inertias are contained in the mass matrix A in eq (1) which is symmetric positive definite and nondiagonal. 2.2. Viscous Friction. Each body has a force and moment applied at and about its mass center to approximate the viscous friction of the fluid through which the motor protein moves, as shown in Figure 2. To truly assess the effects of viscous friction on a rigid body, one should consider drag which depends on its shape and orientation, but here a simple coefficient of viscous friction is used. Further details are given in Supporting Information A.1. 2.3. Conformational Changes and External Forces. Several forces contribute to protein locomotion, including the conformational changes due to ATP hydrolysis. Regardless of their source and application, their resultant can be transformed into equivalent forces at the protein\u2019s joints" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002801_6.2018-1838-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002801_6.2018-1838-Figure8-1.png", "caption": "Figure 8. Gazebo fixed-wing aircraft model.", "texts": [ " The performance variable z and the control input u for RC-PID control of angular-velocity commands about the pitch-axis in the inner loop are given by z(k) 4 = Qref(k)\u2212Q(k), (42) u(k) 4 = Q\u0307ref(k). (43) The filter and weightings are given by Gf(z) = 1/z, Ru = 1, and R\u03b8 = I2. The performance variable z and the control input u for RC-PID control of angular-velocity commands about the yaw-axis in the inner loop are given by z(k) 4 = Rref(k)\u2212R(k), (44) u(k) 4 = R\u0307ref(k). (45) The filter and weightings are given by Gf(z) = 1/z, Ru = 0.01, and R\u03b8 = I2. The Gazebo fixed-wing aircraft model that we use in the simulation is shown in Figure 8. The model has a wing span of 0.94 m and tip-chords of length 0.12 m. It has one propeller engine T , one set of differential ailerons a, one rudder r, and one elevator e. Figure 9 shows the reference waypoints (Xref , Yref) and altitude href for the mission planner. Note that the command is to take off and then loiter around the commanded waypoint while maintaining the altitude at 40 m. Note that the fixed-wing aircraft follows the commanded altitude, while loitering around the commanded waypoint" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000939_s11665-010-9659-4-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000939_s11665-010-9659-4-Figure1-1.png", "caption": "Fig. 1 (a) Schematic of laser melt-deposition process. (b) A turbine blade being made by laser melt deposition (Ref 2). Close examination of the blade surface shows ripples made by layering", "texts": [ " Direct manufacturing is not suitable for mass production, but is ideal for mass customization. It is a revolutionary approach to manufacturing. Laser or e-beam melt-deposition techniques are examples of additive or direct deposition processes for metals. A single material in powder or wire form is added to a melt pool formed by a laser or e-beam. Following a predetermined beam path, a \u2018\u2018homogeneous\u2019\u2019 or single-material three-dimensional (3D) structure is built. A schematic of the laser melt-deposition process is shown in Fig. 1(a). A component being made by laser melt deposition is shown in Fig. 1(b) (Ref 2). K.P. Cooper and S.G. Lambrakos, Materials Science and Technology Division, Naval Research Laboratory, 4555 Overlook Ave., SW, Washington, DC 20375. Contact e-mail: lambrakos@anvil.nrl.navy. mil. JMEPEG (2011) 20:48\u201356 ASM International DOI: 10.1007/s11665-010-9659-4 1059-9495/$19.00 48\u2014Volume 20(1) February 2011 Journal of Materials Engineering and Performance Direct digital manufacturing (DDM) is the method to build objects by digitally controlling highly localized and incremental processing" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003850_s12046-019-1168-z-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003850_s12046-019-1168-z-Figure1-1.png", "caption": "Figure 1. Dual flexible rotor with active magnetic bearings.", "texts": [ " To demonstrate the developed methodology, a numerical experiment has been performed and the effectiveness has been established by verifying the methodology against modelling and measurement error. Also, the effectiveness of the algorithm is verified with repeatability analysis on estimated parameters at different frequency ranges or different modes of excitation. This section explains the assumptions involved in modelling the turbogenerator system as a dual flexible rotor with AMB. 2.1 Assumptions and description of the model A system comprises of a dual flexible rotor with AMB as depicted in figure 1, is taken into account to mimic and online health monitoring of the real turbogenerator system. A known beam theory (Euler Bernoulli) and FEM (figure 2) is utilized to describe the flexible shafts and to obtain elemental equations, respectively. With four stiffness kBn ij and four damping cBn ij bearings are defined. The coupling is modelled with stiffness kCij ; k C ux and k C uy and damping cCij parameters. Along with linear stiffness, two addi- tional direct angular stiffness parameters are used in coupling to accommodate parallel as well as angular misalignment, respectively", " The two cases proposed to acquire numerical signals independently are, Case A: Operating speeds in between the second and third critical frequency Case B: Operating speeds in between the fourth and fifth critical frequency In the subsequent section, based on the above two cases, operating speeds are selected to generate independent sets of response data. Also, to analyze the adaptability of the algorithm, the repeatability analysis is performed by estimating the parameters at different frequency ranges. The abscissa in figures 10\u201314, represent the parameters listed in column 2 in tables 2 and 3. For a demonstration of the proposed algorithm, figure 1 is numerically tested in this section. 6.1 Case A: Operating speeds in between the second and third critical frequency The signals are generated at randomly picked running speeds in between the second (10.66 Hz) and third (31.84 Hz) critical frequency. The running speeds picked are 16 Hz, 17 Hz, 18 Hz, 19 Hz, 20 Hz, 21 Hz, 22 Hz, Table 3. Evaluated parameters with percentage deviation against measurement noise for Case B. Sl.No. Parameters (units) Assumed values Evaluated values 0% Noise 1% Noise 5% Noise Values (% Error) Values (% Error) Values (% Error) 1 e1(mm) 2" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000670_09596518jsce737-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000670_09596518jsce737-Figure1-1.png", "caption": "Fig. 1 Diagram of the ball\u2013screw servosystem", "texts": [ " The paper is organized as follows: first, the description of the LuGre friction model with a servomechanical system is given, and the design procedure of the backstepping controller and friction state observer is presented. Next, a proposed RFNN structure and derivation of a robust friction state observer and an adaptive reconstructed error compensator are explained. The simulation and experiment with discussions on their results are also presented. Finally, conclusions are outlined. As shown in Fig. 1, the dynamics for the servosystem in the presence of non-linear friction is J\u20achzs2 _hzTf~u \u00f01\u00de where J is a moment of inertia, s2 is a viscous friction coefficient, h is an angular position, Tf is a non-linear Proc. IMechE Vol. 223 Part I: J. Systems and Control Engineering JSCE737 dynamic friction, and u is a control input. In the well-known LuGre friction model [1], the interface between two surfaces is modelled by contacts between sets of elastic bristles shown in Fig. 2. When a tangential torque is applied, the elastic bristles will deflect like a spring, which gives rise to the friction torque", " The time derivative of equation (54) is _V 4~ _V 3z 1 g ~U _~U ~{k1z 2 1{k2z 2 2{bpWz2~z{bpz2 ~U zs1~z _z{ _\u0302z z 1 g ~U { _\u0302 U \u00f055\u00de In this case, a friction state observer can be modified as z\u0302~w{bp z3 s1 zk3z1 \u00f056\u00de _w~ 1 s1 {s0w{s2x2zbp s0 s1 z3zu {s0k3z1{b{1 p \u20acxdz 1{k2 1 z1{ k1zk2\u00f0 \u00dez2 {T\u0302 d{U\u0302 i {k3 _z1 \u00f057\u00de Next, differentiating equation (56) and introducing equation (57) into it, equation (55) can be rewritten by _V4~{k1z 2 1{k2z 2 2{s1f x2\u00f0 \u00de~z2z ~U {bpz2{ 1 g _\u0302 U \u00f058\u00de The adaptive compensation law for the reconstructed error is chosen by _\u0302 U~{gbpz2 \u00f059\u00de Then, equation (58) can be written by _V4~{k1z 2 1{k1z 2 2{s1f x2\u00f0 \u00de~z2\u00a10 \u00f060\u00de As V\u03074( 0, then, z1R 0, z2R 0, sR 0, z*R 0, and U\u0303R 0 as tR\u2018 by Barbalat\u2019s lemma [21]. Therefore, the backstepping control system that considers the unknown friction uncertainty and the approximation error can have the asymptotic stability and good robustness to the disturbance. The schematic diagram of the proposed control system is depicted in Fig. 4. In order to verify the performance of a proposed control scheme, some simulations and experiments are carried out for the position tracking control of a servosystem, which is composed of ball\u2013screw and DC servomotor as shown in Fig. 1 and Fig. 5. The identified system parameters through experiments are given in Table 1, and the specifications of the system components are also given in Table 2. The identification process of the dynamic friction parameters is omitted in this paper. To investigate the effectiveness of a proposed control system, three control schemes are designed: backstepping controller (Back), backstepping controller with friction state observer (Back_OB), and backstepping controller using RFNN and robust friction state observer with adaptive reconstructed compensator (Back_RFNR)" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002433_0954410017706990-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002433_0954410017706990-Figure3-1.png", "caption": "Figure 3. Rubbing experiment and sensors installed position diagram: (a) turbine casing single-point rubbing experiment; (b) local partial rubbing experiment; (c) sensors installed position diagram of turbine casing.", "texts": [ " Considering that rubbing position is distributed on casing whole circumference, the paper respectively sets four uniform distribution rubbing points on single-point rubbing state and two rubbing positions on partial rubbing state. The specific rubbing positions are as follows: (1) single-point rubbing: vertical upper, vertical lower, horizontal left, and horizontal right on turbine casing. (2) Local rub: (a) the turbine casing local left or right, (b) the compressor casing local left or right. The diagrams of the rubbing experiment in different rubbing states are shown in Figure 3. Figure 3(a) shows the single-point rubbing experimental diagram. Figure 3(b) depicts the partial rubbing experimental diagram. Different extents of single-point rubbing experiments and local partial rubbing experiments could respectively be embodied by adjusting the rubbing screw against rubbing ring and adjust the compressor partial rubbing adjusting mechanism. The installation position of acceleration sensors always includes vertical upper, vertical lower, horizontal left, and horizontal right of turbine casing. All the rubbing experiments involved in the paper are based on the acceleration signal collected by the acceleration sensors Model 4508, which is provided by Demark Bru\u0308el&Kj\u00e6r, and the rotating speed measured by SE series eddy current displacement sensors, which is provided by instrument factory Southeast University. Data collector model is USB9234 provided by National Instruments. The experiment is conducted under room temperature. Diagrams of installation position of sensors are shown in Figure 3(c). Aero-engine rotor\u2013stator rubbing characteristic extract Due to the limited space, single-point rubbing experimental data are randomly selected from 17 May 2014, and the rotational speed is about 1500 r/min; local partial rubbing experimental data are randomly selected from 28 April 2013, where the rubbing extent is light, and the rotational speed is about 1200 r/min. 1T\u20135T respectively represent 1\u20135 integer multiple rubbing frequencies involved in the paper. Aero-engine rotor\u2013stator rubbing characteristics extraction based on autocorrelation function of casing acceleration signal Cyclic autocorrelation function is used to analyze the rubbing fault on casing vibration acceleration signal" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001074_10402004.2012.681342-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001074_10402004.2012.681342-Figure4-1.png", "caption": "Fig. 4\u2014Crack initiation and propagation by surface shear stress and conjugate tensile stress.", "texts": [ " [19]: (L10 \u2212 \u03b3)e = ( CSe \u03c40 )q , \u03b3 = ( C \u2032 Se \u03c40 )q\u2032 [19] D ow nl oa de d by [ U ni ve rs ity o f C on ne ct ic ut ] at 0 6: 18 0 8 O ct ob er 2 01 4 P-S-N Test Specimen Figure 3 shows the shape of the alternating torsion test specimen and the equal stress line le receiving the maximum shear stress amplitude \u03c4max as a result of torque Tq. Due to the maximum shear stress occurring on the circumference of diameter De at the minimum cross section, the shearing cracks will initiate from points on the equal stress line in the circumferential and axial directions as well as in the radial direction. The critical maximum shear stress is given by Eq. [20] at the minimum cross section: \u03c4max = \u00b116Tq \u03c0D3 e [20] Thereafter, as shown in Fig. 4, the fatigue crack propagates as a result of the conjugate tensile and compressive stresses \u03c31 = \u00b1\u03c4max in a 45\u25e6 direction (in case of hardened materials), finally leading to fracture. This result is for a specimen with an equal stress line similar to the point contact bearing as shown in Fig. 1, and so the number of product law of probabilities K may be considered to follow as K \u221d De (Shimizu (1)). Following a similar method as in Eq. [13] and assuming the specimen\u2019s Weibull slope as mS and taking A0 as the proportionality constant, the life equation may be derived as given by Eq" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002971_apec.2018.8341174-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002971_apec.2018.8341174-Figure1-1.png", "caption": "Fig. 1. Topology of 12/10 DC-biased sinusoidal current vernier motor (b)stator winding current", "texts": [ "eywords\u2014 DC-VRM; Motor drive; three-phase four-leg inverter; 180\u00b0 phase-shifted PWM; I. INTRODUCTION Recently, less or no rare-earth magnet motors attract a lot of attention in electric vehicle field for their low cost, robust structure and so on.[1-2]. DC-Biased Sinusoidal Current Vernier Reluctance Machine (DC-VRM) is a kind of electric field motor proposed in recent years. As shown in Figure 1(a),the DC-VRM have only one set of concentrated windings in the stator side and the rotor side contains only silicon steel, so the motor is easy to manufacture and have a robust rotor structure. The structure of the DC-VRM is very similar to the switched reluctance motor (SRM). However, it can exhibit sinusoidal back-EMF and low torque ripple compared to SRM. The most important feature of the DC-VRM is that the stator current of the DC-VRM is the DC-biased sinusoidal current and the control method of the DCVRM is similar to the synchronous motor. As shown in Fig1. (b), the DC field current is injected into the stator windings with the AC armature current in the DC-VRM [3]. The DC-biased sinusoidal stator current can reduce the copper losses in the stator windings and it also reduce a power supply for excitation. For DC-VRM drive, [4] proposed a vector control system for the motor which stator current is DC-biased sinusoidal current. [5] proposed an integrated field and armature current control strategy for VFRMs using three-phase H-bridge inverter topology", " L\u03b4 is the varying components of the self-inductance of the stator winding. if is the DC component in the stator current which acts as field current. iq is the AC component in the stator current which acts as armature current. From (1), Average electromagnetic torque is generated by the interaction of DC component and AC component in stator current. When the RMS values of the DC component and the AC component are equal, the maximum torque per copper loss can be obtained in DC-VRM, which is called as the MTPA control strategy[3]. As shown in Figure 1(b), bidirectional current flows through the stator winding and the forward current is greater than the reverse current under the MTPA control strategy. This paper introduces a novel four-leg topology for the DCVRM which can obviously reduce the power electronics devices in comparison of traditional three phase H-bridge topology. The drive topology and control strategy are discussed in part II. The simulation results are presented in part III. The experimental results are presented in part IV. Finally, the conclusions are summarized in part V" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003126_tmag.2018.2852800-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003126_tmag.2018.2852800-Figure8-1.png", "caption": "Fig. 8. Illustration of (a) 2.1 kW radial flux AA PMSM structure, (b) stator, and (c) rotor.", "texts": [ " Modal shapes of the AA-stacked core using modified Young\u2019s modulus and shear modulus are basically consistent with modal shapes in Fig. 7. The natural frequencies of the AA-stacked core from the simulation using modified Young\u2019s modulus and shear modulus parameters and experiment are compared in Table II. It is shown that the maximum relative error between the calculated and experimental data is 3.9%. V. IMPLEMENTATION ANALYSIS The numerical model was implemented on a 2.1 kW radial flux surface-mounted AA PMSM. The parameters of the AAPMSM are listed in Table III. The illustration of the AA PMSM structure is shown in Fig. 8. The electromagnetic vibration of a motor is a multi-physical field coupling problem. The magnetic field of the AA PMSM is calculated, and the magnetic flux density distribution of the AA PMSM is shown in Fig. 9. The electromagnetic vibration of the AA PMSM under two different conditions, which are 1) only RFs and 2) both RFs and MS, is calculated. Fig. 10 shows the stator core and housing deformations of the AA PMSM under rated working frequencies. Table IV shows the electromagnetic vibration acceleration of the AA PMSM operating under different working frequencies" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001491_icpe.2011.5944421-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001491_icpe.2011.5944421-Figure1-1.png", "caption": "Fig. 1. Eccentric load torque", "texts": [], "surrounding_texts": [ "The control objective is to determine T\u0303 so that the speed fluctuation vanishes, i.e., \u03c5 \u2192 0. Obvious solution will be T\u0303 = mgr sin(\u03c9mt\u2212\u03b80). But, the laundry mass is unknown so that we cannot use it. We should find a compensating method that utilizes the speed (ripple) information. According to the proposed method, the compensating torque is computed as T\u0303 = A sin(\u03c9at\u2212 \u03b8), (6) where A is adjusted repeatedly until the speed ripple minimizes. The overall control block diagram is shown in Fig.2. The main control action is performed by a PI controller, but a compensating action is done by injecting A sin(\u03c9at \u2212 \u03b8). As for a tuning method of A, we utilize a version of MPPT method, which we call MRPT here." ] }, { "image_filename": "designv11_29_0001414_j.mechmachtheory.2012.01.003-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001414_j.mechmachtheory.2012.01.003-Figure1-1.png", "caption": "Fig. 1. The structures of a 5-5B in-parallel platform and the equivalent 4\u20134 parallel platform.", "texts": [ " Lee and Shim [15] devised a resultant elimination procedure to work out the final input\u2013output equation. Please note that given these works for the general case of 6\u20136 in-parallel platform, their solution procedures do not necessarily lead to a solution to special cases like 5-5B or 4\u20136, etc., as the yielded resultant matrix may be invalid for these cases and it can cause the extraneous roots due to the special geometries. In this paper, we seek to obtain a closed-form solution to the forward displacement analysis of the general 5-5B in-parallel platform [5,16] shown in Fig. 1. Hunt and Primrose [16] pointed out that this problem was equivalent to the forward kinematics of a 4\u20134 parallel platform and that it had in general 24 solutions over the complex number field. The closed-from solution of this problem has been previously studied by Innocenti [17] and Han [1]. However, the former solution did not directly lead to a 24thdegree input\u2013output equation but led to a 48th-degree one, and then the spurious solutions needed to be removed. Although the later work gave the 24th-degree input\u2013output equation, the procedure was complicated and not in symbolic form, especially the GCD was not directly obtained, but by calculating remainder for polynomials", " In this paper, we will derive a 10 by 10 resultant matrix whose elements are all in symbolic form of geometric parameters. The determinant of this resultant matrix, which cannot be computed without specifying the geometry of the platform, gives the 24th-degree input\u2013output equation we are seeking for. Finally, a numerical example confirms the new solution procedure. 2. Constraint equations A 5-5B in-parallel platform PQBCD\u2013EMNGH has its six SPS (S: Spherical joint, P: Prismatic joint) legs connected at the five points in the moving platform and the five points in the base platform, shown in Fig. 1. The six leg lengths (R3\u2013R8) provided by Nomenclature \u2022 The dot product of three-dimensional vectors \u00d7 The cross product of three-dimensional vectors * Scalar product A A point in R3 and the corresponding vector written in the fixed frame A' A vector A written in the moving frame Ab(A'b') A-B(A'-B') |Ab| Norm of vector Ab or the distance between point A and point B in the fixed frame |A'b'| Norm of vector A'b' or the distance between point A and point B in the moving frame AB The edge from point A pointing to point B \u0394ABC The triangle consists of three points A, B and C or the plane where the triangle lies i ffiffiffiffiffiffiffi \u22121 p Imaginary number unit prismatic joint in every leg are the six inputs to control the location and orientation of the moving platform. For both the moving and the base platform, the spherical joints are not restricted to lie in a plane. 2.1. Changing the structure According to Refs. [16] and [17], in Fig. 1, the point E can be only located on a circle with axis PQ. Therefore we can replace the two SPS links PE and QE by one RPS (R: Revolute joint) link AE where point A denotes the foot point on PQwith respect to point E. Analogously, the two SPS links. MB and NB are replaced by one RPS link FB where point F denotes the foot point on MN with respect to point B. Now clearly, the forward displacement analysis of 5-5B in-parallel platform is equivalent to the one of the special 4\u20134 parallel platform ABCD\u2013 EFGH seen in Fig. 1, where two revolute pairs are introduced in place of the couples of legs converging at points E and B. Then we choose point A as the origin O of the fixed coordinate frame and the axis of rotation PQ as the Z axis of the fixed frame, and we assume the point C is located in the YZ plane of the fixed frame. And we choose point F as the origin O' of the moving coordinate frame and the axis of rotation MN as the X axis of the moving frame, and moreover we assume the point H is located in the XY plane of the moving frame. See Fig. 1. The fixed frame is denoted by O\u2212XYZ and the moving frame is denoted by O'\u2212X'Y'Z'.The coordinates of points P, Q, B, C, D and E, M, N, G, H are known respectively in fixed frame and moving frame, that is to say, the coordinates of vectors P, Q, B, C, D, E', M', N', G', H' are known. Two variables \u03b8 and \u03b3 are used for computing the locations and orientations of the moving platform relative to the base as shown in Fig. 1. They are respectively the dihedral angles between \u0394PEQ and \u0394PCQ,\u0394MBN and \u0394MHN,where \u0394PCQ represents the base plane and \u0394MHN represents the moving plane with respect of the above assumption. Now the coordinate of the vector E in the fixed frame and the coordinate of the vector B' in the moving frame can be written as follows: E \u00bc Ea \u00bc \u03b8\u00bd R1 0 0\u00bd T \u00bc R1 cos \u03b8 R1 sin \u03b8 0\u00bd \u00f01\u00de B 0 \u00bc B 0 f 0 \u00bc \u03b3\u00bd 0 R2 0\u00bd T \u00bc 0 R2 cos \u03b3 R2 sin \u03b3\u00bd \u00f02\u00de where [\u03b8] and [\u03b3] respectively denotes the rotation matrix with axis Z and axis X , and R1=|Ea| andR2=|B'f '| can be determined by using the sine law for a planar triangle \u0394PEQ and \u0394MBN. In Fig. 1, let |Pe|=R5, |Qe|=R6, |Bm|=R7, |Bn|=R8, |Cg|=R3, |Dh|=R4, |Eb|=L1, |Gb|=L2, |Ge|=L3, |Gh|=L4, |He|=L5, |Hb|=L6, where R3\u2013R8, L3=|G'e'|, L4=|G'h '|, L5=|H'e'| are known quantities and L1, L2, L6 are unknown quantities. In themoving frame, L1, L2, L6 can be obtained as follows, L1 2 \u00bc E 0b0 \u2022E 0b0 \u00f03\u00de L2 2 \u00bc G 0b0 \u2022G 0b0 \u00f04\u00de L6 2 \u00bc H 0b0 \u2022H 0b0 \u00f05\u00de where L1 2, L22, L62 contain the unknown variables cos \u03b3 and sin \u03b3. Introducing the Euler equations cos \u03b3=(ei\u03b3+e\u2212 i\u03b3)/2 and sin \u03b3=(ei\u03b3\u2212e\u2212 i\u03b3)/(2\u2217 i), they can be changed into quadratic polynomials form in ei\u03b3" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000288_s11705-009-0305-3-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000288_s11705-009-0305-3-Figure3-1.png", "caption": "Fig. 3 Formation process for ZnS hollow spheres", "texts": [ " The hollow and solid ZnS nanospheres were synthesized by refluxing the aqueous solution of the reagents using thioacetamide (TAA) as a S2\u2013 source with the temperature held at 103\u00b0C (Fig. 2) [20]. The spherical morphology has been formed through the oriented aggregation of the formed ZnS primary nanocrystals, and the morphology and size of the samples can be tuned easily by adjusting the experimental parameters properly. The probable reaction process for the formation of ZnS nanospheres can be summarized as Fig. 3. Based on the same reactions, the MWCNT/ZnS heterostructures (Fig. 4) were synthesized by a mild solution-chemical reaction using TAA and Zn(CH3COO)2 (a) chain like aggregates of TiO2 nanoparticles; (b) TiO2/SiO2 composites with dispersion structure; (c) TiO2/SiO2 composites with core-shell structure; (d) ball-in-shell structured TiO2 nanomaterials as S2\u2013 and Zn2+ sources, respectively, as well as using MWCNT as a substrate [21]. In comparison with previous studies on metal-sulfide nanoparticles, the probable reaction process for the formation of MWCNT/ZnS heterostructures can be summarized as follows" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001274_iccke.2012.6395389-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001274_iccke.2012.6395389-Figure1-1.png", "caption": "Figure 1. Heuristic greedy search for sensor section and configuration", "texts": [ " It is used in such a way that through definition of several binary parameters sets, all non-linear calculations are performed in a stage prior to optimization problem, and the optimization problem is described as linear form in the beginning. III. 2BNETWORK MODEL We consider a visual sensor network in which the sensors are randomly distributed on a 3-D area. The main task of the sensors is to capture the images of targets and transmit them to the sink. We use sensor with PTZ capability and full angle coverage respectively. Details of the models come as follows. A. 6BSensor and Target Model We apply the sensor model used in some related works [6] with some extensions as follow: ((xRsR,yRsR,zRsR), , ) (1) As shown in \u201cFig.1.a\u201d, (xRsR,yRsR,zRsR) is the coordinate of sensor node SRi Rin a 3-D area, Parameters , and can be constant or adjustable if Pan-Tilt-Zoom capability be available for visual sensors. is the bisect line-of-sight of the sensing direction adjusted by pan capability, is the inclined angle of view (tilt) enlargement. The zoom range of visual sensor can be shown as: RminR RmaxR (2) Point target model can be written as and circular target model can be written as follow: ((xRRR,yRRR,zRRR), RRtR) (3) Where (xRRR,yRRR,zRRR) is the coordinate of target TRiR located in a 3D area and RRtR is the radius of target", " 7BTarget Coverage According to parameters defined for sensor and target model, the covered area of the network is obtained as follows: Minimum radius of view RR1R: (4) Maximum radius of view RR2 R: (5) Corresponding arc length of the minimum radius of view LR1 R: (6) Corresponding arc length of the maximum radius of view LR2 R: (7) To configure a visual sensor in such a way that it could cover a target in the best possible form, sensor parameters have to be adjusted as below to maximize the coverage quality of a target: Calculation of the horizontal angle of view: (8) Calculation of the vertical angle of view: (9) In this equation, d is the distance between target and sensor and is calculated as: (10) Calculation of the enlargement angle: (11) In this relation, R is the appropriate value for arc length of the sensing area, which has covered the target, and based on the target dimensions, RRtR is achievable as follows: (12) The K coefficient determines the percentage that target takes form the whole image. The appropriate value of this coefficient can be specified based on the application type. The projection of sensing area in the target plan is shown in \u201cFig.1.b\u201d. The portion of target covered by a visual sensor is shown by the bold red arc. Details about computation of angles of this arc were explained in [6]. For full angle coverage, a subset of sensors should be selected such that the total cost will be minimized with an additional constraint that the union of the angles covered by the sensors for each targets will be 360\u00b0: Coverage of Target IV. 3BPROBLEM FORMULATION We consider the following problem; given a set of targets, a set of sensors with predefined position in 3-D surface and configurable parameters for pan, tilt, and zoom adjustment" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000942_978-4-431-53856-1_4-Figure4.6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000942_978-4-431-53856-1_4-Figure4.6-1.png", "caption": "Fig. 4.6 Simplified model of QTW-UAV", "texts": [ "Xb axis indicates the forward direction of the body; Yb axis, the rightward direction of the body; and Zb axis, the downward direction of the body. In this chapter, we use Euler\u2019s angle for attitude expression. The roll angle , the pitch angle , and yaw angle are defined as the attitude of the Fb frame for the Fi frame. Moreover, the 3-axis angular rate p, q, r is defined around all the three axes of the body-fixed frame, respectively. In this section, the yaw attitude model of a QTW-UAV is derived by using the simple figure of the QTW-UAV shown in Fig. 4.6. Four rotors are located symmetrically around the center of gravity of the body. L is the length between the center of the rotor and center of gravity. Moreover, the X 0 b axis and Y 0 b axis are along the center of rotorsR1 andR2, respectively, and are at right angles to each other. Therefore,\u2030 in the figure is 45\u0131. Now, let us consider that fp is the force on each flaperon caused by the slip stream effect; the direction of fp is defined as shown in Fig. 4.6. The moment around the center of the gravity caused by fp is calculated as fpLsin\u2030, and the entire moment around the Zb axis is calculated as follows: Mz D 4fpL sin\u2030 (4.1) Here the transfer function between this moment and yaw rate r is assumed to be first order; further, 4Lsin\u2030 in (4.1) is constant and determined by the geometrical arrangement of rotors. Now, we consider this constant value to be K1. In such a case, the mathematical model between the force caused on the flaperon and yaw rate is obtained as follows: R D TrK1 s C Tr Fp (4", " First, the relationship between the moment in the roll or pitch direction and the thrust of four rotors is introduced. The thrust generated by each rotor is expressed as the sum of DC elements and fluctuations, and shown in (4.5)\u2013(4.8). Here, TR is the thrust of each rotor; Td , the DC element of thrust; and TxR, the fluctuation in thrust. Further, the suffix implies the number of rotors. TR1 D Td C TxR1 (4.5) TR2 D Td C TxR2 (4.6) TR3 D Td C TxR3 (4.7) TR4 D Td C TxR4 (4.8) Next, a simple figure of the QTW-UAV, which is shown in Fig. 4.6, is used in a similar manner as in the previous section. The moment around the center of gravity of the body, which is generated by the differences in the thrust of each rotor, is expressed by (4.9), (4.10). MX 0 b D L.TR2 TR4 / D L.TxR2 TxR4 / (4.9) MY 0 b D L.TR1 TR3 / D L.TxR1 TxR3 / (4.10) Here MX 0 b and MY 0 b in the above equation are the X 0 b axis and Y 0 b axis components of the moment around the center of gravity of the body, respectively. The coordinate transformation ofMX 0 b andMY 0 b in the coordinate system Fb is then performed, and the next equation is obtained" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001363_s1063773711120073-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001363_s1063773711120073-Figure4-1.png", "caption": "Fig. 4. The geometric model of GS 1826\u2013238 is shown for the orbital phase \u03c6 = 0 for three orbital inclinations: (a) i = 0\u25e6, (b) i = 60\u25e6, and (c) i = 80\u25e6.", "texts": [ " (16) To calculate the mean optical flux and the optical response to an X-ray burst as functions of the orbital parameters of the binary and the parameters of its accretion disk and optical star, we computed a LMXB model that in many respects is similar to those considered by Tjemkes et al. (1986), Vrtilek et al. (1990), O\u2019Brien et al. (2002), and others. We considered the following geometric LMXB model: a low-mass companion filling its Roche lobe and a disk forming around a compact object (see Fig. 4). The optical flux from the binary at wavelength \u03bb is the sum of the fluxes from the disk and the companion star: F\u03bb = F d \u03bb + F \u03bb . (17) We neglected the radiation of the accretion stream starting from the Lagrangian point L1 and ending at the accretion disk boundary. Below, we will consider the star and accretion disk models as well as the calculation of the optical response to an X-ray burst in the binary in more detail. 3.1. The Optical Star We assumed the shape of the star in the LMXB to coincide with the shape of its Roche lobe (see, e" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000806_icma.2010.2-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000806_icma.2010.2-Figure2-1.png", "caption": "Fig 2. The designed mechanism", "texts": [ " This design has a uniform joint clearance c. When a non-assembly is fabricated using this joint design, the joint clearance must be large for mobility [8]. In order to reduce the clearance, a drum shaped pin joint design as in Fig.1 (b) has been 978-0-7695-4293-5/10 $26.00 \u00a9 2010 IEEE DOI 10.1109/ICMA.2010.22 21161 proposed [8]. The joint clearances c at both ends are kept the same as the one of the conventional joints and the clearance at the peak of the drum shape is smaller than c . A universal joint (Fig. 2c) with drum shaped pin joints is designed in Pro/Engineer. The assembly is made of two links (Fig. 2a) and a cross pin (Fig. 2b). The minimum clearance a is 0.2mm and the joint clearances c at both ends are 0.4mm. The joint can not be manufactured by conventional processing methods since it can not be assembled after each part is manufactured. In this paper, the joint is digitally assembled in computer; then manufactured by RP without assembly after being manufactured. III . THE PROCESS In this paper, a 3D CAD model of the part is first constructed by a CAD software such as ProEngineer, SolidWorks, or Autocad, etc. Then, the CAD model is sliced into layers of 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002548_978-3-319-61134-1_5-Figure5.18-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002548_978-3-319-61134-1_5-Figure5.18-1.png", "caption": "Fig. 5.18 Capacititance microfluidic device: 1 polymeric body, 2 inlet reservoir, 3 wear particle, 4 microchannel, 5 electrodes, 6 outlet reservoir, F filter, P pump [79]", "texts": [ " The use of them for condition monitoring by wear debris is obviously restricted by machines whose lubricating systems are reliably protected against mechanical particles from the outside. In most known devices based on the electric method of diagnostics a filtering element is used. Wear debris precipitate as the oil passes through the filter. This results in variations of the filter conductivity [77] or capacitance, which form the basis for evaluating the condition of the rubbing parts. A microfluidic device (illustrated in Fig. 5.18) was developed to detect metal debris by monitoring the change in capacitance across a pair of microelectrodes in the microfluidic channel [78, 79]. The microfluidic device [79] includes an inlet oil tube, inlet reservoir 2, outlet reservoir 6 and outlet oil tube. The microchannel 4 represents a constriction between the two reservoirs. The height and width of the microchannel are selected to be sufficient to allow typical wear particles 3 that are to be detected to pass there through. For example, to register the particles of size about 40 \u00b5m the channel with dimensions of 40 \u00b5m 100 \u00b5m 400 \u00b5m is used" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002595_1350650117727230-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002595_1350650117727230-Figure4-1.png", "caption": "Figure 4. Quantities used to determine the dynamic forces and moments caused by rotating seal element eccentricity. (a) Position analysis of seal seat eccentricities and tilts (dr not shown for brevity) and (b) imbalance and offset in the rotating seal seat.", "texts": [ " This work assumes that the stationary seal element is eccentrically balanced, that is Cs\u00bcGs; consequently, the acceleration of the stationary element center of mass relative to Cs is found by differentiating equation (6) aGs \u00bc aCs \u00bc ao \u00fe @2 r\u00f0CO\u00des @t2 \u00fe _ l0 r\u00f0CO\u00des \u00fe l0 l0 r\u00f0CO\u00des \u00fe 2 l0 @ r\u00f0CO\u00des @t \u00f09\u00de where l0 is the maneuver rotation of the system, and thus, the system-fixed frame rotation rate. Expressing the rotating seal element center of mass acceleration is complicated by imbalance, axial offset, and shaft rotation; these parameters are shown in Figure 4(a) and (b). The center of mass Gr is laterally offset from Cr by the eccentric imbalance \"rG, occurring at an angle r from the body-fixed spin axis 1r. Furthermore, Gr is axially offset from Cr by the distance dr. The following position vector locates the center of mass relative to the geometric center using the body-fixed stationary seal element spin axes \u00f0xyz\u00depr r\u00f0CG\u00der \u00bc \"rG cos re\u0302xpr \u00fe \"rG sin re\u0302ypr \u00fe dre\u0302zpr \u00f010\u00de where r is the static phase angle locating Gr in the xpry p r plane (referenced from xpr )" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003482_tmrb.2019.2895800-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003482_tmrb.2019.2895800-Figure4-1.png", "caption": "Fig. 4. Section of a crawler unit.", "texts": [ " Section V explains the running characteristics of the funicular flexible crawler. Fig. 3 presents the structure of the funicular flexible crawler: The flexible crawler. The flexible crawler includes an actuation unit, crawler units for propulsion, a crawler unit for turning, a flexible inner shaft, and a flexible outer shaft. The actuation unit has a geared motor. The geared motor output shaft is connected to a flexible inner shaft through a coupling. Multiple crawler units used for propulsion are arranged in the flexible inner shaft. Fig. 4 portrays a section of the crawler unit used for propulsion. The unit comprises a worm, crawler belts, and a frame. Bearings at both ends support the worm, arranged inside the frame. Both worm ends are connected to a flexible inner shaft. Two crawler belts are spaced asymmetrically around the longitudinal axis of the cylindrical frame. Each crawler belt is wound around the frame: both ends are connected, producing a loop. Additionally, teeth having a rake angle corresponding to the lead angle of the worm tooth are formed on the crawler belt outer surface" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001705_kem.554-557.234-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001705_kem.554-557.234-Figure2-1.png", "caption": "Fig. 2. Initial and final geometry after rotary forging", "texts": [], "surrounding_texts": [ "The objective of this work is to find the optimum conditions to adapt rotary forging process to aeronautical Inconel 718 parts\u2019 specifications. Experimental tests will be done to validate the numerical models and microstructural results. In previous works [10] a numerical model was developed for a simple geometry: a rotary upsetting process used to obtain a part with final diameter of 200mm and final height of 20mm. Three main results were obtained. The first one was the determination of the optimal initial process conditions taking into account the specific microstructural requirements for aeronautical sector parts. The second result was the analysis of the recrystallization mechanism occurred during rotary forging process. The last conclusion was that the recrystallized grain size is always the same, independently of the grain size previous to recrystallization [4,11]. Some heating tests were done in order to obtain the grain size after heating and before forging. This is explained in the next section, followed by the simulation work in which three variables were thoroughly studied: initial billet temperature, grain size and process velocity. Heating tests. Heating tests were done at two different temperatures in order to characterize the initial grain size before forging. The chosen temperatures were 1020\u00baC and 1100\u00baC, in order to evaluate the grain growth of Inconel 718 for temperatures higher than the \u03b4 solvus, around 1020\u00baC. After heating, the billet was cooled with water to prevent the evolution of the microstructure. As described in the previous section, Inconel 718 grain size is very sensitive to growth once \u03b4 solvus temperature is reached, due to the complete dissolution of \u03b4 phase in the austenitic matrix. Three thermocouples were introduced in the billet in order to record the temperature evolution during the heating process. Points at three different heights were measured inside the billet: upper, centre and lower part. 1020\u00baC Heating test 0 200 400 600 800 1000 1200 0 500 1000 1500 2000 Time (s) T e m p e ra tu re ( \u00baC ) Upper Centre Lower 1100\u00baC Heating test 0 200 400 600 800 1000 1200 0 500 1000 1500 2000 2500 Time (s) T e m p e ra tu re ( \u00baC ) Upper Centre Lower Fig.3. Thermocouples measurements at 1020\u00baC and 1100\u00baC heating tests The obtained microstructure, before and after the heating process, is shown in the following Figures. Initial billet microstructure. Grain size value: 10ASTM Billet microstructure after heating at 1020\u00baC. Grain size value: 9 ASTM Billet microstructure after heating at 1100\u00baC. Grain size value: 4 ASTM Fig. 4. Microstructure evolution during heating tests Grain growth takes place increasing the heating temperature up to 1020\u00baC. Later on initial grain size was defined as 9ASTM for simulations corresponding to the experimental trials. Simulation work. Aeronautical parts requirements are focused on grain size, delta phase geometry and concentration of carbides or oxides. Taking into account only grain size aspects, unacceptable final microstructures are those ones with general grain size lower than 6ASTM (coarse grains). Another criterion is that the value difference between maximum and minimum grain size is higher than 2ASTM. Grain size evolution during and after forming process is analysed with the software FORGE 3D. This software makes possible this calculation thanks to the programming of the equations that characterize recrystallization and grain growth behaviour of the material [12], in this case Inconel 718. It is possible to obtain grain size and recrystallization fractions from simulation as microstructural output data. Three input variables were studied in detail taking into account the aeronautical parts criterions described: initial billet temperature, grain size and process velocity. Initial billet temperature. The objective was to study the influence of this variable in the final grain size microstructure obtained at the end of the forming process. Several initial temperatures were evaluated: 950\u00baC, 960\u00baC, 970\u00baC, 980\u00baC and 1000\u00baC. Higher values were not studied due to the temperature increase during forming, because of plastic deformation. Temperature can increase around 60\u00baC for Inconel 718 [13]. The other input data for simulation are listed next. The upper tool temperature was 150\u00baC and the lower one\u2019s 500\u00baC. This difference in tool temperature is explained afterwards, in the experimental section. The process velocity was settled at 15mm/s, using a rotation speed of 300rpm. Initial grain size was 9ASTM. The final temperature and grain size distribution in a longitudinal section was plotted in order to study their influence in the process. The images are shown below comparing both variables. Fig.5. Initial billet temperature variation: final temperature and grain size distribution in a longitudinal section The increase of the initial billet temperature produces higher inner temperatures, due to plastic deformation. This effect causes temperatures higher than \u03b4 solvus one, which is associated with grain growth in these particular zones. Looking at the aeronautical criteria used to evaluate acceptable and unacceptable microstructures, the following two plots summarize the influence of the initial billet temperature in the final rotary forged part microstructure. 950\u00baC 960\u00baC 970\u00baC 980\u00baC 1000\u00baC Initial billet temperature The plot on the left represents criterion 1: unacceptable final microstructures are those ones with grain size lower than 6ASTM (coarse grains). The maximum and minimum grain size value in the final part is plotted for each case. For higher initial billet temperatures, the lower grain size value is smaller (in ASTM scale), which means grain growth. The plot on the right represents criterion 2: unacceptable final microstructures are those ones with a difference between maximum and minimum grain size value higher than 2ASTM. The difference between the maximum and the minimum grain size for the final part is plotted. This difference is becoming bigger with increasing initial billet temperature. According to this data, the best case is the one with 960\u00baC as initial billet temperature. Initial billet grain size. The aim of studying this variable was to analyse the influence of initial grain size on the final microstructure, as well as in recrystallized grain size. Two initial grain sizes were taken: 9ASTM and 4ASTM. In the same way two initial temperatures were chosen: 970\u00baC and 1000\u00baC. The study of the tendency of an initial fine and coarse grain size at two different temperatures was performed. The other input data for simulation are listed next. The upper tool temperature was 150\u00baC and the lower one 500\u00baC. The process velocity was settled at 15mm/s, using a rotation speed of 300rpm. Final temperature and grain size distribution in a longitudinal section was studied. Fine or coarse microstructure requirements depend on the mechanical requirements for the working life of the part. Fine grain size is used for resistance to fatigue crack initiation and growth [4]. Independently of initial temperature, a homogeneous microstructure is obtained with an initial fine grain size. One of the results shown in the previous work [10] is also validated here. The recrystallized grain size is always the same, independently of previous recrystallization size. Taking into account these grain size distribution results, two ways of forging can be defined in order to obtain fine microstructure. Starting with a coarse grain size, the aim of the forging process is to refine the grain by means of the recrystallization process. For this purpose, increasing the temperature can be a solution to facilitate this grain transformation. However starting with a fine grain size, the aim of the forging process is to avoid grain growth. To achieve this goal, the temperature during the rotary forging process cannot increase more than the \u03b4 solvus temperature. This is the explanation why the case with 1000\u00baC initial billet temperature has a bigger grain size in the inner part of the section, due to higher temperature caused by plastic deformation. This result is in line with the conclusions stated in the previous section. The following Figures present these data according to aeronautical parts requirements. The plot on the left represents criterion 1. Summing up, starting the rotary forging process with fine grain distribution ensures a final part with fine microstructure, always paying attention not to overcome too high temperatures. The plot on the right represents criterion 2. For both plots, the most homogeneous microstructure is the one with fine initial billet grain size. Process velocity. This variable is directly related to strain rate: increasing the velocity of the forming process causes increase of strain rate. The objective of the analysis of this variable is to determine the influence of the strain rate on the final microstructure. Two different process speeds were selected: 5mm/s and 15mm/s.Using a rotation speed of 300rpm, these process velocities can be translated into 1mm/rev and 3mm/rev respectively. This means increasing velocity three times. The other input data for simulation are listed next. The initial temperature was 1000\u00baC and the initial grain size was settled at 9ASTM. The upper tool temperature was 150\u00baC and the lower one 500\u00baC. Final temperature and grain size distribution in a longitudinal section was analysed. A homogeneous microstructure is obtained when increasing process speed. On the contrary, temperature raises causing grain growth. This phenomenon is less noteworthy than the first one. Next plots present the relation of these data vs. aeronautical requirements. Fig.10. Aeronautical requirements evaluated according to process velocity variation The plot on the left represents criterion 1 and the plot on the right represents criterion 2. The most homogeneous microstructure is the one with the highest process velocity. Slow processes cause finer grain size, but a much more inhomogeneous microstructure." ] }, { "image_filename": "designv11_29_0002127_s1068798x12040119-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002127_s1068798x12040119-Figure1-1.png", "caption": "Fig. 1. Calculation schemes for first (a) and second (b) stages of simulation.", "texts": [ " First, we determine the temperature and stress at control points of cutting plates made of differ ent refractory compounds (Tables 1 and 2). Then we investigate the influence of the ceramic\u2019s properties on the thermal and stress state of the cutting plate. In each series of numerical experiments, only one char acteristic varies. Thus, in investigating the influence of the elastic modulus on the stress\u2013strain state, it varies from 219 to 840 GPa, while the other properties take the values for Al2O3. In the first stage, the cutting plate is loaded by a dis tributed force P = 3.5 \u00d7 108 Pa and a heat flux Q = 1.1 \u00d7 108 W/m2 (Fig. 1a). In the second stage, the cutting DOI: 10.3103/S1068798X12040119 RUSSIAN ENGINEERING RESEARCH Vol. 32 No. 4 2012 INFLUENCE OF CERAMIC PROPERTIES ON THE STRESS\u2013STRAIN STATE OF A PLATE 375 plate is loaded by two point forces F1 = F2 = 0.01 N (\u03b21 = \u03b22 = 45\u00b0), a distributed force P = 108 Pa, and a heat flux Q = 108 W/m2 (Fig. 1b). From the surfaces of the ceramic plate with no heat flux, heat transfer to the surroundings is possible. Quantitative assessment of the temperature and stress in the cutting plates is based on control points\u2014 fixed points of finite elements of the structure. Four control points are selected (Fig. 1; Table 3). The num ber of the corresponding control point is introduced as a superscript in presenting the results (for example, T1 and for control point 1). Table 4 presents data for the refractory compounds in order of increasing temperature in the cutting plate, under the action of a heat flux Q = 1.1 \u00d7 108 W/m2. \u03c3i 1 376 GRIGOR\u2019EV et al. Analysis shows that the properties of the refractory compounds have considerable influence on the ther mal state of the cutting plate. The temperature is low est in the beryllium oxide plate and greatest in the boron nitride plate" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000844_robot.2010.5509937-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000844_robot.2010.5509937-Figure7-1.png", "caption": "Fig. 7. (a) An example work space for which no contact-preserving push plan exists, (b) its configuration space, and (c) an unrestricted push plan for it, doing one release at position \u03c4(r).", "texts": [ " Each of these will follow one of \u03c3i,1 or \u03c3i,2, and then end in a tangent line to this path, or a bitangent of this path and one of ci+1\u2019s bounding curves (possibly followed by the rest of this curve). Fig. 6(c) shows an example. The point until which \u03c3i,1 or \u03c3i,2 is followed can be found by binary search. Since there are O(kq) cells, we need to do O(kq) such searches, using O(log(kq)) time each, to compute the shortest-path tree of the work-space cells. Until now we\u2019ve assumed the pusher can maintain contact with the object at all times. However, the situation depicted in Fig. 7(a)\u2013(b) does not admit such contact-preserving push plans. (In fact, we\u2019ve proven [6] that this is the case for any object path with the same start and end point.) It does admit an unrestricted push plan, as can be seen in Fig. 7(b)\u2013(c). Canonical releasing positions: Whenever the push range is split into multiple contiguous ranges by obstacles, it may make sense for P to let go of O and try to reach one of these other positions. In the configuration space this situation corresponds to a vertical line intersecting multiple cells. In general, there are infinitely many such potential releasing positions, thus it\u2019s infeasible to try them all. Instead we consider only vertical lines that go through a vertex of a cell or configuration-space obstacle" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000821_mwscas.2009.5236089-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000821_mwscas.2009.5236089-Figure2-1.png", "caption": "Fig. 2. Propulsion system.", "texts": [ " Considering that the kinetic energy induced in the air by the airship motion is given as [9] TA = 1 2 ( Xu\u0307u 2 + Yv\u0307v 2 + Zw\u0307w 2 +Kp\u0307p 2 +Mq\u0307q 2 +Nr\u0307r 2 ) then, the added mass and inertia forces are F bAM = MAV\u0307 b CV + C12\u2126 M b IM = IA\u2126\u0307 + C12V b CV + C22\u2126 where MA = diag{Xu\u0307, Yv\u0307, Zw\u0307}, IA = diag{Kp\u0307,Mq\u0307, Nr\u0307} C12 = 0 Zw\u0307w \u2212Yv\u0307v \u2212Zw\u0307w 0 Xu\u0307u Yv\u0307v \u2212Xu\u0307u 0 C22 = 0 Nr\u0307r \u2212Mq\u0307q \u2212Nr\u0307r 0 Kp\u0307p Mq\u0307q \u2212Kp\u0307p 0 The restoring forces are given by F bR = (W \u2212B)r3, M b R = (W \u2212B)rcg \u00d7 r3 with r3 the third column of the rotation matrix that describes the orientation of the body frame relative to the inertial frame, that is, R = c\u03b8c\u03c8 c\u03b8s\u03c8 \u2212s\u03b8 c\u03c8s\u03b8s\u03c6 \u2212 s\u03c8c\u03c6 s\u03c8s\u03b8s\u03c6 + c\u03c8c\u03c6 c\u03b8s\u03c6 c\u03c8s\u03b8c\u03c6 + s\u03c8s\u03c6 s\u03c8s\u03b8c\u03c6 \u2212 c\u03c8s\u03c6 c\u03b8c\u03c6 The airship is driven by a vectored thrust whose configuration is described in Figure 2. We apply the Denavit Hartenberg procedure, whose param- eters are \u03b1 a d \u03b8 \u03c0 \u21131 \u2212\u21133 \u2212\u03b41 0 0 \u2212\u21134 0 \u03c0 2 0 0 \u03b42 0 \u21132 0 0 In this Section we present the main contribution of this paper, that is to say a nonlinear controller yielding local asymptotic stability of the trajectory tracking error. Proposition 1: Assume FL = 0 and let xd and yd be the desired airship trajectories with bounded time derivatives. Consider the lateral airship dynamics (2) in closed\u2013loop with the dynamic state feedback control uL = uLd \u2212KB\u22a4 LeVL (3) where K = diag{k1, k2}, eVL = VL \u2212 VLd = eu ev er = u\u2212 ud v \u2212 vd r \u2212 rd [ ud vd ] = \u2212KX tanh(n) +R\u22a4 \u03c8 X\u0307d KX = diag{kx, ky}and n = R\u22a4 \u03c8 [ ex ey ] , Xd = [ xd yd ] Moreover, ex = x \u2212 xd, ey = y \u2212 yd, rd the solution of the differential equation B\u22a5 { MLV\u0307Ld \u2212 [ JL(VLd) \u2212DL ] VLd } = 0 (4) and uLd = [ B\u22a4B ]\u22121 B\u22a4 { MLV\u0307Ld + [ JL(VLd) \u2212DL ] VLd } Assume that in the subspace S \u2282 R 7 there exist a bounded solution for (4)" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002635_s11771-017-3585-7-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002635_s11771-017-3585-7-Figure3-1.png", "caption": "Fig. 3 Spatial error model of worm wheel rotation axis", "texts": [ " South Univ. (2017) 24: 1767\u22121778 1769 Worm wheel installation errors mainly include worm wheel calculation error, worm wheel shaft thermal distortion error, fixture error, etc. When these errors exist, deviation and misalignment may appear for the rotation center of the worm wheel (axis of rotation), resulting in errors of the tooth surface during the grinding. The rotational axis of the worm wheel has three linear and three rotational degrees of freedom, and its spatial error model is shown in Fig. 3. As shown in Fig. 3, in the theoretical case, A-axis is the worm wheel rotation axis which coincides with X-axis of the coordinate system. Then, the angles between the actual rotation axis and the theoretical one of the worm wheel are defined in the x\u2212z and x-y planes as yaw angle error Ey(A) and pitch angle error Ez(A) of A-axis, respectively. The rotating angle error of A-axis is called angular error Ex(A). The deviation between the actual rotation axis and the theoretical one is defined as linear position error", " Fixed coordinate systems Ss(xs, ys, zs) and Sf(xf, yf, zf) are rigidly connected to the shaper cutter and the face gear, and fixed coordinate systems of the shaper cutter with errors are Ss1(xs1, ys1, zs1), Ss2(xs2, ys2, zs2), Ss3(xs3, ys3, zs3) and Ss4(xs4, ys4, zs4). The parameter d is the location datum of the shaper cutter from the face gear, and Ews is the distance from the axis of the face gear to the worm wheel. In Fig. 4(a), Ex and Ey represent, respectively, the errors produced by the shaper cutter along the tangential and axial directions of the face gear, which are equivalent to axial linear position error Dx(A) and tangential linear position error Dz(A) in the spatial error model of the worm wheel(see Fig. 3). In Fig. 4(b), Ex and Ez represent the respective angles between the actual J. Cent. South Univ. (2017) 24: 1767\u22121778 1770 rotation axis and the theoretical one of the shaper cutter in the y\u2212z and x\u2212y planes, which are equivalent to yaw angle error Ey(A) and pitch angle error Ez(A). Therefore, the effect is equivalent through introducing the errors into the shaper cutter coordinate system and into the worm wheel coordinate system to derive the error tooth surface of the face gear. The relative position coordinate systems of the face gear and the worm wheel enveloped by the shaper cutter are established, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000639_cisp.2009.5304462-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000639_cisp.2009.5304462-Figure8-1.png", "caption": "Figure 8. A testing experiment of wire rope.", "texts": [ "5mm, depth of flaw 8 mm , length 5 mm , width 8 mm, air gap radial lengths are, respectively, 15 mm, 25mm and 35mm. We change the air gap radial length at the step of 10mm, which can show the effects of air gap radial length on the SNR of signals clearly. From figure 7, we can see that for the same lift-off of the sensor, the SNR can be increased by reducing the radial length of the air gap within a certain range. VI. LABORATORY EXPERIMENTAL RESULTS To verify the methods of improving the SNR of MFL signal in flaws detection of coal mine wire ropes, lab experiments are performed. Figure 8 shows the picture of the experimental setup. The static magnetic field is provided by two permanent magnets, made of NdFeB material. Table 1 shows the properties of the NdFeB permanent magnet. The material trademark of the magnet is N48. This material has a coercive force of 876,000 A/m~955,000 A/m, and its residual magnetism is 1.37T~1.43T, which just satisfies our needs. In our experiments, we used a 6 19 + FC\u00d7 , 24.5\u03a6 mm wire rope as our test object, a kind of wire rope widely used in coal mine" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003553_s40684-019-00087-4-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003553_s40684-019-00087-4-Figure4-1.png", "caption": "Fig. 4 Normal section for generating the concave tooth profile", "texts": [ " The upper \u201c+\u201d represents the left-side normal section, while the lower \u201c\u2212\u201d indicates the right-side normal section. The transverse section of rack cutter can be determined utilizing the coordinate transformation as follows (1) \u23a7\u23aa\u23a8\u23aa\u23a9 xn = cv sin a yn = \u2213( cv cos a \u2212 lcv) zn = 0 1 3 where ucv is the distance between the two coordinate systems origins. \u03b2 is helix angle. The basic parameters of normal section for generating convex tooth profile are shown in Table\u00a01. 3.2 Normal section for\u00a0generating concave tooth profile As displayed in Fig.\u00a04, the normal section for generating the concave tooth profile mainly includes the working regions: circular arc part I(W\u03022P ) and circular arc part II(W\u03021P ). hcc is the tooth depth and Scc is tooth thickness. Suppose that E1 and E2 are the contact points of tooth profile, the pressure angles of two points are 1 and 2 , respectively. is the corresponding angle of point P, which is also coincide with the proposed normal section for generating convex tooth profile. lcc represents the distance from the centre point O to the symmetrical line K\u2013K" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000719_iraniancee.2010.5506995-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000719_iraniancee.2010.5506995-Figure3-1.png", "caption": "Fig. 3: Defined path for object centre of mass in 2D task.", "texts": [ " Also weighting factors, 1W , 2W and 3W , are included to put different emphasis on each terms. The total sum of these three factors is equal to one. The normalizing factor 01/( )ft t\u2212 puts the total index between zero to one. Therefore, a good grasp has a MAG of close to one, and a poor grasp has a MAG of close to zero, [22]. Fig. 2: Two Cooperative SCARA type manipulators grasp an object. The geometric and inertial parameters of the manipulators are shown in TABLE I. The task is moving the object based on a given trajectory, as shown in Fig.3. The simulations are run for three types of objects. The symmetric rectangular object(No.1). The symmetric long bar(No.2), and the non-symmetric L-Shape object(No.3). The geometric and inertial parameters of the grasped objects are shown in TABLE II. The object path is the straight line along X-axis. Joints trajectory are quintic functions as follows, ( ) ( ) 2 3 4 5 0 1 2 3 4 5 ( ) 1 10 X t a a t a t a t a t a t Y t t\u03c8 = + + + + + = = \u00b0 (8) with coefficients that presented in [18]. Fig. 4 shows trajectory of ( )x t and its derivatives" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001855_ifost.2012.6357708-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001855_ifost.2012.6357708-Figure1-1.png", "caption": "Figure 1. Shematic of Method of Layered Laser Sintering of Reinforced Solids", "texts": [ " INTRODUCTION In previously published works a layered laser sintering of reinforced solids was suggested [1]. Fundamentally, this process is similar to that of the selective laser sintering and, in a less degree, to the stereolithography. A subject matter of the process is that a reinforcing element is inserted in a special vat, polymer suspension is added and then the surface of the suspension is processed with a laser beam. Particles of the suspension dispersed phase are sintered and form a single layer attached to the reinforcing element (Fig.1). The reinforced element can be made of polymer, metal or ceramics. Reinforced solid is resulted from layer-by-layer building. This method allows reducing power consumption of the layered sintering by means of reducing of layered solid volume. The method may be employed at production of consumable cast patterns as it allows producing highly porous products. Such porous products have small volumes of non-gasifiable residue, and reinforcing element may be used as pouring gate system. As other laser processes the layered laser sintering of reinforced solids includes laser emission efficiency, scan rate, laser beam concentration and hatch spacing" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002411_s00170-017-0378-y-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002411_s00170-017-0378-y-Figure6-1.png", "caption": "Fig. 6 Three-view drawing of die", "texts": [ " An experimental test was conducted for forming the LM rail. The results indicate that this approach can extrude the billet to turn toward the LM rail with an excellent burnished surface within only a few minutes. Figure 4 provides a perspective and expanded view of this device. The device comprises a die, container, and press module that includes the ram and punch, wherein the die has an opening hole that the punch penetrates through. Figure 5a illustrates a detailed size of the LM rail; Fig. 5b illustrates the desired LM rail measurement location. Figure 6 illustrates the shape of the die that takes the shape of the desired LM rail cross section. The container is adapted to close around the die, and the press module comprises a punch and ram. The punch is adapted to move along the axial direction of the container inside the ram; hence, this forming device can be used to extrude and cut a billet. In this design, the punch has a negative clearance (the diameter of the punch is larger than that of the die) with the die. Briefly, the punch cannot enter the die opening" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003994_s00419-019-01609-x-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003994_s00419-019-01609-x-Figure1-1.png", "caption": "Fig. 1 Physical model of the rotating flexible beam", "texts": [ " Several simplifying assumptions are made to limit the range of applications of the planar rotating hub-beam system model to be derived. 1. The rotating beam is a uniform, homogeneous Euler\u2013Bernoulli beam. A cross section of the beam is perpendicular to the centroid line of the beam and remains in a plane after deformation. 2. While stretch along the centroid line of the beam is considered, the area of any cross section of the beam remains the same after deformation. 3. The beam moves in a horizontal plane, and gravity is not considered. As shown in Fig. 1, the flexible hub-beammoves within the horizontal plane. To be specific, the hub rotates around a fixed axis, and its upper part is fixed by a flexible cantilever beam. An inertial coordinate system oi j is established through the center of rotation of the hub. A floating coordinate system o\u2032i \u2032 j \u2032 is built on the flexible beam. The rotational inertia of the hub around the rotational center o is Joh ; the rotating angle of the hub is \u03b8 measured counterclockwise with respect to the i \u2032-axis of the floating coordinate system o\u2032i \u2032 j \u2032. The radius of the hub is a; the length of flexible beam is L; the density, cross-sectional area, and second moment of area are \u03c1, S, and I , respectively; the bending stiffness and compressive stiffness of the beam are E I and ES, respectively. It is shown in Fig. 1 that the radius vector based on the floating coordinate system from the origin o to a certain point P on the flexible beam after the deformation can be written as r = rA + r0 + u (1) where rA is the radius vector from the center o of the hub to the base point o\u2032 of the floating coordinate system, and r0 is the radius vector of point P under the floating coordinate system before the deformation. The deformation vector of point P is u = [ux , uy]T, which can be written as { ux = ux1 + ux2 uy = uy (2) where ux1 is the longitudinal deformation, uy is the transverse bending deformation, and ux2 is the longitudinal shortening caused by transverse bending" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002295_1.4972177-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002295_1.4972177-Figure3-1.png", "caption": "Fig. 3. The apparatus used to determine the angle the ball loses contact with a circular track: (a) schematic diagram and (b) photograph that shows the ball B, the optical detector S, the electromagnetic device E to release the ball, and the microphone M. The inset in (a) shows the separated plates used to keep the ball on the circular path. The inset in (b) shows the optical sensor; the LED is placed below the track with the photodetector above.", "texts": [ " (11) and (12) allows us to solve for hc and vc in terms of the measurable quantities d and tf. The results are cos hc \u00bc AB\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 A2 \u00fe B2 p 1\u00fe B2 ; (13) and vc \u00bc d \u00fe a a\u00fe 1\u00f0 \u00de 1 sin hc\u00f0 \u00de cos hc\u00f0 \u00detf ; (14) where A a\u00fe 1\u00f0 \u00dea a\u00fe 1\u00f0 \u00dea\u00fe d ; (15) and B rb \u00fe gt2 f =2 a\u00fe 1\u00f0 \u00dea\u00fe d : (16) Thus, we can determine hc by measuring d and tf and using Eq. (13). Two electrically isolated aluminum plates make up the circular track for the steel ball (Fig. 3). A quarter circle track was constructed using computerized machining in order to guarantee a circular path as much as possible. We used the two plates as part of an electronic circuit with the ball acting as a switch between the plates. When the ball is on the track, an electrical contact between the plates is established that produces a HIGH signal. When the ball loses contact with at least one of the plates, a LOW signal is produced. In this way, we can determine the time tc at which the ball flies off the track", " To validate data from the Arduino, we have also collected data for some experiments using a Tektronix TBS1052B-EDU 50-MHz digital oscilloscope. The geometrical characteristics of our apparatus are: rb\u00bc 7.50 6 0.05 mm, a\u00bc 487 6 1 mm, h0\u00bc 0.29 6 0.12 , l\u00bc 5.0 6 0.5 mm, and g\u00bc 1.12. The (maximum) coefficient of static friction between the ball and the aluminum plates was l\u00bc 0.21 6 0.01. This value was measured by joining two balls together using adhesive tape and placing them on the straight part of the setup (the bottom portion of the track in Fig. 3). The angle with the horizontal was then slowly increased until the pair of balls starts to move (at angle c, with l \u00bc tan c). Using the measured l, the predicted angles from Eqs. (4), (6), and (8) are found to be hs\u00bc 28.7 6 0.8 , hc0\u00bc 50.1 6 0.1 , and hcl\u00bc 53.4 6 0.1 . The angular position of the ball and the speed of its center of mass are shown in Fig. 4. Data from the photodetector revealed, as expected, an increase in the ball speed as the ball moves down the track (inset). Whereas, the photodetector data from the Arduino were easily reproducible, measurements of the voltage between the plates exhibited a large variation from independent runs of the experiment (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001413_2073370.2073378-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001413_2073370.2073378-Figure1-1.png", "caption": "Figure 1: a) Telepresence robotic system b) Mobile robot control and feedback c) ProInterface: tilt torso \u2013 feel object", "texts": [ " The factors that affect the level of immersion are the type of visual facilities (monitor, virtual-reality goggles), auditory feedback, and haptic perception of the remote environment. The novelty of our idea is to engage the user into teleoperation and provide a high level of immersion through proprioceptive telepresence and tactile feedback. The developed interface allows the operator to use their body posture and gestures for controlling the mobile robot and at the same time to feel the remote object through tactile stimuli (Fig. 1(a)). The mobile robot is equipped with two laser range finder (LRF) sensors scanning the total 360 degrees. The developed algorithms allow mobile robot to detect the distance, shape and velocity (with Kalman filter) of the object robustly against LRF scan noises. The example of the LRF scan data is given on Fig. 1(b) \u2013 the black point depicts the robot location, red point is the moving object location, and red line is the velocity vector. Human operator is capable of changing the robot traveling direction in a smooth and natural manner by twisting and bending the trunk (Fig. 1(b)). The bending flex sensor changes in resistance depending on the amount of the sensor bend. The torso along with the flex sensors acts as joystick. For example, to move the robot forward or backward, the user leans the torso slightly forward or backward, correspondingly. The velocity of the robot is congruent with the trunk tilt angle. When the operator straightens up, the robot stops smoothly. Such operations allow the human to experience a sense of absolute, natural, instinctive, and safe control. In ProInterface, we employ the tactile stimuli as a modality to deliver the information about the remote environment. The interface allows the operator to devote visual faculties to the exploration of the remote dynamic environment. The device is represented by a wearable belt, which is integrated with 16 vibration motors (tactors), four flex sensors, 3-axis accelerometer, and plastic holders linked by elastic bend (Fig. 1(c)). The tactors are equally distributed around the user\u2019s waist. The motors vibrate to produce the tactile stimuli indicating the direction, distance, shape, and mobility of the moving obstacle (object, human, etc.). The developed algorithm analyses the information about the environment and sends it to the wearable master robot. For example, when the detected obstacle is located on the right side of the robot, the user feels the vibration of the tactor at the right side. The belt interface provides the wearer with high resolution vibrotactile signals. Thus, it can also present the shape and speed of the object. For example, the convex obstacle is presented by simultaneous activation of three tactors, but with different vibration intensities. The vibration frequency in the middle tactor is larger than in neighboring ones (Fig. 1(b)). The mobile object is represented by the tactile stimuli moving along the waist in the direction of the object travelling (Fig. 1(b)). The haptic vision allows operator to feel the entire space around the mobile robot. The stereoscopic 3D image from the robot cameras is transferred to the HMD through wireless communication. The developed technology potentially can have a big impact on multi-modal communication with remote robot engaging the user to utilize as many senses as possible, namely, vision, hearing, sense of touch, proprioception (posture, gestures). We believe that such telepresence robotic system will result in a high level of immersion into robot space" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001899_memsys.2013.6474298-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001899_memsys.2013.6474298-Figure1-1.png", "caption": "Figure 1: (A) Fabrication of the Zn/Pt beads. Cross-section of (B) Zn/Pt, (C) Zn/Ni/Pt, and (D) Au/Pt beads. (E) SEM image of a fabricated Zn/Pt bead.", "texts": [ " The area coated with Pt in the previous sputtering process oriented randomly. Therefore, for most of the spheres, the entire surface was covered with Pt by the second deposition. Then, after collecting the beads and depositing them on a cover glass again, Au and Zn were deposited in this order by vacuum evaporation. The Au layer was used to promote the adhesion between the Pt and Zn layers. Because shadowing effect in the vacuum evaporation was strong, beads half coated with Zn and half coated with Pt (Zn/Pt beads (motors)) were obtained (Figure 1(B)). The completed beads were then released from the substrate, centrifuged, washed repeatedly in ultrapure water, and finally dispersed in ultrapure water. Zn/Ni/Pt beads (motors) (Figure 1(C)) and Au/Pt beads (Figure 1(D)) were also fabricated in the same manner. Figure 1(E) shows the fabricated Zn/Pt beads observed with a scanning electron microscope (SEM) (LEO1550, Zeiss, Germany). Because the equilibrium potential of a redox system is determined by the Nernst equation, the potential of a zinc electrode in contact with a solution that does not contain zinc ions shifts to the negative side from the standard electrode potential (\u22120.762 V (vs. SHE)), which is enough to reduce many possible fuel redox compounds or ions. In this work, bromine, p-benzoquinone, and methanol were used for the fuel" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002408_s12283-017-0232-3-Figure12-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002408_s12283-017-0232-3-Figure12-1.png", "caption": "Fig. 12 Model of hand and glove including flesh, bone, and viscoelastic foam", "texts": [ " Contact between the blade and puck, blade and ice, ice and puck, and hands and stick were managed using the surface-to-surface contact control in LS Dyna. A coefficient of friction between the blade and the puck of 0.7 was used [29]. During a slap shot, the blade will dig into the ice, which can increase friction. Friction with the ice can increase stick loading [17], but it is complex, not well understood, and not an aim of this work. Since the blade did not dig into the artificial surface used in this work, friction with the ice was not considered. The glove was modeled with three concentric regions as shown in Fig. 12. The glove exterior was given an intermediate stiffness so the prescribed motion was followed while accommodating small discontinuities in the prescribed path. The intermediate section was given high stiffness to impart structure to the glove as occurs from a bony hand. The interior region was given a low fleshy stiffness to allow the stick to move relative to the glove as occurs in play (THUMS, Toyota Motor Corporation). A summary of the properties used for the glove materials is given in Table 4" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001508_kem.508.152-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001508_kem.508.152-Figure1-1.png", "caption": "Fig. 1. A schematic illustration of HPT processing.", "texts": [ "2 ks (TNTZAT) in vacuum, followed by water-quenching. Finally, TNTZAT was machined into coin-shaped specimens with a diameter of 20 mm and a thickness of 0.8 mm for HPT processing. HPT processing. The coin-shaped specimens of TNTZAT were subjected to HPT processing between two anvils opposed vertically by rotating the lower anvil under a pressure of 1.25 GPa at rotation numbers (N) of 1 to 20 at a rotation speed of 0.2 rpm at room temperature. A schematic illustration of the HPT processing is shown in Fig. 1. The applied force was maintained at a Key Engineering Materials Vol. 508 153 constant value of 40 tons, corresponding to a pressure of 1.25 GPa. The flat bottoms of the holders were roughened to increase the frictional force between the specimen and the anvils. At the same time, a lubricant containing MoS2 was applied around the periphery of the holder for the lower anvil to decrease the frictional force between the anvils. Hereafter, the coin-shaped specimen of TNTZAT subjected to HPT processing is referred to as TNTZAHPT" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003279_chicc.2018.8482899-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003279_chicc.2018.8482899-Figure3-1.png", "caption": "Fig. 3: The structure of Tilt-rotor in Adams", "texts": [ " This work can improve our engineering efficiency and discover the potential problems in our tilt-rotor dynamic model which would be neglected by us. Compared to Adams, SolidWorks has more advantages in 3D drawing. So we utilize SolidWorks to draw the structure of the tilt-rotor and import model into Adams environment for analysing. In Adams environment, through selecting parts, constrains and force we can establish the model of tiltrotor on the basis of section 2. The structure of tilt-rotor can be depicted in Fig.3. Every joint rotating along axis is defined through rotary deputy which can describe any rotating movement of tiltrotor part. It is necessary to emphasize that Adams can edit the configurations of each part. So the parameters of each part should not only be reasonable, but also realistic. Most time, we can calculate the parameters of tilt-rotor automatically by Adams software. However, sometimes we should alter some characteristic to make every part correct and reasonable with practical environment" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001533_20130410-3-cn-2034.00060-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001533_20130410-3-cn-2034.00060-Figure3-1.png", "caption": "Figure 3. Example output sketch of a system consisting of a DC motor and a two-stage planetary gearbox.", "texts": [ " This is handled automatically and where possible it is done symbolically before optimization is carried out. Hence the equation system only needs to be solved once during setup instead of once for each function evaluation since it is enough that the model calculates and returns the constant values corresponding to the system instance specified by the design variables. The generated transfer function can then be used to analyze different dynamic properties. The framework is capable of generating scaled visualizations of designed systems through a sketching algorithm. See Figure 3 for an example sketch. The underlying component models were developed in Roos (2007). As is mentioned before, the core idea of the component modeling is to describe models in such a way that they allow for quick calculation and evaluation. For that reason, the component models are derived such that physical properties are captured by algebraic equations only. As the concept phase is targeted, it is suitable to keep the level of detail of the models at a reasonable level. This also facilitates the earlier mentioned desire to quickly evaluate the system, and it also makes it easier for the designer to handle and understand the underlying physics" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001930_00207179.2011.592998-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001930_00207179.2011.592998-Figure5-1.png", "caption": "Figure 5. Coordinates for a gradient computation in 2D.", "texts": [ " Once the velocity ud of the desired formation structure and the desired formation structure shape lid are available, the formation control design proposed in Section 3 can be used directly to drive the agents in the group. The following section gives a method to estimate an approximation of the gradient average, J , of the distributed environment (t, g) from measurements (t, qi) on the boundary, i.e. the contour or surface C, carried out by the agents in the group. Therefore, we will present a method to calculate the gradient average of both 2D and 3D distributed fields in the following subsections. 4.1.2 Average gradient estimate of a 2D distributed field We consider a 2D region A, see Figure 5, bounded by a contour C, such that any line through A parallel to either one of the coordinate axes intersects C in only two points. The curve C is divided by its leftmost and rightmost points (x\u00bc a and x\u00bc b) into a lower segment C1, described by y\u00bc f1(x), and an upper segment C2 described by y\u00bc f2(x). With the position vector to a point P on C given by r \u00bc xex \u00fe yey, \u00f031\u00de where ex and ey are the unit vector on the OX and OY axes, respectively. The unit tangent vector at P is t \u00bc dr ds \u00bc dx ds ex \u00fe dy ds ey, \u00f032\u00de D ow nl oa de d by [ N or th ea st er n U ni ve rs ity ] at 0 6: 49 1 0 O ct ob er 2 01 4 where ds is the differential length along C, and the unit normal vector is n \u00bc t ez \u00bc dy ds ex dx ds ey \u00bc nxex \u00fe nyey: \u00f033\u00de For the function (t, x, y) defined in A, consider the area integralZ A @ @y dA \u00bc Z b a Z f2\u00f0x\u00de f1\u00f0x\u00de @ @y dy dx \u00bc Z b a \u00f0t, x, f2\u00f0x\u00de\u00de \u00f0t, x, f1\u00f0x\u00de\u00de dx \u00bc Z b a \u00bd C2 \u00bd C1 dx: \u00f034\u00de As shown in Figure 5, a positive contour integration corresponds to a counter-clockwise traversal of C. To make the first integral in (34) consistent with this connection, we writeZ A @ @y dA \u00bc Z a b \u00bd C2 dx Z b a \u00bd C1 dx \u00bc Z C dx \u00bc Z C dx ds ds, \u00f035\u00de which combines with (33) to yieldZ A @ @y dA \u00bc Z C ny ds: \u00f036\u00de A similar computation givesZ A @ @x dA \u00bc Z C nxds: \u00f037\u00de Combining (36) and (37) givesZ A J dA \u00bc Z C n ds, \u00f038\u00de where n is given in (33), and J \u00bc @ @x , @ @y T . It is noted that the total gradient R Ar dA of the distributed field (t, g) over the region A is completely determined from the line integral2 tCn ds carried out on the boundary C only" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001342_j.ijnonlinmec.2012.11.003-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001342_j.ijnonlinmec.2012.11.003-Figure1-1.png", "caption": "Fig. 1. A photo of a linear planimeter (see [25]).", "texts": [ " (A brief characterization of semiholonomic constraints is given in Section 2.3. For details of the theoretical approach see e.g. [16,17], for a detail study of concrete non-trivial system of this kind see e.g. [15] and references therein.) It is not quite easy to find real mechanical systems subjected to true (non-integrable) nonholonomic constraint conditions. One of them is the planimeter\u2014a mechanism for measuring areas. Various types of planimeters now used can be found on the Internet. For our purposes we consider a very simple one, the linear planimeter (see Fig. 1). The planimeter is, of course, a nonholonomic system with the (non-integrable) nonholonomic linear constraint condition (and certain holonomic constraint conditions as well), and thus it could be solved by commonly used methods developed for linear constraints. (The system is non-linear in the sense of equations of motion.) However, with Krupkova\u0301\u2019s reduced equations we have at hand a new method which makes the corresponding calculations to a certain extent simpler, hence more advantageous. The system we study has been practically used in technical and other experimental disciplines for measuring" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003589_1464419319832485-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003589_1464419319832485-Figure1-1.png", "caption": "Figure 1. A planetary gear train with a local fault in the planet bearing.", "texts": [ " The MBD model is solved by a commercial MBD analysis software. In order to validate the proposed model, its simulation results are directly compared with those from theoretical methods and experimental methods reported in the literature. Parameter study is also conducted to investigate the effects of the fault in the planet-bearing races, the sun gear speed, and the carrier moment on the timeand frequency-domain vibrations of the planetary gear train. When a local fault occurs in the planet-bearing component, as depicted in Figure 1, the vibration characteristics of the planet bearing should be changed, as well as the planetary gear train. The vibration changes are determined by the fault sizes and locations. Therefore, the vibration characteristics of the planetary gear train can provide useful information as to the fault size and location. In this study, the local fault profile is formulated as a rectangular one as suggested in Vafaei and Rahnejat.6 Besides, the elastic ring gear foundation also has some effects on the vibration of planet gear train as analyzed in Vafaei et al" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002437_978-3-319-55128-9_5-Figure5.60-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002437_978-3-319-55128-9_5-Figure5.60-1.png", "caption": "Fig. 5.60 Comparison of honeycomb structure under two loading cases that are equivalent for continuum", "texts": [ " However, with honeycomb structures, the global and local stress status of the structure exhibit different characteristics when loaded under an \u201cequivalent\u201d case with principal stresses compared to the original loading case. This could be help understood through the fact that honeycomb cellular structures only possess a certain degree of rotational symmetry, which implies that not all orientations can be treated equally as is the case for a continuous solid media. Such argument is visually illustrated in Fig. 5.60, in which the deformation of the honeycomb structure under a combined loading of compression and shear is significantly different from the case with the same structure subject to equivalent principal stress at a rotated orientation according to the principal stress formulation. Note that the deformation in Fig. 5.60 is exaggerated for visual comparison. In the modeling of the size effect, structural symmetry in relation to the loading stress must be considered. As shown in Fig. 5.61, when the stress is applied along the X2 direction of the honeycomb structure, the unit cell structure exhibits multiple types of symmetry including mirror symmetry and two-fold rotational symmetry. When the size effect is minimized, the unit cell could be considered to also meet the translational symmetry along X1 direction, which indicates that the vertical cell walls (i" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000872_2009-01-1052-Figure12-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000872_2009-01-1052-Figure12-1.png", "caption": "Figure 12: 2-Stage Oil Pump System", "texts": [ " In this condition the aluminium piston skirt will be exerting loads on the bore surface reducing oil film thickness and increasing friction. The total benefit of the optimized PCU with the MONOTHERM\u00ae piston including a higher block temperature leads to a friction benefit of up to 40%. On this engine the standard oil pump is a single stage system with a bypass. The lower oil flow requirement due to the new roller bearing camshaft and crankshaft bearings allows the use of a modified oil pump system, shown in Figure 12. Furthermore the oil pump was converted to a two-stage oil pressure system, which could be switched during the testing by an ECU controlled solenoid valve. The sizing of the pump was based on the remaining oil demands e.g. bearings, piston cooling and cam phasers. With a two-stage system the oil pressure could be regulated more accurately to the requirements of the engine. Predictions show that the combination of reduced oil flow and pressure, parasitic losses can be reduced by 310W at 2500rpm and 700W at 6000rpm" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001544_j.protcy.2013.12.294-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001544_j.protcy.2013.12.294-Figure4-1.png", "caption": "Fig. 4. Transaxle system [3].", "texts": [], "surrounding_texts": [ "8. Power train 1 delivers power to power train 2, and power train 2 delivers power to load 9. Power train 1 delivers power to load, and load delivers power to power train 2. [1]\nPower train 1 in the picture is Internal Combustion Engine (ICE) with gasoline fuel in the real condition, power train 2 is electric motor with battery for it energy source. Power train 1 is unidirectional, because it can only give power to load. Power train 2 can receive power from regenerative braking, and power train 1.\nWith many operation mode on the hybrid vehicle, the flexibility is better than vehicle with one power train. With good configuration and control, best efficiency with little emissit ition can be achieved from each operation mode. However, on the real condition, there are problem on selecting the operation mode depend on many things, such as : physical configuration from drive train, efficiency from power train, power characteristic, etc.\nPower from the load on the real condition changes because road condition, acceleration and deceleration. These condition can be seen from the picture below.\nFrom the picture it can be seen, there are two types of load, average power and dynamic power. On the hybrid vehicle, average power is supplied by ICE because it\u2019s efficiency is good when supplying average power. For the dynamic power, electric motor is used for supplying the power, because it\u2019s characteristic is good for supplying this power. Electric motor have big and stable torque characteristic until rated speed. Because of this characteristic, electric motor is a correct choice for acceleration condition, for deceleration, electrical power train receive energy for recharge the battery. Because of this combination of two power train on one driving cycle, total energy output on the dynamic power will be zero, then the electric energy capacity that will be used will be zero. Gasoline used can be minimized, when energy from ICE is used, as only ICE is considered a stable power that works efficiently.\n2.2. Type of the Hybrid Vehicle\nHybrid Vehicle have three types of the power train : 1. Series Hybrid 2. Parallel Hybrid 3. Series/parallel Hybrid\nSeries hybrid use electric motor for the main propulsion device with sources of power are battery and generator powered by ICE. Parallel hybrid use two main propulsion device which is combination of ICE and small electric motor. Series/parallel hybrid combine both systems for the source of power and propulsion device. In this research, we will use Toyota Camry Hybrid that uses series/parallel hybrid for its drive train, then we will describe how this hybrid system works.\nSeries/parallel hybrid or commonly called power split hybrid, combined with the other two drive train system. This system can give the advantages of the other two drive train system, while minimize their disadvantages. The advantages this system can give like the car can move by electic motor only, ICE only, or combination of them. Generation function like the series system can be achieved too. For the easier explanation, this picture shows the series parallel drive train system.", "From the picture can be seen, there is a component named power split device connecting motor, generator, and ICE. This component is Planetary Gear set. On the next section we will describe on the work system of the series parallel hybrid system from Toyota which is named Toyota Hybrid Synergy Drive because in this research we will analyze this technology.\n2.3. Toyota Hybrid Synergy Drive and it\u2019s working principal\nToyota hybrid synergy drive uses series/parallel hybrid for it\u2019s drive train system. This system transaxle is consisted of ICE, motor, and generator. This three component is connected by power split device.\nIn this transaxle system, power is splitted depend on the driving condition. In the next subsection, will be explained about this power splitting.", "Start to low speed condition (a), ICE will stop, then car is moved by electric motor (A) [2]. Constant speed (b), power from ICE is splitted by power split device. Some of it used to move the generator, which it\u2019s output are the source of power for electric motor (B), and the rest of it is used directly to the final drive [2]. Acceleration (c), extra power is obtained from battery for additional power to the motor (A), while ICE is supplying the power directly to the final drive and moving the generator for the source of power for electric motor (B+C) [2]. Deceleration and braking (d), motor with big output became generator with big output moved by wheels. Regenerative braking system transform kinetic energy to electrical energy, that will stored in battery (D) [2]. Battery Charging (e), battery state of charge is controlled so that keep the reserve energy. ICE moving generator for charging the battery when needed (E) [2].\n3. Hybrid Vehicle Explanation\nTo know about how the hybrid system work, we will test the car in the dyno test to know the power characteristic an how the power splitting system work. From this test, we will know the comparison of the performance from the test an performance Toyota claimed of.\n3.1 Toyota Hybrid Synergy Drive and it\u2019s working principal\nIn this research, we will use Toyota Camry Hybrid 2012, that used hybrid synergy drive technology for it\u2019s hybrid power train system. The following table is the general specification of this car." ] }, { "image_filename": "designv11_29_0000033_roman.2008.4600696-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000033_roman.2008.4600696-Figure2-1.png", "caption": "Fig. 2. Two grasps to be evaluated. Which one is task related?.", "texts": [ " To this purpose, in this paper we report experiments in the application of task-based quality measures allowing comparison across diverse grasps. Figure 1 shows a set of three examplar grasps applied to an object, a model airplane, in a series of demonstrations. The grasping device is a 3D model of the Barrett hand, a three fingers and four degrees of freedom device. Clearly the intention of the teacher is to instruct the learner to grasp the airplane on its fuselage. After the demonstration phase new grasps can be analyzed. Figure 2 shows two different grasps for the same object. Note that the grasp on the right applies contacts on a wing of the airplane. Intuitively, a useful criterion should rank higher the grasp on the left, which complies to the global task knowledge provided by the teacher through its demonstration. The PbD system exploited for this research comprises a CyberTouch glove (by Immersion Corporation) and a FasTrack 3D motion tracking device (by Polhemus, Inc.) which allow an operator to perform real-time manipulation tasks in a virtual environment" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002098_fuzzy.2011.6007645-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002098_fuzzy.2011.6007645-Figure7-1.png", "caption": "Fig. 7. Five-Fingered Prosthetic Hand Grasping a Rectangular Object", "texts": [ " (21) Then we use mamdani fuzzy inference system to tune the time-varying parameters KP(t) and KD(t) of PD controller. Figure 4 shows the structural characteristics of proposed fuzzy inference system, which includes two inputs (error e and error change e\u0307) on the left and one output (KP) on the right. Each input or output layer contains seven triangular membership functions as shown in Figure 5 and 49 logic rules as listed in Table I. After using 49 logic rules, the output surface KP of fuzzy inference system is generated as shown in Figure 6. Similarly, KD can be computed by the same way. Figure 7 shows that a five-fingered prosthetic hand with 14 DOFs is reaching a rectangular rod in order to grasp the object. When thumb and the other four fingers are performing extension/flexion movements, the workspace of fingertips is restricted to the maximum angles of joints. Referring to inverse kinematics, the first and second joint angles of the thumb fingertip are constrained in the ranges of [0,90] and [-80,0] (degrees). The first, second, and third joint angles of the other four fingers are constrained in the ranges of [0,90], [0,110] and [0,80] (degrees), respectively [35]" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003039_978-3-319-79099-2_10-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003039_978-3-319-79099-2_10-Figure2-1.png", "caption": "Fig. 2 Schematic representation of the putative changes in the shape of a cell wall fragment due to matrix swelling. a If two unbound layers (a) extend differently, no buckling occurs (a\u2019) but if they are bound and their ends are fixed, when the compression threshold is surpassed, they lose stability and bend due to buckling (a\u201d). b and c Schemes of a cell wall fragment comprising layers with different swelling capacities. Layers are labeled with capital letters (A, B) and a number, 1 or 2, referring to different cells. B indicates layers with an increased capacity for matrix swelling. The orientation of CMFs is represented by blue (gray) line segments; black arrows represent forces; gray arrows\u2014water penetration. A boundary between the walls of two cells is indicated by a thicker line. b Symmetric swelling on both sides of the fragment of a compound wall (the wall comprising the adhering walls of two cells bound by the middle lamella) results in the compression of the B1, B2 layers and tension of layers A1, A2 (b), which is a prerequisite for growth (b\u2019). c If the distribution of the swelling layers is asymmetric, like in a wall fragment of a single cell (c), buckling occurs (c\u2019) analogous to a\u201d", "texts": [ " An extreme case in which the tensile in-plane stress could not be driven by turgor would be a wall fragment that is folded into the cell (like a wall invagination), which would grow more and more into the cell, while the entire cell was not growing. In such cases, an alternative mechanism for generating stress was postulated (Hejnowicz 2011), i.e., the tensile stress in a wall layer can be generated by swelling in the adjoining layer. In a theoretical situation, if the two layers are not attached, the one that was swelling would simply expand more than the other (Fig. 2a-a\u2019). However, if the layers were tightly joined like in the cell wall, the static equilibrium condition would require that the sum of the forces is zero, and therefore the compression in the swelling layer would bring the other layer under tension. In the case of the cell wall, the swelling of a wall matrix that fills the spaces between stiff CMFs would result in compressive stress in the swelling wall layer (e.g., B1 in Fig. 2b, c). If the CMFs in the swelling layer were aligned, i.e., their arrangement was anisotropic, the compressive in-plane stress in this layer would also be anisotropic with the greatest compression in the direction perpendicular to the orientation of the CMFs. Accordingly, the tensile stress generated in the adjoining layer (A1 in Fig. 2b, c) would also be anisotropic with the maximal tension in the same direction. If the distribution of the swelling layers within the compound wall (comprising two walls of neighboring cells that are tightly joined by middle lamella) was symmetric and all of the layers remained attached, the tensile stress generated in such a manner could explain the wall growth (Fig. 2b-b\u2019). However, in some cases, such a mode of stress generation could lead to local cell wall buckling. An example is a straight wall fragment, the two ends of which are fixed by the remaining cell walls, where the distribution of the swelling layers is not symmetrical (Fig. 2c-c\u2019). In such a case, when a critical value of the compressive in-plane force is surpassed, thewall fragment loses its stability and the two joined layers buckle. This could explain the initiation of a cell wall folding into the cell lumen, which is an initial stage in the generation of a complex cell shape. Below we discuss examples of cell morphogenesis in which differential growth and local buckling are likely involved. During stomata morphogenesis, the two guard cells, which exhibit a structural symmetry, undergo profound shape changes that are accompanied by growth", " a Two stages of stomata development in the micrograph of the Arabidopsis leaf epidermis\u2014in the stomata on left, the two guard cells (GC) are not yet separated; in the stomata on right, the pore is already formed. Scale bars 20 \u00b5m. b Schematic representation of an epidermis fragment with a stomata cut at its center across the pore. Blue (gray) lines represent CMFs orientation; PWi and PWo indicate the inner and outer periclinal walls, respectively; DW\u2014the dorsal anticlinal wall; VW\u2014the ventral anticlinal wall. c Scheme of a fragment of a compound cell wall comprising layers with different swelling capacities. Labeling as in Fig. 2b, c. Symmetric swelling on both sides of the compound wall results in the compression of the B1, B2 layers and tension in the A1, A2 layers (c). If the fragment ends are fixed by remaining cell walls and the middle lamella is weakened, the two single walls buckle and the space between them opens forming a pore (c\u2019) the cell lumen. The necessary compressive stress may arise in the inner layers of the thickenedwall portions, i.e., those facing the protoplast (B1 and B2 in Fig. 3c), where it results from an increase in the matrix swelling capacity during the maturation of the wall" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002437_978-3-319-55128-9_5-Figure5.58-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002437_978-3-319-55128-9_5-Figure5.58-1.png", "caption": "Fig. 5.58 Stress\u2013strain characteristics of different deformation mechanisms [158]", "texts": [ " For cellular structures withM = 0, a mixed deformation mode is often observed, however the structure could still be considered primarily stretch-dominated. There exist significant difference of mechanical characteristics between stretch-dominated and bending-dominated cellular structures. Bending-dominated structures usually exhibit lower modulus and strength compared to stretch-dominated structures due to the lower resistance of strut and thin wall structures to bending deformation. As shown in Fig. 5.58a, the bending-dominated structures usually exhibit the classical plateau stress\u2013strain curve, which has been discussed previously in details. In fact, most commercial stochastic cellular structures have Maxwell stability M < 0 and exhibit bending-dominated deformation mechanism. In comparison, the stretch-dominated structures exhibit a slightly different stress\u2013strain characteristic. As shown in Fig. 5.58b, the initial failure of stretch-dominated structures usually occurs at higher stress levels. However, upon initial failure the local catastrophic of structure collapse will often cause sudden drop of stress as a result of structural relaxation, which can be termed as post-yield softening. Such structural collapse is also often accompanied by macroscopic geometrical distortion of the structures, which sometimes alter the deformation mechanism of the remaining structures into bending-dominated structures by introducing loading misalignment. The example stress\u2013strain curve shown in Fig. 5.58b demonstrates such case, in which the consequent deformation exhibits plateau stage before densification occurs. However, in some cases the local collapse does not cause the change of deformation mechanism, and consequently the post-yield softening could happen again when another local collapse takes place. For hexagonal honeycomb structures, the deformation mode under in-plane loading exhibits bending-dominated mechanism, whereas the deformation mode under the out-of-plane loading exhibits stretch-dominated mechanism" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003250_ssp.284.312-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003250_ssp.284.312-Figure1-1.png", "caption": "Fig. 1. Diagram of the location of stress concentrators at the bottom of the depressions of a microprofile of a rough surface", "texts": [ " The Ti-6Al-4V refers to \u03b1+\u03b2 phase in a stable state contain 5 to 25% of the \u03b2 phase. These alloys are characterized by a good ratio of strength and plasticity. The roughness of the surface of the products reaches Ra = 150 \u03bcm, but the structural elements of parts with higher requirements for roughness, flatness of the surface, mechanical properties must be polished. Surface roughness - a technological stress concentrator, reduces the strength characteristics of a metal, regardless of the type of stress condition. Figure 1 shows a diagram of the location of stress concentrators at the bottom of the depressions of a micro-profile of a rough surface. There are several ways to remove roughness, for example, laser polishing or mechanical grinding. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.scientific.net. (#110064860, University of British Columbia, Kelowna, Canada-16/10/18,05:42:41) Laser polishing has been considered as a potential method to reduce surface roughness of additive manufactured metals" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003154_j.jsv.2018.08.016-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003154_j.jsv.2018.08.016-Figure3-1.png", "caption": "Fig. 3. Different basis definitions for a generalized cyclically symmetric system. (a). The basis {ei 1 , ei 2 , ei 3 } is oriented with a fixed angle \ud835\udefci = 2\ud835\udf0b(i \u2212 1)\u2215N to the basis {e1 , e2, e3}. (b). {e\u0302i 1 , e\u0302i 2 , e\u0302i 3 } is oriented with a fixed angle \ud835\udefci to {e\u03021, e\u03022, e\u03023}. The axis e\u03021 in {e\u03021 , e\u03022, e\u03023} is oriented with the angle 2n\ud835\udf0b\u2215N to e1 in (a). {e\u0302i 1 , e\u0302i 2 , e\u0302i 3 } in (b) and {ei+n 1 , ei+n 2 , ei+n 3 } in (a) are identical and applied to the same substructure.", "texts": [ " (12b) connect the central components with the substructures. Dcs can be partitioned as Dcs = \u239b\u239c\u239c\u239c\u239c\u239c\u239d Dc1s1 Dc1s2 \u2026 Dc1sN Dc2s1 Dc2s2 \u2026 Dc2sN \u22ee \u22ee \u22f1 \u22ee DcPs1 DcPs2 \u2026 DcPsN \u239e\u239f\u239f\u239f\u239f\u239f\u23a0 , (16) where each 6 \u00d7 L block expresses the impact of the lth substructure on the ith central component. Dsc can be similarly partitioned into NP L \u00d7 6 blocks. To obtain the properties of Dcs and Dsc, a general cyclically symmetric system with vibrating central components is analyzed under two different basis definitions depicted in Fig. 3. The equations of motion under the reference frames in Fig. 3(a) are formulated in Eq. (12). An alternative basis definition is given in Fig. 3(b). The rotating frame for central component motions, {e\u03021, e\u03022, e\u03023}, is directed with a fixed angle 2n\ud835\udf0b\u2215N relative to the rotating frame {e1, e2, e3}, where n is an arbitrary integer between 1 and N. {e\u0302i 1 , e\u0302i 2 , e\u0302i 3 } is oriented with a fixed angle \ud835\udefci = 2\ud835\udf0b(i \u2212 1)\u2215N relative to {e\u03021, e\u03022, e\u03023}. A new generalized coordinate vector q\u0302 is defined similarly to the vector q in Eq. (12c). The equations of motion using the new generalized coordinate vector are M\u0302 \u0308\u0302q + B\u0302 \u0307\u0302q + L\u0302q\u0302 = D\u0302q\u0302 = F\u0302, (17a) D\u0302 = ( D\u0302cc D\u0302cs D\u0302sc D\u0302ss ) = M\u0302 d2 dt2 + B\u0302 d dt + L\u0302. (17b) Eqs. (12) and (17) are different equations of motions for the same system, where the generalized coordinates are defined differently. Proving the properties of Dcs and Dsc requires building a connection between Eqs. (12) and (17). The reference frames in Fig. 3(b) can be obtained by rotating their counterpart frames in Fig. 3(a) about the system symmetry axis by an integer (n) multiple of the substructure spacing angle 2\ud835\udf0b\u2215N. Because the full system is cyclically symmetric, the couplings between all the components are independent of whether the degrees of freedom are defined under the bases in Fig. 3(a) or (b). For example, the first substructure in Fig. 3(a) couples with any specified substructure or central component identically as the first substructure in Fig. 3(b) couples with the corresponding substructure or central component having the same relative position, although these two substructures are not the same substructure in the global reference frame {E1,E2,E3}. Therefore, the operator D\u0302 associated with the basis definition in Fig. 3(b) is identical to the D in Eq. (12), D = D\u0302 (18) and only D is used subsequently. The relations between q and q\u0302 (or F and F\u0302) can be obtained by observation. In Fig. 3, both the subvectors qsi+n (under {ei+n 1 , ei+n 2 , ei+n 3 }) and q\u0302si (under {e\u0302i 1 , e\u0302i 2 , e\u0302i 3 }) describe the motion of the (i + n)th substructure in Fig. 3(a), i.e., q\u0302si = qsi+n . (19) Such relation between the subvectors of q\u0302s and qs can be expressed as q\u0302s = (\ud835\udf48n N \u2297 IL)qs, (20) where \ud835\udf48N is the N \u00d7 N cyclic forward shift matrix \ud835\udf48N = \u239b\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d 0 1 0 \u2026 0 0 0 0 1 \u2026 0 0 \u22ee \u22ee \u22ee \u22f1 \u22ee \u22ee 0 0 0 \u2026 1 0 0 0 0 \u2026 0 1 1 0 0 \u2026 0 0 \u239e\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 N\u00d7N . (21) When an N \u00d7 1 vector a is multiplied by \ud835\udf48 n N (nth power of \ud835\udf48N), it is equivalent to upwardly and cyclically shifting all the elements of a by n elements. In a similar style, multiplication by \ud835\udf48 n N \u2297 IL as done in Eq", " (22) The subvectors q\u0302c and qc (or F\u0302c and Fc) expressing the motions (or driving forces and moments) of the central components are related by a rotational coordinate transformation along the cyclic symmetry axis, i.e., q\u0302c = (I2P \u2297 RT n)qc, (23) F\u0302c = (I2P \u2297 RT n)Fc, (24) where I2P is the 2P \u00d7 2P identity matrix, Rn is the rotational transformation matrix, Rn = R(2n\ud835\udf0b N ) = R(\ud835\udefcn+1) = \u239b\u239c\u239c\u239c\u239c\u239c\u239d cos 2n\ud835\udf0b N \u2212 sin 2n\ud835\udf0b N 0 sin 2n\ud835\udf0b N cos 2n\ud835\udf0b N 0 0 0 1 \u239e\u239f\u239f\u239f\u239f\u239f\u23a0 , (25) and n is the arbitrary integer relating the alternative basis definitions in Fig. 3. Based on Eqs. (12b), (18), and (20)\u2013(24), Eqs. (12a) and (17a) are rewritten as( Dcc Dcs Dsc Dss )( qc qs ) = ( Fc Fs ) , (26a) ( Dcc Dcs Dsc Dss )( (I2P \u2297 RT n )qc (\ud835\udf48n N \u2297 IL)qs ) = ( (I2P \u2297 RT n )Fc (\ud835\udf48n N \u2297 IL)Fs ) . (26b) Starting separately from Eqs. (26a) and (26b), each set of L equations governing the motion of a single substructure is written as P\u2211 l=1 Dsicl qcl = Fsi \u2212 N\u2211 l=1 Dsisl qsl , i = 1, 2,\u2026 ,N, (27a) P\u2211 l=1 Dsicl (I2 \u2297 RT n )qcl = Fsi+n \u2212 N\u2211 l=1 Dsisl qsl+n , i = 1, 2,\u2026 ,N. (27b) Manipulation of Eq" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003653_cdc40024.2019.9029274-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003653_cdc40024.2019.9029274-Figure1-1.png", "caption": "Fig. 1. Frames and forces", "texts": [ " \u2022 \u03a0u denotes the operator of projection on the plane orthogonal to u. \u2022 G denotes the aircraft center of mass (CoM). \u2022 B = {G; \u0131, ,k} is the chosen aircraft-fixed frame, with \u0131 and parallel to the so-called zero-lift plane of the aircraft. We assume that this latter plane is not affected by thrust direction changes. This implies in particular that the aircraft is designed so as to minimize aerodynamic interference between the propulsion system and the main wing. The vector \u0131 (resp. ) is along the longitudinal (resp. lateral) axis of the aircraft (see Fig. 1). \u2022 l = sin(\u03b8)\u0131\u2212 cos(\u03b8)k is the unitary vector characterizing the thrust direction, with \u03b8 the tilting thrust angle. \u2022 \u03c9 is the angular velocity of B w.r.t. I, i.e. d dt (\u0131, ,k) = \u03c9 \u00d7 (\u0131, ,k) (1) The vector of coordinates of \u03c9 in the body-fixed frame B is denoted as \u03c9. \u2022 m is the body mass. \u2022 p is the CoM position w.r.t. the inertial frame. \u2022 v is the CoM velocity w.r.t. the inertial frame, i.e. p\u0307 = v (2) The vector of coordinates of v in the body-fixed frame B is denoted as v. \u2022 v\u0307 is the CoM acceleration w", " We assume that the control inputs consist of a thrust force T = T l, typically produced by propellers or jet turbines, and a torque vector \u0393. This torque is used to modify the vehicle\u2019s orientation at will. It can be produced in various ways by using tilting control surfaces (standard airplanes), differential multi-rotors speeds (classical multirotor drones), cyclic blade control (helicopters), a combination of tilting control surfaces with cyclic blade control (V-22 Osprey, Bell V-280 Valor), or a combination of tilting control surfaces with differential multi-rotors speeds (the quad tilt rotor aircraft represented in Fig. 1), etc. Due to the large number of possible configurations, and for the sake of genericity, the actuation system producing this torque is not specified in the first control design stages. More specifically, we assume the pre-existence of low level feedback loops that control the production of a torque vector ensuring the asymptotic stabilization of any desired angular velocity for the vehicle\u2019s body. This is a standard backstepping assumption. Under this assumption the body angular velocity \u03c9 becomes an intermediate control variable", " Let \u03c9\u2217 denote the desired aircraft angular velocity (derived according the methodology proposed in the preceding section, for instance), and let \u0393 denote a control torque vector in charge of ensuring the (near) asymptotic stabilization at zero of the angular velocity error \u03c9 \u2212 \u03c9\u2217. In view of the classical Newton-Euler equation J\u03c9\u0307 = J\u03c9 \u00d7 \u03c9 + \u0393 (+parasitic terms) (32) with J denoting the aircraft inertia matrix, a simple possibility consists in setting \u0393 = \u2212k\u03b3J(\u03c9 \u2212 \u03c9\u2217) + \u03c9 \u00d7 J\u03c9\u2217 (33) with k\u03b3 > 0 denoting a large control gain. In the case of a quad tilt rotor aircraft, like the one represented in Fig. 1, this control torque can be produced either by the four propellers (using differential multi-rotors speeds), or by the moving (ailerons/rudder/elevator) control surfaces of the aircraft, or by a combination of the two systems, i.e. \u0393 = \u0393m + \u0393a (34) with \u0393m the torque vector produced by the set of propellers, and \u0393a the torque vector produced by the aircraft moving surfaces. Now, given a desired control torque vector \u0393, an issue is to distribute the torque production between the two systems knowing that at low airspeeds moving control surfaces are inefficient, and that at high airspeeds they typically produce torques more effectively than the propellers", " The code implementation is based on the open-source PX4 flight stack [12]. To perform hardware-in-the-loop simulations, this hardware is connected to a flight simulator. We use the Gazebo robot simulator, along with open source plugins (based on the RotorS Project) whose purpose is to simulate UAV models and interface them with the controller hardware (https://github.com/PX4/sitl gazebo). The aircraft model used for this simulation mimics a 2.5 kg tilt-rotor fixed-wing drone, alike the one shown in Fig 1. The flight mode transition airspeed v\u2217 is set equal to 4 m/s, and the airspeed v\u0304\u2217 for the torque production transition (between the rotors and the control surfaces) is set equal to 7 m/s. The tilt angle \u03b8 is bound to remain in the interval [0, \u03c0/2] and is calculated to minimize the thrust intensity, as explained in Section III-A.2. At low airspeeds the objective is to keep the aircraft fuselage horizontal (see Section III-B). For this simulation there is no wind so that va = v. The chosen reference trajectory (see Figures 3 and 4) consists of an ascending phase, at an airspeed of 2 m/s, followed by a horizontal flight along a straight line during which the reference speed increases from 0 m/s to 10 m/s" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000043_rspa.2007.0372-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000043_rspa.2007.0372-Figure4-1.png", "caption": "Figure 4. Schematic end views of a sheet of arc length 2S. (a) The sheet touches the circle at the two ends when R/SZ1. (b) Here, the radius is R/SZ0.932 and f0Zp/3. (c) R/SZ0.741 and f0Zp/6. (d ) The midpoint first contacts the circle when R/SZe1, where e1 is defined in the text. This new contact point is at the angle fZp/2.", "texts": [ " Therefore, any layer with the same curvature will have the same cross-sectional force. In particular, if all the layers in a given section of the coil have approximately the curvature of the tube wall, we conclude that ftZf and formula (2.7) remains valid at those locations. We now study the series of events that lead to the coiling of the sheet inside the tube as the radius R decreases from a large value. The minimal length needed for the sheet to exert force on the tube is the diameter 2R. At this condition, we put the sheet along the direction e1 for the axes defined in figure 4a. If the tube diameter is a bit smaller than the sheet length, the sheet starts to bend to one of the two sides of the tube as we observe in figure 4b. Note that both contact points must remain on the diameter line because this is the only way the external point forces Q0 and Q1 can add to zero. The force Q0 is normal to the contact point at the lower part of the strip and can be written as Q0ZKq0e1, where q0 is the magnitude of the force. It is straightforward to see that the equation for the curvature is B \u20acfK q0 cos fZ0. A first integration of this relation gives, for the curvature, _fZ \u00f02q0=B\u00de1=2\u00f0sin fKsin f0\u00de1=2; \u00f03:1\u00de where f0 is the touchdown angle at the lower point", " The average pressure is the sum of the magnitude of the normal forces divided by the perimeter. In this case, we obtain pZ2q0=\u00f02pR\u00de. This definition is equivalent to the expression pZ\u00f0vAUB\u00deS used in \u00a72b. We note that the force R2q0=B and the average pressure decrease as the radius is further decreased (figures 7b and 12), so that the sheet is more easily bent by the tube. In addition, the curvature of the midpoint decreases when R/S is reduced until the condition R=SZe1Z0:659. Here, the point at fZp/2 makes contact with the frame (figure 4d ). The angle f0 decreases from the value f0Zp/2, where the sheet is straight, to the value f0z0.358 (z20.58). We can see from figure 4d that our solution remains valid until the sheet touches the tube in the position (x, y)Z(0, R). At R/SZe1, there are three external point forces over the surface such that Q0CQ1CQ2Z0 (figure 5b). Here, we name the point forces, tangent angles, arc length positions and points where they are located in anticlockwise order. The first point 0 is located at sZ0, the tangent angle at this point is f0 and the point force is Q0; the second point 1 is located at sZs1, its tangent is f1 and the point force is Q1, etc" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001953_icca.2013.6565105-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001953_icca.2013.6565105-Figure1-1.png", "caption": "Figure 1. Relationship between relative and inertial coordinate frame", "texts": [ " Relative coordinate frame r r r ro x y z The origin ro of this coordinate coincides with centroid of the leader, axis r ro x points to leader velocity direction, r ro y is up-vertical to r ro x in the vertical plane, r ro z composes a right-handed coordinate frame together with other two axes. 2. Inertial coordinate frame system I I I IO X Y Z The origin IO of this coordinate frame is fixed to an arbitrary point on the ground, axis I IO X lies in a horizontal plane and points to a target, axis I IO Y is vertical upwards, and axis I IO Z composes a right-handed coordinate frame system together with those two axes mentioned above. The relationship between these two coordinate frames is depicted in Fig.1. B. Design for missile formation PD controller The kinematics of followers in a missile formation can be described as follows in the inertial coordinate frame: cos cos sin ( 1, 2,...) cos sin i i i vi i i i i i i vi X V Y V i follower follower Z V (2) where , ,i i iX Y Z are position components of each follower in the inertial coordinate; the meanings of , , i i viV of each follower can be found in Eq. (1). The kinematics relationship between a follower and the leader in the inertial and relative coordinate frame is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003223_j.mechmachtheory.2018.08.018-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003223_j.mechmachtheory.2018.08.018-Figure4-1.png", "caption": "Fig. 4. 3-D schematic chart of a CNC internal gear honing machine.", "texts": [ " According to the theory of gearing [ 22 , 23 ], the meshing condition between the right helical gear surface and right honing wheel surface can be obtained by: f 2 (u, v , \u03d5, \u03b8h ) = n h \u00b7 \u2202 r h (u, v , \u03d5, \u03b8h ) \u2202 \u03b8h = 0 (11) Finally, the equation of honing wheel surface can be obtained by solving Eqs. (6) , (7) and (11) simultaneously. The profile of the generating surface of the work gear is generated by a honing wheel on an internal gear honing machine as shown in Figs. 4 and 5 . The honing process for lead dual-crowning of a long face-width work gear is expressed as shown in Fig. 6 . The calculation method of the normal deviation of work gear tooth flank is shown in Fig. 7 . Fig. 4 shows a 3-D schematic of an internal gear honing machine (F\u00e4ssler HMX-400) with nine moving axes for the CNC internal gear honing machine, wherein Z 1 is the longitudinal slide for axial movement of the honing stone, Z 2 is the moving of the headstock that carries the work spindles to honing or loading/unloading position tangential and X is cross slide for the radial movement (infeed) of the honing stone towards the work piece or dressing tool. B is the swivel axis of honing- 1 stone head for lead crowning, A is the swivel axis of the honing stone for adjusting the crossed-axis angle, B 2 is the swivel axis of headstock turntable, C 3 is the spindle axis of the dressing tool, C 2 is the spindle axis of workpiece, and C 1 is the spindle axis of honing wheel", " The relative motion coordinate systems between the honing wheel and the workpiece are established in Fig. 5 . The coordinate systems S c ( x c , y c , z c ), S g ( x g , y g , z g ) and S 11 ( x 11 , y 11 , z 11 ) are rigidly attached to the honing wheel, the work gear and the frame, respectively; while S 7 ( x 7 , y 7 , z 7 ), S 8 ( x 8 , y 8 , z 8 ) , S 9 ( x 9 , y 9 , z 9 ), S 10 ( x 10 , y 10 , z 10 ) and S d ( x d , y d , z d ) are auxiliary coordinate systems for the simplification of coordinate transformation. The relation of coordinate systems ( Fig. 5 ) with the honing machine ( Fig. 4 ) are described as follows: the rotational motions \u03c6c , \u03c6g , \u03b3 and \u03c8 c in the coordinate systems correspond to the rotational motions C 1 , C 2 , A and B, respectively, and the axial feed \u03bb corresponds to the axial movement axis Z 1 . Among of them four motions, C 1 , C 2 , B 1 , and Z 1 , are used to generate the tooth flank gear surface. For the lead-crowning on a work gear, an additional linear function of axial motion of the work gear is given to the swivel angle of honing-stone head around the B 1 axis, \u03c8 c , as the following equation: \u03c8 c = k \u03bb (12) where k is an adjusting coefficient of the swivel angle function, and \u03bb is the axial feed of honing wheel " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003223_j.mechmachtheory.2018.08.018-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003223_j.mechmachtheory.2018.08.018-Figure5-1.png", "caption": "Fig. 5. Coordinate systems for F\u00e4ssler HMX-400 internal gear honing machine.", "texts": [ " 4 shows a 3-D schematic of an internal gear honing machine (F\u00e4ssler HMX-400) with nine moving axes for the CNC internal gear honing machine, wherein Z 1 is the longitudinal slide for axial movement of the honing stone, Z 2 is the moving of the headstock that carries the work spindles to honing or loading/unloading position tangential and X is cross slide for the radial movement (infeed) of the honing stone towards the work piece or dressing tool. B is the swivel axis of honing- 1 stone head for lead crowning, A is the swivel axis of the honing stone for adjusting the crossed-axis angle, B 2 is the swivel axis of headstock turntable, C 3 is the spindle axis of the dressing tool, C 2 is the spindle axis of workpiece, and C 1 is the spindle axis of honing wheel. The relative motion coordinate systems between the honing wheel and the workpiece are established in Fig. 5 . The coordinate systems S c ( x c , y c , z c ), S g ( x g , y g , z g ) and S 11 ( x 11 , y 11 , z 11 ) are rigidly attached to the honing wheel, the work gear and the frame, respectively; while S 7 ( x 7 , y 7 , z 7 ), S 8 ( x 8 , y 8 , z 8 ) , S 9 ( x 9 , y 9 , z 9 ), S 10 ( x 10 , y 10 , z 10 ) and S d ( x d , y d , z d ) are auxiliary coordinate systems for the simplification of coordinate transformation. The relation of coordinate systems ( Fig. 5 ) with the honing machine ( Fig. 4 ) are described as follows: the rotational motions \u03c6c , \u03c6g , \u03b3 and \u03c8 c in the coordinate systems correspond to the rotational motions C 1 , C 2 , A and B, respectively, and the axial feed \u03bb corresponds to the axial movement axis Z 1 . Among of them four motions, C 1 , C 2 , B 1 , and Z 1 , are used to generate the tooth flank gear surface. For the lead-crowning on a work gear, an additional linear function of axial motion of the work gear is given to the swivel angle of honing-stone head around the B 1 axis, \u03c8 c , as the following equation: \u03c8 c = k \u03bb (12) where k is an adjusting coefficient of the swivel angle function, and \u03bb is the axial feed of honing wheel " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000020_6.2008-6331-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000020_6.2008-6331-Figure6-1.png", "caption": "Figure 6: The NASA Hover Boards \u2013 Parallax Board Schematic and with VAAC", "texts": [ " The impact of this prudent safety mitigation was that the compelling visual cues for precise hover positioning that are apparent at the ship hover heights of 30 feet are virtually non-existent at 100 feet. Since the American Institute of Aeronautics and Astronautics 7 principle focus of this flight trial was in the area of precision hover maneuvering, a solution to the visual cueing environment consistent with that of shipboard operations had to be overcome at low costs. Previous VSRA trials at NASA Ames had made use of visual targets, shown in Figure 6. The design used a reference base board in conjunction with two parallax boards which results in extremely precise positioning for lateral capture tasks from one target to the next. If the pilot eye-point is at the correct X, Y and Z position, he will see a continuous black line across the center of the base board. Any deviation laterally, vertically or in range to the board will be detected by seeing errors in the parallax board by exposing white areas of the base board. In addition, marks on the base board allow setting of desired and adequate position tolerances" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002575_ectc.2017.232-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002575_ectc.2017.232-Figure3-1.png", "caption": "Figure 3: 3D CAD Design of the a. Heat sink's outer structure; b. inner structure with microchannels.", "texts": [ " Two inlet and outlet connectors for the pipes attachment have been included. The inner structures of the heat sink consist of a micro-channeled block. The designed micro channels follow the path established in the previous part of the paper. Moreover, the distribution and number of the channels is selected so that the volumetric flow matches the designed percentage medium distribution. Additionally, the block includes extra structures outside to better guide the flow into the channels and reduce the pressure drop as in Fig. 3. The final design including inlet and outlet pipes connectors consists of a 67 mm x 42 mm x 10 mm box with a net volume of 28.1 cm3. The calculation methodology and results of the parametric study which are not part of thios paper, determined that the dimensions of the micro-channel i.e. width (W) = 500 \u03bcm and height (H) = 1000 \u03bcm offer a good tradeoff between heat transfer and pressure drop and thus the selected dimension for the final 3D design. To estimate the diode junction temperatures in design with standard air-cooled heat sink and SLM constructed actively water coolable heat sink, thermal simulations were performed for the simplified models as in Fig", " Both powders are available and, at a first glance, would be the best fitting materials for AM heat sinks. As pure copper materials are still in research phase and involve process complexities of overheating and improper melting and Al components exhibit lower densities, the next best combination available with excellent melt characteristics CL80 CU was selected for the prototype development. The prototypes were built initially to check the microchannel stability and fineness during the SLM process. As explained in Fig. 3, the inner structure was divided into multiple individual planes. The feasibility initially was to obtain an excellent microstructure design to be able to build and fit inside the heat sink outer design (Fig 3.a). As first mockup, single plate was built using SLM with microstructures with and without supporting structures and can be observed from Fig 6a. Another prototype with both inner and outer structures combined was built to check this possibility. Here the focus was also to examine the residual powders and corresponding process-generated defects. The high quality geometrical definition of channel plates was possible without support structures, suggesting the possibility of building the whole assembly in a single shot without internal support structures for the channels" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002020_s11012-010-9415-8-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002020_s11012-010-9415-8-Figure1-1.png", "caption": "Fig. 1 Test rig used for the ultrasonic analysis (left), detail of the tooth-plane contact (right)", "texts": [ " Thus, the contacting elements, which represent the heart of the test rig, were designed as follows: the rack tooth surface is a plate (27 mm thickness) which is also the bottom of a prismatic container (open on the upper side) designed to host the ultrasonic transducer and the medium needed to efficiently transmit the beam from the transducer to the contact region. The gear tooth is basically a rectangular plate (370 \u00d7 110 \u00d7 34 mm) in which one of the extremities is shaped as a spur gear tooth (module = 20, number of teeth = 30, face width = 110 mm, pitch diameter = 600 mm) and is loaded on the bottom side (free to move). The relative position of both contacting elements (see Fig. 1 for details) can be varied so as to simulate a number of contact conditions: in particular, the container can be moved both horizontally and vertically, while the tooth is hinged on one side to the metallic frame at three different positions and this allows us to change both the pressure angle (which can range from 3\u00b0 to 30\u00b0) and the initial contact point as would occur during a cycle. Both elements were built using A284 Grade D steel (yield strength 205 MPa, ultimate strength 415 MPa). Located below the tooth, a hydraulic jack and a force transducer allow application and monitoring of the load respectively (maximum applicable force 50 kN); all components are housed inside a steel frame" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001477_icit.2012.6210052-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001477_icit.2012.6210052-Figure2-1.png", "caption": "Fig. 2. Schematic diagram of magnetic tape position control", "texts": [], "surrounding_texts": [ "The algorithm for obtaining a sliding surface, S(k) Mx(k) for the system (14) is presented here, in a similar manner as explained in [20], for a general nth order square system with m inputs. Let the system (14) is transformed by x = Ux to 0 0 0 0 x(k+l) = 0 0 o 0 o 0 o o o 0 o 0 o o x(k) o An-l 0 o 0 An (16) where 0, Am+l,' ..... , An-l, An are the eigenvalues of the system. Here it is assumed that, the eigen values are real and distinct. Therefore, (16) can be written as, xl(k + 1) = OXl(k) so, xn(k) = (An)kxn(O) But, x(k) = Ux(k). Now, xl(k) = UllXl(k) + Ul2X2(k) + ..... . ... + ulnxn(k) x2(k) = U2lXl(k) + U22X2(k) + ..... . ... + u2nxn(k) xn(k) = UnlXl(k) +Un2X2(k) + ..... . ... + unnxn(k) Using equation (17) , (18) can be written as, xl(k) = Ul(m+l)xm+1(k) + ..... . ... + ulnxn(k) x2(k) = U2(m+1)Xm+l(k) + ..... . ... + u2nxn(k) x3(k) = U3(m+1)xm+1(k) + ..... . ... + u3nxn(k) (17) (18) (19a) (19b) (19c) xn(k) = Un(m+1)xm+l(k) +...... (19d) ... + unnxn(k) The linear relation between Xl (k), X2 (k), ... , Xn (k) is ob tained in a similar manner as presented in [20], taking the scalars as m2, m3, ' \" , mn. Thus the sliding surface becomes, xI(k) - m2x2(k) - m3x3(k) - ... - mnxn(k) = 0, Mx(k) = O. (20) IV. ILLUSTRATIVE ApPLICATION The proposed method is illustrated in this section with the help of a magnetic tape drive servo system for its position control [24]. A schematic diagram of magnetic tape position control is shown in Fig-2 [25]. The control of tension and position of a moving tape is one of the major control problems in industries. The detailed dynamics are given in [26]. The control objective here is to achieve the commanded position of the tape over the read-write head. A specific tension in the tape is to be maintained while achieving the required position. The continuous time model of the system assuming zero disturbance is represented as [24], where A\ufffd [ 3Lo 3.3150 ;i; = Ax +Bu y=Cx, 0 -10 0 0 -3.3150 -0.5882 -3.3150 -0.5882 B \ufffd [ 8 5}30 sL] and o ] 10 -0.5882 ' -0.5882 C = [ -g ' \ufffd13 2\ufffdi\ufffd3 0.\ufffd75 0.\ufffd75 ] \u00b7 Here, the system states are the positions of the tape at capstans (in millimeters), and the angular velocities of mo tor/capstan assemblies [24]. The currents supplied to the drive motors are the two inputs. The outputs of the system are the position of the tape over the read-write head in millimeters and the tension in the tape in newtons . The control objectives need to be achieved are, the magnetic tape should achieve the commanded position over read-write head as 1mm and the tape tension should be maintained at 2N. The discrete sliding mode controller is designed by dis cretizing the above continuous-time system by sampling it at T = O.lsec and \ufffd = 0.05sec to obtain the corresponding discrete T system and \ufffd system models. The number of gain changes for the periodic output feedback is chosen as N = 2 since the controllability index of the system is 2. The T system matrices are, [ 0.8491 0.1509 -0.9213 0.0787 ] < >: \u00f04\u00de where ventrp,i, pentrp,i and pclosure,i are, respectively, the ventrp, pentrp and pclosure at i-th position. nsidered to be sealed if the closing pressure of crack lips is above the fluid pressure d body: transition steps. In this section, the modifications applied to the FE model PEHM are described. The present model, named Pure Entrapment Model (PEM), is meant to reproduce a rotating rolling disk pressed against a semi-infinite flat plane body, in which a prospective shallow crack has been inserted as geometrical discontinuity through the mesh, as shown in Fig. 5. The radius of the disk and compressive load have been chosen in order to have the same Hertzian pressure distribution as the experimental tribological disk-on-disk system presented in [27,28], and summarized in Table 1. For this purpose, the FE model reproduces the same composite radius as the tribological system; being infinite the radius of curvature of the flat plane, the radius of the cylinder is expressed by: R \u00bc R1R2 R1 \u00fe R2 \u00f05\u00de where R1 and R2 are the radii of the cylinders of the real tribological system" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001430_10402004.2013.812760-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001430_10402004.2013.812760-Figure1-1.png", "caption": "Fig. 1\u2014Schematic diagram of roller\u2013race contact.", "texts": [ " The effects of skew angle, rotational speed, load, length of the roller, radius of the outer race, and amplitude of profile modification for the roller\u2019s generatrix on the EHL behavior were investigated. In addition, the effect of skew combined with the tilting effect is studied. Usually, the non-Newtonian effect is important and essential for a high-shear sliding case; however, the shear sliding is low in cylindrical roller bearings. Therefore, an isothermal Newtonian EHL solution without sliding is considered in this article, although the Newtonian simplicity sometimes may exaggerate the pressure spike to some extent. Figure 1 shows the simplified contact model of a roller\u2013race, where, x is along the entrainment direction before roller skew, y is the axial direction of the roller before the roller skew, and z is the radial load direction of the roller. In the present study, it was assumed that roller skew occurs on the x\u2013y plane and roller tilt occurs on the y\u2013z plane. Note that both the roller and races had dub-off end profile modifications in cylindrical roller bearings. As the roller became skewed, the contact pressure at the end parts of the contact zone increased in the roller\u2013outer race contact, whereas the contact pressure at the center of the contact increased in the roller\u2013inner race contact" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001057_0954410013493237-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001057_0954410013493237-Figure1-1.png", "caption": "Figure 1. One degree of freedom stabilized platform.", "texts": [ " Three-axis gyro-stabilized platform modeling With the use of mechanical gyros in a gyro-stabilized platform structure, its model has been derived. Analytical study of mechanical gyro is based on the Euler equation of motion for a solid object where its center of mass is located on its center of rotation. The symbolic equation of motion is18: M \u00bc _H\u00fe ! H \u00f01\u00de There is a single-frame gyroscope in the stabilizer structure for which the rotor angular momentum is H \u00bc Ir:!r where M is the external inserted moment to the outer frame and ! is the angular rotation perpendicular to gyro axis. As shown in Figure 1, the outer frame is the stabilized platform which can only rotate about y axis or input axis of the single axis gyro. The equations of motion of a single axis gyro with output axis z and the input axis y and the input\u2013 output axis moments Tn Up are as follows18: Tn \u00bc Jy:s 2: y \u00feH:s: z \u00f02\u00de Up \u00bc H:s: y \u00fe I:s2 \u00feD:s\u00fe K : z \u00f03\u00de The open-loop transfer function of the single-axis gyroscope is described as: z Tn \u00bc H Jy\u00f0Jy:s2: y \u00feH:s: z\u00de \u00f04\u00de And the open loop state equation is: s2: y \u00bc Tn Jy \u00f05\u00de I:s2 \u00feD:s\u00fe K z \u00bc H:s: y \u00feUp \u00f06\u00de at NANYANG TECH UNIV LIBRARY on May 31, 2015pig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000055_tpds.2008.40-Figure12-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000055_tpds.2008.40-Figure12-1.png", "caption": "Fig. 12. The Markov chain for jointly connected switching graphs, each of which is disconnected. (a) Two-mode SHS. (b) Three-mode SHS. (c) Four-mode SHS.", "texts": [ " Our analysis can be easily extended to the general case of switching amid more than two graphs. Fig. 11a is one of the simplest examples of such a set of graphs. Note that G1 and G2 can be of any graph topology and size as long as they are individually disconnected but jointly connected. In each round, the network graph can be either G1 or G2. Hence, in the SHS model, the space of discrete modes is Q \u00bc fG1; G2g. The mode transition pattern can be characterized by a two-state Markov chain shown in Fig. 12a. Since G1 and G2 are each disconnected, the lower bound on the convergence rate for each of them in a single round is zero. However, in two rounds, the network may switch between these two jointly connected graphs with positive probability, resulting in a positive expected potential decrement. Thus, to lower bound the expected potential decrement rate, we need to consider two rounds of DRG iterations. Since this is a worst case analysis, we assume the worst scenario: only one group is formed in each round", " A lower bound h on the h-step convergence rate is given by h \u00bc 1 2\u00f0K\u00de, where K \u00bc E\u00bd eWT eW and eW \u00bcW\u00f0k\u00fe h 1\u00de . . .W\u00f0k\u00fe 1\u00deW \u00f0k\u00de. In Fig. 11, four cases under study are plotted. In case 1 and case 3, the union of possible graphs forms a linear array with three and four nodes, respectively. In case 2 and case 4, the union of possible graphs forms a ring with three and four nodes, respectively. The Markov chains (the randomly graph-changing model) describing the transitions among possible graphs are shown in Fig. 12: Fig. 12a for case 1, Fig. 12b for case 2 and case 3, and Fig. 12c for case 4. We compute 2 for case 1, 3 for cases 2 and 3, and 4 for case 4, under different transition probabilities p and q. Fig. 13a plots the computed 2\u00f0K\u00de of case 1 as a function of the transition probabilities p and q. It can be seen that, as p and q both approach 0, 2\u00f0K\u00de achieves its minimum; hence, 2 \u00bc 1 2\u00f0K\u00de achieves its maximum, implying the fastest convergence rate of the DRG algorithm. This is understandable as, in this case, the transitions between the two possible graphs are the most frequent and occur in each round, remedying the slow convergence caused by the individual disconnected graph" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002097_ijvnv.2012.048167-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002097_ijvnv.2012.048167-Figure2-1.png", "caption": "Figure 2 Configuration of ALT pulley, OAD and ALT rotor (see online version for colours)", "texts": [ " The pulleys and belt spans are numbered counter-clockwise. The crankshaft pulley (CS, No. 1) is driving pulley, and is regarded as the first pulley. The belt span between pulleys 1 and 2 is numbered as the first span. The ith belt span is denoted by Bi. The driven pulleys in the FEAD are: air conditioner (AC, No. 2) pulley, alternator (ALT, No. 4) pulley, power steering (PS, No. 5) pump pulley, water pump (WP, No. 7) pulley, and two idler (IDL1 and IDL2, No. 3 and No. 6) pulleys. ALT pulley is connected to ALT rotor through an OAD, as shown in Figure 2. Assumptions used for modelling of rotation vibration of an FEAD are (Hwang et al., 1994; Leamy and Perkins, 1998): a the belt is uniform, perfectly flexible, and stretches in a quasi-static manner b the slip zone between pulley and belt remains a fraction of the entire pulley wrap arc c transverse belt motion (perpendicular to the direction of belt velocity) decouples from longitudinal belt motion (along with the direction of belt velocity) d the bending stiffness of belt is ignored e the tensioner is modelled as linear spring stiffness Kt, and an equivalent viscous damping Ct" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002175_detc2011-48824-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002175_detc2011-48824-Figure7-1.png", "caption": "Figure 7. Assembly error and gear shaft angle error", "texts": [ "org/about-asme/terms-of-use 5 Copyright \u00a9 2011 by ASME flank, another is rectangular. The amount and direction for each modification can be changed independently. The influence of machining and assembly errors on tooth contact pattern was investigated using TCA [11]. In order to calculate the assembly condition, the following are defined. If the designing axes of the pinion and gear axes coincide with each other and the shaft angle is equal to the design value, this position of the face gear is named the regular one. Figure 7 shows the assembly and shaft angle errors. If the gear is fixed, the assembly errors H and V are defined as the deviations of the pinion in H and V directions from the regular position, and also the shaft angle error is defined as the difference from the regular shaft angle. Figure 8 shows the tooth contact pattern on the gear tooth and transmission errors of face gears with modification of gear tooth surface. These results are obtained by TCA calculation. The modification of gear tooth surface was given to get a proper tooth contact pattern" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002259_b978-0-12-385204-5.00001-x-Figure1.3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002259_b978-0-12-385204-5.00001-x-Figure1.3-1.png", "caption": "Figure 1.3 Generic loads input forces under various events.", "texts": [ " However, if both front and rear suspensions are analyzed at their respective GAWRs and the loads are combined to obtain the frame loads, it should be realized that the frame is being overloaded. Alternatively, we may appropriately scale down the loads such that the frame will never experience initial static loads higher than GVWR. Under all events except for curb push-off, all the lateral and longitudinal forces are applied at the corresponding tire patch, and all vertical forces are applied at the corresponding wheel center, as shown in Figure 1.3(a). For the curb pushoff event, as shown in Figure 1.3(b), the left (FYLF) and right (FYRF) tire patch friction forces being against the curb push-off force are applied at the corresponding tire patch. The vertical loads (FZLF and FZRF) are applied at the corresponding wheel center, but the lateral curb push-off force (FYRF_CP or FYLF_CP, depending on the corner of the curb push-off) is applied at a certain height (e.g., 8 inches) above the tire patch and several inches ahead or behind the wheel center, depending on the tire dimensions (see Figure 1" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001578_s11432-011-4257-0-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001578_s11432-011-4257-0-Figure1-1.png", "caption": "Figure 1 X-35B engine layout. Figure 2 Advanced V/STOL aircraft prototype.", "texts": [], "surrounding_texts": [ "Initially we present the controller of the V-1 aircraft, which has an engine layout similar to the X-35B (see Figures 1 and 2). The control inputs of the aircraft include \u03b4vT , \u03b4vq, \u03b4vr, \u03b4fT , \u03b4f , \u03b4Tl, \u03b4Tr, \u03b4a, \u03b4r, \u03b4c, and \u03b4e. \u03b4vT is the ratio of the three bearing swivel duct (3BSD) nozzle thrust to the maximal 3BSD nozzle thrust. \u03b4vq is the pitch angle of the 3BSD nozzle. \u03b4vr is the yaw angle of the 3BSD nozzle. \u03b4fT is the ratio of the lift-fan thrust to the maximal lift-fan thrust. \u03b4f is the pitch angle of the lift-fan nozzle. \u03b4Tl and \u03b4Tr are the thrusts of the left and right roll nozzles. \u03b4a is the aileron deflection. \u03b4r is the rudder deflection. \u03b4c is the canard deflection. \u03b4e is the elevator deflection. All the input dynamics are second-order with position and rate saturation. This controller can be stated in the form \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa \u23aa\u23a9 \u03b8\u0307 = q, q\u0307 = 1 Iyy [ \u2212 Tv max\u03b4vT Rv sin \u03b4vq cos \u03b4vr + Tf max\u03b4fT Rf sin \u03b4f + 1 2 \u03c1V 2Sc\u0304Cm(H, M, \u03b1, q, \u03b4e, \u03b4c) ] , V\u0307xg = 1 m [ (Tf max\u03b4fT cos \u03b4f + Tv max\u03b4vT cos \u03b4vq) cos \u03b8 \u2212 (Tf max\u03b4fT sin \u03b4f +Tv max\u03b4vT sin \u03b4vq cos \u03b4vr) sin \u03b8 \u2212 1 2 \u03c1V 2SCD(H, M, \u03b1, \u03b4e, \u03b4c) cos \u03b3 \u22121 2 \u03c1V 2SCL(H, M, \u03b1, \u03b4e, \u03b4c) sin \u03b3 ] , V\u0307zg = 1 m [ \u2212 (Tf max\u03b4fT cos \u03b4f + Tv max\u03b4vT cos \u03b4vq) sin \u03b8 \u2212(Tf max\u03b4fT sin \u03b4f + Tv max\u03b4vT sin \u03b4vq cos \u03b4vr) cos \u03b8 + 1 2 \u03c1V 2SCD(H, M, \u03b1, \u03b4e, \u03b4c) sin\u03b3 \u2212 1 2 \u03c1V 2SCL(H, M, \u03b1, \u03b4e, \u03b4c) cos \u03b3 ] + g. (1) Here Vxg and Vzg are the components of velocity in the earth axis system. \u03b8 is the pitch angle. q is the pitching angular velocity. m is the vehicle mass. g is the acceleration of gravity. Rv and Rf are the ranges from Xcg, the center of gravity of the aircraft, to the 3BSD and lift-fan nozzles respectively. Tvmax and Tfmax are the maximal thrusts of the 3BSD and lift-fan nozzles respectively. Iyy is the moment of inertia. CD, CL, and Cm are the moment coefficients of drag, lift, and pitch respectively. S is the area of the wing. c\u0304 is the mean aerodynamic chord. H is the flight height. M is the Mach number. \u03b1 is the angle of attack. \u03b3 is the flight path angle. The controlled variable is the flight path angle \u03b3, \u03b3 = arctan(\u2212Vzg/Vxg). (2) The system defined by eqs. (1) and (2) is nonlinear, non-affine, and non-analytic, with multiple inputs and a single output. It has two special control inputs, namely the pitch angle of the 3BSD nozzles and the lift-fan thrust. These inputs should arrive at specified end values to achieve transition flight." ] }, { "image_filename": "designv11_29_0002568_s12206-017-0630-2-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002568_s12206-017-0630-2-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of the cylindrical roller bearing.", "texts": [ " In order to obtain more information on lubrication of finite line contact, the present study employs the deterministic mixed EHL model recently developed by Hu and Zhu [1] to solve engineering problems with real machined roughness. The study aims to extend the pitting life prediction approach presented in Ref. [35] to finite line contact with realistic contact geometry. The effects of working conditions and lubrication parameters on lubrication performance and pitting life are discussed. In order to investigate the basic characteristics of finite line contact, the cylindrical roller bearing has been selected in this paper. The scheme of cylindrical roller bearing is shown in Fig. 1. The cylindrical roller bearing NU204ET is taken as an example and its relevant data are listed in Table 1. As shown in Fig. 1, a half of rollers have been subjected to load depends on the radial load F in theory. The calculation of deformation between single roller and raceway is as follows [36] 0.9 l ik Fd = \u00d7 (1a) where Fi is the load as shown in Fig. 1, b is the contact length, kl is the coefficient of contact deformation, then 0.92 2 1 2 0.8 1 2 1 1 13.81 .l v vk E E bp p \u00e9 \u00f9- - = \u00b4 + \u00d7\u00ea \u00fa \u00eb \u00fb (1b) So, the total deformation between inner and outer raceway, 0.92 2 .i l ik Fd d= = \u00d7 (2) As shown in Fig. 1, the no. 0 selected as a reference. The \u03b4max and F0 is the maximum deformation and load on the reference roller, respectively. Meanwhile, the bearing clearance has been considered. So, the deformation of the roller with angle \u03c6i is calculated by ( )max 0 0= cos i ic cjd d j+ \u00d7 - (3) where c0 is the bearing clearance. The maximum angle of loaded roller with reference roller call be expressed as follows 0 max 0 max arccos .c c j d \u00e6 \u00f6 = \u00e7 \u00f7\u00e7 \u00f7+\u00e8 \u00f8 (4) The radial load F is balanced by the integral of roller load Fi over the entire load region" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003007_1.5034999-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003007_1.5034999-Figure1-1.png", "caption": "FIGURE 1. Sample profile to define the sample geometry in order to evalue the chemical etching on EBM parts", "texts": [ " To help predicting the excess thickness to be provided, the dimensional impact of chemical polishing on EBM parts was estimated. 15 parts produced in 5 different batches were measured before and after chemical machining. The improvement of surface quality was also evaluated after each treatment. Samples were used to evaluate the impact of chemical etching on dimensions and roughness. All the parts were produced by an ARCAM Q20+ machine. For these parts, a set of standard parameters optimized for 90\u03bcm layers was used. 4 different geometries of sample were built (see Fig. 1). Only 15 parts underwent chemical machining to improve the surface quality. In order to minimize the number of batches needed to reach the entire number of parts, the build envelope is filled as much as possible. Due to the part dimensions and EBM process constraints, the following solution was defined as the baseline (see Fig. 2). The supports of the parts follow the standard Arcam recommandations and standard features (i.e. type, density, teeth,...). Especially, the recommanded length of 20mm for floating supports is the reason for the vertical spacing between levels" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003955_j.energy.2019.116092-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003955_j.energy.2019.116092-Figure7-1.png", "caption": "Fig. 7. Ventilation test positions of the turbine generator.", "texts": [ " Analysis on rotor multi-physical fields for the 1100MW turbine generator In the actual operation of the 1100MW nuclear turbine generator, the fluid flowing state is very complex in the closed domain with high turbulent state and affects the temperature rise of rotor windings. Therefore, the fluid flowing state, heat dissipation capacity and rotor coil temperatures are highlighted and analyzed. 1) Analysis on pressure and flow distributions of the wind resistance network model To verify the accuracy of wind resistance calculation model, the ventilation test of the turbine generator is conducted and the test device is depicted in Fig. 6. The pressures at ten positions in Fig. 7, which are the excitation cap, outlet box, core top and core bottom, fan inlet and outlet, steam cap, respectively, are measured. The pressure rise and flow of fan at work point are also tested. The calculated and experimental values of the test points are compared in Table 3. In Table 3, the errors of the pressure rise in the fan outlet is 7.5%, and the flow error between the calculated value at the working point of the fan, 46.3m3/s, and the experimental value, 48.8m3/s, is 5.1%, which verify that the calculation method of the wind resistance network satisfy the calculation accuracy", " The z1 and z2 are the center lines of the ventilation duct with the shortest radial inlet area and the longest radial inlet area, respectively, while z3 and z4 are the center lines of the ventilation duct with the longest radial outlet area and the shortest radial outlet area in axial inlet mode, respectively. For clear explanation, the closed domain is divided into four parts, inlet area (i area), which includes radial part (i1 area) and axial part (i2 area), transition area (ii area), stable area (iii area) and outlet area (iv area), which also includes axial part (iv1 area) and radial part (iv2 area). The change laws of velocity components along three direction of the sampling lines z1~z4 in 4th coil is investigated. In addition, as shown in Fig. 7, the bisection A1, A2, A3 along axial direction in the radial outlet area of 4-1 copper bank is selected to investigate the relation between velocity components and resultant velocity. The gradient of velocity is related to the molecular structure of the fluid, the interfacial force, temperature and velocity. The greater the gradient of velocity, the greater the velocity difference between adjacent units in the direction of partial differentiation. Based on the calculation results, the fluid flowing states in the rotor coils between two inlet modes are obviously different" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003352_b978-0-12-813068-1.00019-1-Figure19.1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003352_b978-0-12-813068-1.00019-1-Figure19.1-1.png", "caption": "Figure 19.1 The medical technology innovation process. Steps further to the right are more costly. PMA, Premarket approval; FDA, Food and Drug Administration; VC, Venture capitalists.", "texts": [ " The academic inventor perhaps may focus on publishing a highly cited paper on the new technology in a high-impact journal. The clinician is looking for innovations that can improve patient outcomes. The medical technology company is searching for ideas to increase market share or open new markets. Investors want to see a return on their investment, while insurers are looking for innovations that can lower the cost of health care. There are many documented processes for new product development that are followed by leading companies, described in books, and taught at business schools around the world. Fig. 19.1 captures the essentials of how most medical technologies are developed. In general, there is an initial phase of opportunity identification, where the problem to be solved is identified. This is followed by concept development and testing, which could start with a rough sketch on a piece of paper. Should the idea pass the initial screens described below, it moves into the detailed design phase, which may include bench and preclinical (animal) testing. If the device still looks promising and continues to pass the evaluation screens, it moves into the initial phase of testing in humans, known as first-in-human tests" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001249_j.compind.2013.08.001-Figure18-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001249_j.compind.2013.08.001-Figure18-1.png", "caption": "Fig. 18. The first layout of the virtual facility for fabrication of the hand skeleton.", "texts": [], "surrounding_texts": [ "The biomedical field has also benefited hugely from LM technology, with which doctors can study prototypes of human organs or injured bones to prepare for complex surgical operations. Similarly, medical students can better understand the intricacy of body organs and structures. In recent years, functional biomedical products have been fabricated directly with LM systems, including highly-customized artificial limbs and porous tissue scaffolds which are difficult to fabricate with traditional manufacturing techniques [6]. VPRA can facilitate fabrication planning of biomedical products. Fig. 17 shows a multi-material hand skeleton model to be made of five materials with dimensions enlarged to 318 mm 223 mm 109 mm. To fabricate this skeleton, a support table and two SCARA robotic arms are loaded from the library to synthesize a virtual MMLM facility. These two actuators can be positioned in two different layouts as shown in Figs. 18 and 19. Moreover, based on the distribution of the five materials of the skeleton, two material strategies may bring about higher efficiency for each layout. In the first strategy, the first robotic arm will Table 1 Build times of the hand skeleton. Concurrent toolpath 1 Concurrent toolpath 2 Concurrent toolpath 3 Concurrent toolpath 4 Sequential toolpath Estimated build time (min) 245.02 253.94 240.86 244.40 293.34 Comparison with sequential toolpath 16.47% 13.43% 17.89% 16.68% \u2013 deposit the blue, green and red materials, while it will only deposit the blue and green materials in the second strategy. Therefore, there are a total of four strategies of actuator layout and material assignment to fabricate the hand skeleton. As stated before, a toolpath planning module based on deposition groups and division of work regions has been incorporated into VPRA. With this module, toolpaths for concurrent deposition by multiple actuators are generated accordingly for these four strategies in which the hand skeleton is sliced into 200 layers with a hatch width of 1 mm. Table 1 shows a comparison of the resulting build times of digital fabrication of the hand skeleton. It can be seen that all the concurrent toolpaths save build time when compared to sequential deposition. Moreover, the third strategy, where the two robotic arms are on the opposite sides of the support table and the first arm deposits the blue, green and red materials, is most efficient. Fig. 20 shows a few screen shots of the hand skeleton being digitally fabricated with the third strategy in the virtual MMLM facility. To reduce the computational burden, the cuboid dexel resolution can be dynamically adjusted during digital fabrication. Fig. 21 shows the digital hand skeleton when the simplification factor s is 1, 3 and 5, respectively. It appears that s = 3 gives a good balance between the computational burden and the dexel resolution of the digital hand skeleton. This case study demonstrates that VPRA can facilitate determination of suitable MMLM facility layouts for specific fabrication tasks by trying out various toolpath planning strategies. Moreover, the dynamic simplification algorithm can properly balance computational burden and simulation perceptual reality." ] }, { "image_filename": "designv11_29_0002389_s11071-017-3504-3-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002389_s11071-017-3504-3-Figure1-1.png", "caption": "Fig. 1 Dynamic model of a pair of spur gears", "texts": [ " 3, a new numerical method using double-changed time steps is formulated, and then, the multipliers of the Floquet are calculated by using the proposed numerical method (PNM). In Sect. 4, the validation of the PNM is confirmed bymaking a comparison between the PNM and the Runge\u2013 Kutta\u2013Fehlberg (RKF45) method. Then, the influences of the lubricant and the stability of the systemwith various cases are demonstrated. Finally, Sect. 5 presents some brief conclusions. The system in this study consists of two gears mounted onwell-aligned input and output shaftswith rotary inertias Ip,g and pitch radius Rp,g as shown in Fig. 1. \u03b8\u0307p,g is the absolute angler velocity of pinion and gear, respectively. Td is the drag torque acted on the gear. In this paper, each gear is represented by a rigid disk that coupled through the nonlinear stiffness and damping forces as shown in Fig. 2. In the initial arrangement, the total backlash is L and the pinion tooth is placed in a central relative position, where the tooth separation is half of the backlash on both side. This relative motion of the gear system defines the behavior of the gear oscillator with a new coordinate, which leads to a much simpler form of the multistate equation in the analysis below", " Therefore, extremely small integration step is required when the solid contact takes place. So the initial resolution N should be larger enough to ensure accurate simulation. In this paper, N is equal to 212. However, when the gear is in lubricant contact area, the case is much different because the stiffness of the lubricant film is much smaller than that of solid contact. In order to decrease the whole computing time, the maximum time step at lubricant contact area is defined by tmax+ \u2265 100 tmax\u2212 (19) With the equations of motion for the gear system of Fig. 1, the motion of the system is simulated using a discrete time step algorithm. Since the DTE in the gear system is very small, double- precision calculation must be performed in order to ensure accurate simulation. Firstly, the current state of the motion (lubricant and solid contact) should be determined. If the state of the motion is in lubricant contact, then the changes in time from lubricant contact to the next possible solid contact needed to be estimated.A possible solid contact after lubricant contact will occur when \u03b4(t0 + t+k) = L sign(\u03b4\u0307(t0))/2 (20) where t+k = t+k \u2212 t0 is the time interval from lubricant contact to the solid contact" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002063_1.4006364-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002063_1.4006364-Figure3-1.png", "caption": "Fig. 3 CAD drawing of OCTA", "texts": [ " In comparison, the bias stability of accelerometers used in cruise missiles can be as low as 0.01 mg, whereas that of accelerometers in strategic missiles is below 1 lg [35]. Moreover, the noise density of the ADXL320 is rated at 250mg= ffiffiffiffiffiffi Hz p , whereas it is in the orders of 0:01mg= ffiffiffiffiffiffi Hz p for military-grade accelerometers. A TrackSTAR tracking sensor from Ascension Technology Corporation [36] is also attached on OCTA and will serve as a reference in the experiments. Displacements are produced by shaking OCTA by hand. The geometry of OCTA is shown on Fig. 3. Its six pairs of accelerometers are located close to the vertices of a regular octahedron. Each pair of accelerometers is directly screwed onto the 2 in 2 in square tubing that composes the accelerometer-array structure. Also, they are attached with dowel pins in an effort to reduce misalignments between the sensors. Journal of Dynamic Systems, Measurement, and Control NOVEMBER 2012, Vol. 134 / 061015-5 Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 08/08/2013 Terms of Use: http://asme" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000033_roman.2008.4600696-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000033_roman.2008.4600696-Figure7-1.png", "caption": "Fig. 7. Example grasps for FWS approximation (top row) and demonstrated grasp to be optimized (bottom row).", "texts": [ " The optimization procedure can be exploited for finding suboptimal grasps close to the demonstrated grasp, but it can also be applied for solving automatic motion planning problems. The algorithm is a brute-force search in the state-space neighborhood of the demonstrated grasp. The state space is spatially discretized for each of the seven degrees of freedom. Six of them determine translation and rotation of the robot hand while one last degree of freedom controls the spread angle between the lateral fingers. The size of the searched neighborhood is \u00b110% of each degree of freedom range. Figure 7 shows three force closed grasps performed by an expert operator to teach the FWS, along with the grasp to be optimized (which is not force closed). The selected object is a hourglass, which is highly nonconvex. The grasp to be optimized is force closed but has a very low quality, close to instability. Indeed, it can be noted that the lateral fingers of the Barrett hand are poorly positioned around the object. Figure 8 reports two grasps generated by the optimization process with increasing grasp quality" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001954_tcbb.2012.126-Figure12-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001954_tcbb.2012.126-Figure12-1.png", "caption": "Fig. 12. The Laplace-Young Law relates the pressure difference p over a surface to the surface tension T .", "texts": [ " Thanks to the limited dynamics of the ventral cells this drawback is not too severe: assuming symmetry between two vertical halves of the embryo and because of their adjacency to the ventral line, the ventral vertices are constrained to move exclusively along the ventral line, that is in x-direction. This means that the dynamics in the y- and z-direction are set to zero. How to prevent the global cellular network from collapsing over itself? The inner body of the embryo can be imagined as a fluid mass exerting a pressure force on the ectoderm, whenever there is a pressure difference between the interior and the exterior of the embryo. This phenomenon can be modeled using the Laplace-Young law [44]. Assume that the embryo is a cylindrical vessel, as depicted in Fig. 12. The larger the cylindrical radius Rbody, the larger the boundary tension T (dashed red arrows in Fig. 12) required to withstand a given pressure difference p (solid cyan arrows in Fig. 12) over the boundary. This property can be derived from the Laplace-Young equation, which relates the pressure difference to the shape of the surface: p \u00bc T Rbody . This effect is implemented over the whole cellular network, assuming a constant pressure difference p. Dorsal closure is the preponderant morphogenetic movement showing in the experimental data for the case study, and is driven by the leading edge cells, namely the row of cells lying most dorsally within the epithelium. The leading edge is pulled locally, and the corresponding cells move over the embryo surface up toward the dorsal line, while propagating the pull over the rest of the epithelium" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001195_b978-1-4557-2550-2.00004-3-Figure4.53-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001195_b978-1-4557-2550-2.00004-3-Figure4.53-1.png", "caption": "FIGURE 4.53", "texts": [ " [40] have tested electrowetting on a substrate constituted of microfabricated pillars; however, reversibility is not always achieved by such systems. The originality of the work of McHale et al. [41] is the transposition of the idea of superhydrophobicity to the droplet itself (Figure 4.52). The starting point is that an aqueous droplet can be coated with hydrophobic particles. This can be shown theoretically by considering the surface energy of the droplet. Suppose we have a spherical grain at the surface of the liquid, as shown in Figure 4.53A. The surface area ALP is given by ALP 5\u03c0R2 S sin 2 \u03b8e; (4.102) Sketch of the film of dodecane or air below the droplet (at zero voltage). (A) Sketch of the electrowetting device, the aqueous droplet is coated with hydrophobic grains (lycopodium or silica). (B) A photograph of the droplet showing the granular coating of the interface. Source: Reprinted with permission from Ref. [40] r 2007, American Chemical Society. where RS is the radius of the spherical grain and \u03b8e its Young\u2019s contact angle. On the other hand, the surface APG is APG 5 2\u03c0R2 S\u00f011 cos \u03b8e\u00de: (4", "105) shows that \u0394E is always negative or zero (zero only if \u03b8e5 180 ). As a result, it is always energetically favorable that grains spontaneously attach to the liquid vapor interface, even if they are hydrophobic. If Rg denotes the radius of the grain, the length of a grain protruding into air is dg 5Rg\u00f012 cos \u03b8e\u00de: (4.106) Relation (4.106) shows that highly hydrophobic grains protrude substantially, enough to obtain a hydrophobic configuration similar to that of the nanostructure surface described in the preceding section (Figure 4.53B). It is shown that such an aqueous droplet coated with silica beads reacts to an electric actuation in the same manner as a simple water droplet on a superhydrophobic substrate, and that (A) Schematic of the solid sphere on a liquid interface. (B) A droplet coated with hydrophobic particles can have a hydrophobic behavior similar to that of a droplet on nanostructured pillars. Source: Reprinted with permission from Ref. [41] r 2007, American Chemical Society. the motion is reversible. In biotechnology, an advantage of such a system is the reduction of the possible contamination to the substrate" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000528_iecon.2010.5675450-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000528_iecon.2010.5675450-Figure3-1.png", "caption": "Fig. 3. 3D model of robot", "texts": [ " In section III, the conventional method is explained. In section IV, the proposed method is explained. In section V, the numerical examples are shown. In section VI, the experimental results are shown. Finally, this paper is concluded in section VII. In this section, the model of a biped robot and a controller are explained. A overview of the robot is shown in Fig. 2. The robot is a 3D biped robot with a serial link structure. Each joint has an actuator and an encoder. The 3D model of the biped robot is shown in Fig. 3. The biped robot has 4 degree-offreedom (DOF) in a frontal plane and 6 DOF in a sagittal plane. Besides, in order to calculate the ZMP during walking, force sensors consisted by strain gauges are attached. PD controller and joint space disturbance observer [18] are implemented to the biped robot in this research. The position and the posture of the robot are controlled to track to the desired trajectory by this controller. The reference value of the PD controller is obtained by (1). ?\u0308?\ud835\udc5f\ud835\udc52\ud835\udc53 = \ud835\udc3e\ud835\udc5d(\ud835\udc92 \ud835\udc50\ud835\udc5a\ud835\udc51 \u2212 \ud835\udc92\ud835\udc5f\ud835\udc52\ud835\udc60) +\ud835\udc3e\ud835\udc63(" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001243_cinti.2011.6108548-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001243_cinti.2011.6108548-Figure3-1.png", "caption": "Figure 3. SPMSM (Ld \u2260 L", "texts": [ " The mathemat defined in the d-q rotating sys equations [1] where \u03a8 \u03a8 and , stator voltage compon , stator current compone\u03a8 , \u03a8 stator flux components stator inductance; R stator resistance; rotor electrical speed; \u03a8 electromagnetic force s used in PMSM model q rotating system, because ws the coordinate system e north pole of permanent rection. ous motors can be divided urface permanent magnet s) and second type are t synchronous motors SMs anent synchronous motors e characteristic feature is the stator inductance ical model of SPMSMs is tem by two-phase voltage \u03a8 (1) \u03a8 , (2) \u03a8 (3) , (4) ents in rotating frame; nts in rotating frame; in rotating frame; constant. \u2013 457 \u2013978-1-4577-0045-3/11/$26.00 \u00a92011 IEEE B. Mathematical model of IPMSMs Figure 3 shows interior permanent sy with salient rotor type. The characteri changing stator inductance ( Ld \u2260 mathematical model of IPMSMs is d rotating system by two-phase voltage eq \u03a8 \u03a8 where \u03a8 \u03a8 \u03a8 , and , stator inductance components i Mathematical model of PMSM de rotating system is useless without because we cannot use Park\u2019s transfor stator currents and stator voltage are the position estimator. These stator currents are defined in a-b-c stationary system. F must transform the mathematical model system to the mathematical model system" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001197_iicpe.2011.5728092-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001197_iicpe.2011.5728092-Figure2-1.png", "caption": "Fig. 2. Phasor Diagram of DFIG for subsynchronous generation", "texts": [ " The voltage equations of the DFIG in a stationary reference frame (\ud835\udf14\ud835\udc52=0) are as follows: \ud835\udc49\ud835\udc60 = \ud835\udc45\ud835\udc60\ud835\udc3c\ud835\udc60 + \ud835\udc51\ud835\udf13\ud835\udc60 \ud835\udc51\ud835\udc61 (1) \ud835\udc49\ud835\udc5f = \ud835\udc45\ud835\udc5f\ud835\udc3c\ud835\udc5f + \ud835\udc51\ud835\udf13\ud835\udc5f \ud835\udc51\ud835\udc61 \u2212 \ud835\udc57\ud835\udf14\ud835\udc5f\ud835\udf13\ud835\udc5f (2) \ud835\udc49\ud835\udc51\ud835\udc60 = \ud835\udc45\ud835\udc60\ud835\udc3c\ud835\udc51\ud835\udc60 + \ud835\udc51\ud835\udf13\ud835\udc51\ud835\udc60 \ud835\udc51\ud835\udc61 (3) \ud835\udc49\ud835\udc5e\ud835\udc60 = \ud835\udc45\ud835\udc60\ud835\udc3c\ud835\udc5e\ud835\udc60 + \ud835\udc51\ud835\udf13\ud835\udc5e\ud835\udc60 \ud835\udc51\ud835\udc61 (4) \ud835\udc49\ud835\udc51\ud835\udc5f = \ud835\udc45\ud835\udc5f\ud835\udc3c\ud835\udc51\ud835\udc5f + \ud835\udc51\ud835\udf13\ud835\udc51\ud835\udc5f \ud835\udc51\ud835\udc61 + \ud835\udf14\ud835\udc5f\ud835\udf13\ud835\udc5e\ud835\udc5f (5) \ud835\udc49\ud835\udc5e\ud835\udc5f = \ud835\udc45\ud835\udc5f\ud835\udc3c\ud835\udc5e\ud835\udc5f + \ud835\udc51\ud835\udf13\ud835\udc5e\ud835\udc5f \ud835\udc51\ud835\udc61 \u2212 \ud835\udf14\ud835\udc5f\ud835\udf13\ud835\udc51\ud835\udc5f (6) where \ud835\udf14\ud835\udc52: stator angular frequency in radian per second \ud835\udf14\ud835\udc5f: rotor angular speed in radian per second (\ud835\udf14\ud835\udc52 \u2212 \ud835\udf14\ud835\udc5f): slip angular frequency in radian per second The flux linkages are \ud835\udf13\ud835\udc51\ud835\udc60 = \ud835\udc3f\ud835\udc5a\ud835\udc3c\ud835\udc51\ud835\udc5f + \ud835\udc3f\ud835\udc51\ud835\udc60\ud835\udc3c\ud835\udc51\ud835\udc60 (7) \ud835\udf13\ud835\udc5e\ud835\udc60 = \ud835\udc3f\ud835\udc5a\ud835\udc3c\ud835\udc5e\ud835\udc5f + \ud835\udc3f\ud835\udc5e\ud835\udc60\ud835\udc3c\ud835\udc5e\ud835\udc60 (8) \ud835\udf13\ud835\udc51\ud835\udc5f = \ud835\udc3f\ud835\udc5a\ud835\udc3c\ud835\udc51\ud835\udc60 + \ud835\udc3f\ud835\udc51\ud835\udc5f\ud835\udc3c\ud835\udc51\ud835\udc5f (9) \ud835\udf13\ud835\udc5e\ud835\udc5f = \ud835\udc3f\ud835\udc5a\ud835\udc3c\ud835\udc5e\ud835\udc60 + \ud835\udc3f\ud835\udc5e\ud835\udc5f\ud835\udc3c\ud835\udc5e\ud835\udc5f (10) In DFIG, the rotor flux vector \ud835\udf13\ud835\udc5f leads the stator flux vector \ud835\udf13\ud835\udc60 by an angle \ud835\udeff, called torque angle. The rotor voltage vector \ud835\udc49\ud835\udc5f leads (at sub-synchronous speed) or lags (at supersynchronous speed) the rotor flux vector by an angle \ud835\udefc, rotor impedance angle. This angle depends on rotor speed. The phasor diagram for sub-synchronous operation of DFIG is shown in Fig. 2. The block diagram for the implementation of the control scheme is shown in Fig. 3. The control scheme consists of two different loops. The first loop is the rotor flux loop in which the difference in the rotor flux magnitude from its desired reference value forms an error signal that is processed by the PI regulator to produce the reference magnitude of the controlled rotor voltage vector, \u2223\ud835\udc49\ud835\udc5f\u2223. The second loop is the torque loop in which the difference in the actual torque magnitude from its desired reference value forms an error signal that is processed by the PI regulator to produce the angle (\ud835\udeff + \ud835\udefc) [5]" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002078_2011-01-0986-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002078_2011-01-0986-Figure8-1.png", "caption": "Figure 8. Path clearing by front tires", "texts": [], "surrounding_texts": [ "The normalized sensitivity of UG to changes in front and rear cornering stiffness coefficients is given by: (27) Performing the indicated differentiation we have, for the front tire cornering stiffness: (28) Similarly, for the rear tire cornering stiffness: (29) It is well-known that the discriminant (aCf - bCr) determines US/OS for a linear vehicle model. UG sensitivity to front and rear cornering stiffness coefficients varies inversely with front tire stiffness [Eq (28)] and directly with rear tire cornering stiffness [Eq (29)]; recall that cornering stiffness coefficients are negative values. For the exemplar Ford Crown Victoria vehicle with the dimensions and stiffnesses given in the Appendix, with linear tire load sensitivity, and cornering at ay=0.4g on dry pavement, we have: (30) (31) As noted above, results given in [14] indicate that reductions in cornering stiffness coefficients Cf and Cr can be reduced by \u223c 15-20% at this speed, depending on the tires used and water depth. Using, for example, the 20% figure on the front tires alone while keeping the dry values for the rear tires yields the following changes in car steady state cornering characteristics: (32) (33) (34) (35) As is expected, reduced cornering stiffness on the front tires of the vehicle increases its UG and decreases the sensitivity of changes in the UG to further changes in stiffness at both axles. If instead, all four tires have cornering stiffness SAE Int. J. Mater. Manuf. | Volume 4 | Issue 1 1074 coefficients reduced by 20%, the corresponding values for these variables become: (36) (37) (38) As expected, a constant percentage reduction in cornering stiffness values at all four tires leaves the sensitivities of the UG with respect to each individual tire stiffness value invariant but increases the UG gradient due to the front weight bias of the exemplar vehicle. These results can be summarized in the following table: If the vehicle is not operating at its tangent speed, the vehicle will be operating at a nonzero sideslip angle, as shown in Figure 9: At very low speeds, only Ackermann steer is required to maintain a circular path heading, as given in Eq (1). On a circle with r = 109.4\u2019 as given in Eq (20), the Ackermann steer needed (using the bicycle representation of the vehicle) is given by: (39) The difference in radius d traveled by the front and rear tires is readily calculated for the slow speed, Ackermann steer case from the geometry shown in Figure 10: (40) SAE Int. J. Mater. Manuf. | Volume 4 | Issue 1 1075 For the exemplar Ford Crown Victoria P225/60-R16 tires, the loaded width of the tire contact patch was measured as 8.9\u2033. The front and rear track widths are 62.8\u2033 and 65.6\u2033 respectively. At this combination of tread width, very low speed and vehicle wheelbase, there is no overlap in the tire trajectory footprints and path clearing does not exist except through the mechanism of splash. There is an uncleared strip between the outside edge of each rear tire and the inside edge of each front tire of approximate width: (41) The Ackermann steer situation is shown in Figure 11. As speed increases, vehicle sideslip angle \u00df changes from negative, through the tangent speed sideslip angle of zero, into positive sideslip angle for the exemplar understeer Ford Crown Victoria vehicle. \u00df is obtained by rotating the chassis by the amount of the rear slip angle \u03b1r, which is given by: (42) The equations of motion for a two degree of freedom bicycle model are well known [28]: (43) (44) With v=sideslip velocity, r=yaw rate, u=forwartd velocity, Fy=sum of lateral forces, Izz=yaw moment of inertia and Mz=sum of z-axis moments. In a steady state cornering maneuver, all derivatives are zero, and we can solve for the normalized steady state lateral velocity v/\u03b4: (45) The steady state steer angle needed to traverse a turn of radius r at forward speed u is given by: (46) Substituting Eq (46) into Eq (45) gives the steady state lateral velocity for a given vehicle configuration, turn radius and forward velocity: (47) All of the terms in Eq (47) are known and constant. Substituting Eq (47) into Eq (42) gives the vehicle sideslip angle. Knowledge of \u00df, the radius of the turn and the vehicle wheelbase enables calculation of the amount of tire superposition occurring. The analysis above is only valid when all four tires are operating in the linear range of their slip angle vs. sideforce curves. Fortunately, this operating regime is seldom intentionally exceeded during normal vehicle operation. Considerable research has shown that drivers almost never volitionally exceed \u223c 0.2g lateral acceleration on dry surfaces [29,30]." ] }, { "image_filename": "designv11_29_0000699_iros.2009.5354517-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000699_iros.2009.5354517-Figure4-1.png", "caption": "Fig. 4. DOF configuration of WL-16RV.", "texts": [ " Changing a position gain value is a feedforward approach, and a foot landing-impact force is reduced by a large position following error. However, it is difficult to realize a precise positioning control with a low position gain, and a walking robot becomes unstable in a stance phase. So we change back to a high position gain value after detecting a foot landing on a ground. On the other hand, the leg mechanism of WL-16RV consists of a parallel linkage mechanism called the Stewart Platform (see Fig. 4). Because it has a higher stiffness compared with a serial linkage mechanism, it is not sufficient to obtain a high compliance of the landing-foot only by changing a position gain value as mentioned above. Therefore, we realized a larger position following error by raising the foot\u2019s edge of the traveling direction and concentrating a landing-impact force to an actuator nearest to a contact area as shown in Fig. 5. As a result, we could obtain a higher compliance against ground reaction forces. After detecting a foot-landing on a ground, the foot speed is changed to zero under the law of conservation of momentum" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003826_s10409-019-00888-5-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003826_s10409-019-00888-5-Figure8-1.png", "caption": "Fig. 8 Critical buckling shape of the structure with various modulus ratio of film and substrate from 150 to 510", "texts": [ " According to previous studies, the buckling geometry of thin film on the flexible substrate may also be effected by film thickness and modulus ratio of film and substrate. Here we studied the influence of modulus ratio on critical buckling wavelength. The thickness of film was taken as 0.2 mm, the inner and outer diameters were 14.5 mm and 40 mm, respectively. The modulus ratio ranged from 150 to 510. It was assumed that Poisson\u2019s ratio of the film and substrate was the same, i.e. \u03bds \u03bdf 0.45. In order to save computation time, 1/4 models were built. Simulation results were shown in Fig. 8. The results showed that the critical buckling wavelengths vary significantly in the range of modulus ratios considered. With the increased of modulus ratio from 150 to 510 with 60 intervals, the wavelengths increased as well, from 4.7 to 7.1 mm. The modulus ratio was positively correlated with the critical buckling wavelength. Then the finite element calculation results were compared with the theoretically predicted buckling wavelengths. Epoxy-based SMP material can achieve 100% elastic strain under rubber state" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000043_rspa.2007.0372-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000043_rspa.2007.0372-Figure2-1.png", "caption": "Figure 2. (a) Geometry of a sheet coiled in a cylindrical tube. The deformation can be described by using a two-dimensional systemof coordinates with its origin at the centre of the tube. The anglef gives the position of the tangent with respect to the horizontal direction. The trihedrons {e1, e2, e3} and {n, t, e3} are defined in the figure. (b) A coil made of mica with similar geometry as (a).", "texts": [ " In \u00a75, we study how this mechanism is replicated to describe the deformation for any number of layers, so that the function be(N ) is obtained. Finally, we close with a discussion of our results. (a ) Equilibrium equations and geometry For planar deformations one of the principal curvatures of the sheet vanishes, so that its line of curvature is a straight line or generator. The other line of curvature lies in a plane, so that this line defines a two-dimensional curve. In Cartesian coordinates, the position vector describing the geometry of the curve can be written as r (s)Zx(s)e1Cy(s)e2, as we show in figure 2. Here, s is the arc length of the curve starting from the take-off point, and e1 and e2 are two perpendicular unit vectors lying in the plane. The tangent to the curve is readily Proc. R. Soc. A (2008) obtained as tZvsr, and its normal as nZt!e3, where e3Ze1!e2 points along the generator. The curvature of the principal line is then kZKn$vst (Struik 1988). Now, we proceed to write the equations of force and torque equilibrium (Love 1944; Landau & Lifshitz 1997; Cerda & Mahadevan 2005), vsFCK Z 0 and vsM Ct", " The torques can be connected with the curvature by the Bernoulli\u2013Euler theorem; torques are proportional to the local curvature. The precise relation for planar deformations is MZBke3 (Love 1944; Landau & Lifshitz 1997). We introduce the angle f that the tangent to the curve makes with the vector e2. In terms of this angle, the tangent and the normal are tZKsin fe1Ccos fe2 and nZcos fe1Csin fe2. This allows us to find the curvature as kZKn$vstZ _f. We now turn to the determination of the shape of the innermost layer. The e1 axis was made to cross the sheet at the position of the take-off point in figure 2. In this configuration, it is straightforward to obtain the force balance in equilibrium. We first note that the force F that the rest of the sheet at the left side of the take-off point applies to the detached segment must be horizontal. To the left side of the take-off point, the sheet follows the circular shape of the container and thus has constant curvature. Therefore, in this region vsMZ0 and the torque balance equation (2.1) yields t!FZ0. Thus, the force at the cross section has the direction of the tangent and can be written as FZKft for s", " To see that, we study the equations of equilibrium in intrinsic coordinates FZ fttC fnn. The torque balance gives fnZB \u20acf and the force balance in the tangential direction is _ftC _ffnZ0, since there are no frictional contact forces. Combining both equations, we obtain the relation _ftCB _f \u20acfZ0. An integration yields ft ZK B 2 \u00f0 _f2 K _f 2 1\u00deC f1; \u00f02:8\u00de where _f1 and f1 are integration constants. Assuming that the innermost layer does not interact with the outer detached region because they are in different angular sectors (figure 2), we fix the constants by using the curvature and force at the takeoff point. We obtain _f1Z1=R and f1Zf. Therefore, any layer with the same curvature will have the same cross-sectional force. In particular, if all the layers in a given section of the coil have approximately the curvature of the tube wall, we conclude that ftZf and formula (2.7) remains valid at those locations. We now study the series of events that lead to the coiling of the sheet inside the tube as the radius R decreases from a large value" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002063_1.4006364-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002063_1.4006364-Figure1-1.png", "caption": "Fig. 1 A rigid body equipped with m accelerometers moving in space", "texts": [ " 2, the accelerometer-array model is described, which includes the stochastic representation of the errors. In Sec. 3, the proposed method is presented in detail. Section 4 reports on the experimental validation, which uses reference measurements from a magnetic displacement sensor. Also in Sec. 4, we discuss the experimental results and analyze the proposed method. In Sec. 5, we summarize the main ideas and conclude on the results reported in this article. An accelerometer array is characterized by the positions and sensitive directions of its m accelerometers. Figure 1 represents the model of an accelerometer array, in which a rigid body is equipped with m accelerometers moving in space. ei is a unit vector representing the sensitive direction of the ith accelerometer, while ri represents its position with respect to an arbitrary rigidbody reference point B. Also, bk gives the position of point B at the kth time step, and pi,k represents the position of the ith accelerometer, both with respect to O. Let us consider a single accelerometer located at Pi. The measurement a\u0302i;k of the ith accelerometer can be modeled as a\u0302i;k \u00bc ai;k \u00fe dai;k (1) where ai;k \u00bc eT i \u20acpi;k (2) is the true acceleration-component along the accelerometer sensitive direction and dai,k is the measurement error" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000033_roman.2008.4600696-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000033_roman.2008.4600696-Figure8-1.png", "caption": "Fig. 8. A selection of optimized grasps.", "texts": [ " The size of the searched neighborhood is \u00b110% of each degree of freedom range. Figure 7 shows three force closed grasps performed by an expert operator to teach the FWS, along with the grasp to be optimized (which is not force closed). The selected object is a hourglass, which is highly nonconvex. The grasp to be optimized is force closed but has a very low quality, close to instability. Indeed, it can be noted that the lateral fingers of the Barrett hand are poorly positioned around the object. Figure 8 reports two grasps generated by the optimization process with increasing grasp quality. The first grasp has still a fairly low quality with Q = 0.13, while the second grasp has a high quality with Q = 0.49. The grasp quality measure proposed in this paper has been successfully applied to a system for robot programming by demonstration (PbD) in virtual reality. The system is aimed at performing manipulation tasks. The programming environment consists of three phases. The first phase is an off-line training phase where an expert user performs a sequence of grasps on a target object with the anthropomorphic virtual hand" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000454_sled.2010.5542800-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000454_sled.2010.5542800-Figure8-1.png", "caption": "Fig. 8. Photography of the setup. The main photo shows the three-coil arrangement used as the radial magnetic bearings as well as the x, y eddy current sensors used for calibration purposes. The top-right photo shows the rotor.", "texts": [ " But in this case, the distance to the stator center, which is contained in the real component of the carrier current, is also needed, meaning that both signals are required. It is worth noticing that using the information modulated in the real component requires the decoupling of the I\u03a3R term. Comparison among the three proposed injection techniques should take into consideration issues like estimation resolution, sensitivity to parameters and operating conditions, as well as computational burden for the signal processing. Both simulation and experimenting results are used to compare the techniques. For the experimental results (Fig. 8), the rotor has been slowly rotated around a position not centered with respect to the stator. This experiment allows to analyze the effects of different saliencies on the high frequency signals. Measured position and frequency analysis of the position signals are shown in Fig. 9. Signal processing burden for all the methods is similar (Figs. 6 and 7) but, again, pulsating carrier signal methods require a few more operations for isolating the information signal. For the case of stationary pulsating injection, an average value of the high frequency currents from both positive and negative bands is used in order to improve the signal to noise ratio" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002075_ijmic.2011.039707-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002075_ijmic.2011.039707-Figure4-1.png", "caption": "Figure 4 Two link robot manipulator (see online version for colours)", "texts": [ " 2 Construct the FWN model output using desired output vector dY and adjustable parameters as stated in (24). 3 Deduce the control law vector using equation (28) and apply it to the plant described in equation (5). 4 Update the adjustable parameters C , A and B of the FWN according to the equations (33), (34) and (35). 5 Repeat the calculations for the next iteration by going to step (1). 6 Simulation example In order to validate the proposed controller, two degrees of freedom robot manipulator arm system is considered as numerical example. The dynamic model of MIMO system shown in Figure 4 is given by the following equation: ( ) ( , ) ( ) ( )M q q C q q G q q d+ + = \u0393 + (45) where q , q and q are the angular position, angular velocity and angular acceleration vectors respectively, ( )M q is the inertia matrix, which is positive definite symmetric non-singular matrix given by: 2 1 2 1 2 1 2 1 2 1 2 2 2 1 2 1 2 1 2 2 2 ( ) ( ) ( ) ( ) m m l m l l s s c c M q m l l s s c c m l \u23a1 \u23a4+ + = \u23a2 \u23a5 +\u23a2 \u23a5\u23a3 \u23a6 where sin( )i is q= , cos( )i ic q= , im is the mass of link i and il is the length of link i for 1,2i = " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001948_sav-2010-0577-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001948_sav-2010-0577-Figure2-1.png", "caption": "Fig. 2. Ball bearing elements and coordinate systems.", "texts": [ "2); (4) Effect of using the time-dependent bearing stiffness matrix versus using the the standard formulation bearing stiffness matrix (i.e. cage rotation is neglected) is investigated (Section 3.4.2). Figure 1 shows a noncentral rigid disk mounted through its center to a rotating rigid shaft which in turn is mounted on two rolling element bearings. The bearings are mounted into their rigid housings that are firmly attached to a fixed rigid base (platform). The details of the bearing are depicted in Fig. 2. The position of the disk along shaft axis is at distance Lr (not shown on Fig. 1) from the right bearing and at distance Ll (not shown on Fig. 1) from the left bearing. The rigid shaft inertia is neglected compared to the disk inertia and therefore the system mass center is at the geometric center of the disk. The orientation of the vibrating rigid rotor in space (Fig. 3) is monitored using Euler angles (Fig. 4). In Fig. 3, XsYsZs is an inertial frame (Fig. 1) and its origin (point Os) at the left bearing pedestal center", " (9) then the total kinetic energy T (= Tr + Tt) is given by. T = 1 2 [q\u0307T G\u0304q + q\u0307TMq\u0307]. (16) where M is the disk inertia (mass) matrix. G\u0304 is its gyroscopic matrix. M = diag [Mt Id d I22 ] , G\u0304 = diag [ 0\u030433 \u03a9sI d p I\u030322 ] . (17) Matrix Mt is from Eq. (9). Iii is a i\u00d7 i unit matrix. 0\u0304ij is a i\u00d7 j null matrix. Let \u03bca and \u03bcb be the disk mass center eccentricities in a and b directions. The disk generalized unbalance force vector is Fu = \u03a92 sQ\u0304 T s M [\u03bca \u03bcb 0 0 0 ]T . (18) The matrix Q\u0304s is from Eq. (5) and matrix M is from Eq. (17). Figure 2 depicts a ball bearing system where the global coordinate system XsYsZs has its origin at the bearing center with Zs axis coincides with the bearing axis. The frame x\u0304by\u0304bz\u0304b is a rotating coordinate system that spins at the bearing cage angular speed (\u03a9c rad s\u22121) where the z\u0304b axis coincides with the bearing axis. The bearing inner ring is lightly fitted on its rigid shaft and is modeled as an integral part of it and thus rotates with the angular speed \u03a9s. The bearing outer ring, however, is fitted into its rigid and nonrotating housing" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000010_s1560354708040059-Figure18-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000010_s1560354708040059-Figure18-1.png", "caption": "Fig. 18. Case B. v2 = 2v1, \u22a5 P1P2, m2 = m1 or m2 = \u03b1 m1.", "texts": [ " For equal initial velocities v1 = v2, perpendicular to the segment P1P2, we observe a strange fact: the trajectories are parallel straight lines, Fig. 17. But do not forget the constraints: even if the two points are attracted by a spring, they cannot converge since they must have parallel velocities. Further experiments show that this behavior does not depend on the values of the masses. REGULAR AND CHAOTIC DYNAMICS Vol. 13 No. 4 2008 \u2022 Case B. For parallel and equioriented initial velocities, but with different intensities v1 = v2, we observe a rather different behavior w.r.to the previous case: see Fig. 18. Further experiments show that this qualitative behavior does not depend on the values of the masses. \u2022 Case C. Recall that this case concerns with opposite initial velocities v1 and v2 which are inclined w.r.to the segment P1P2. For velocities of equal intensity, Fig. 19 shows the qualitative behavior for equal masses. For different masses we have a different result as shown by Fig. 20. \u2022 Case C. For opposite initial velocities of different intensity, say v2 = \u2212 2v1, we observe very different kinds of orbits, depending on the initial distance |P1P2| between the two points" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001311_ias.2012.6374017-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001311_ias.2012.6374017-Figure1-1.png", "caption": "Fig. 1. Vector diagram of a pure integrator and a first-order LPF", "texts": [ " dt d iRv s sss \u03bb +\u22c5= (1) where vs is the stator voltage, Rs is the stator resistance, is is the stator current and s is the stator flux The stator flux can be re-written as (2). In the steady state, (2) can be represented as a frequency response function (3). dtiRv ssss )( \u22c5\u2212=\u03bb (2) sEs s 1 = \u03bb (3) where Es is the back-electromotive force (vs \u2013 Rs is) When using a pure integrator same as (3), the dc drift and the saturation problems can occur. To solve these problems, a first-order LPF was proposed [1]. The stator flux by a LPF is given as (4), whose the phase lag (\u03c6LPF) and the gain (M) are given as (5), (6) in the frequency domain. Fig. 1 depicts both the phase lag and the gain of the stator flux by a pure integrator and a LPF respectively asEs LPFs + = 1_\u03bb (4) \u2212= \u2212 a e LPF \u03c9 \u03c6 1tan (5) 22 _ 1 aE M es LPFs + == \u03c9 \u03bb (6) where e is the synchronous angular speed, a is a cutoff frequency of a LPF and s_LPF is the stator flux by a LPF A pure integrator has the lagging phase of 90\u00b0 and the gain of 1/| e|, which are different from (5) and (6) of a LPF. Therefore, a LPF has errors of both gain and phase compared with a pure integrator. The lower a cutoff frequency of a LPF is used to reduce the mentioned errors over a wide speed range, the larger the dc drift problem appears" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003576_iciscae.2018.8666841-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003576_iciscae.2018.8666841-Figure5-1.png", "caption": "Fig. 5 The diagram of the gear transmission", "texts": [ " EXPERIMENTAL ANALYSIS The experimental analysis of the weak fault in the inner ring of rolling bearing was carried out by Drivetrain Diagnostics Simulator shown in Fig. 4, it consists mainly of drive motor, torque sensor, encoder, planetary gearbox, twostage parallel shaft gearboxes, bearing radial load, magnetic brake and data acquisition system. The Drivetrain Diagnostics Simulator simulates the incipient fault of the bearing inner ring. The acceleration sensor typed 608A11 is mounted on the left middle bearing pedestal of the shaft-fixed gearbox, and collects the inner fault vibration signal. The drive system is shown in Fig. 5. The tooth number of gears Z1, Z2, Z3, Z4, Z5, Z6 and Z7 are 25, 36, 100, 29, 100, 36 and 90, respectively. The experimental fault bearing, installed on the right bearing house of the intermediate shaft in the two-stage fixed-shaft gearbox, is deep groove ball rolling bearing. Its model is ER16K. Outer diameter, pitch diameter, inner ring diameter and rolling body diameter are 51mm, 38mm, 25.4mm and 8mm, respectively. The bearing has 9 rolling elements, whose contact angle is zero. The bearing radial load is 1570N", " The sampling frequency is 12.8 kHz. Data length is 8.2 seconds. The theoretical fault frequencies of rolling bearing can be calculated as follows: In planetary gearbox, the meshing frequency fg is 1203Hz. In fixed-shaft gearbox, the shaft rotating frequencies are fr1=12Hz, fr2=3.5Hz and fr3=1.4Hz, respectively; the meshing frequencies are fm1 =348.3 Hz, fm2 =125.6 Hz, respectively; the Ball Pass Frequency Inner fi, Ball Pass Frequency Outer fO, and Ball Spin Frequency fb are 18.9Hz, 12.5Hz and 8.1Hz, respectively. Fig. 5 shows the time-domain waveforms and its frequency spectral of the vibration signal collected by the acceleration sensor. We can see that the main frequency components are the motor rotating frequency fe (54.9Hz), the planetary gearbox meshing frequency fg (1203Hz) and its harmonics 2fg(2406Hz), 3fg (3609Hz), 4fg(4812Hz), around which there are plentiful modulation sidebands. Through identifying the local zooming spectrum, the modulation sidebands spacing is the planet carrier rotating frequency fr1 (12Hz)" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002369_ilt-04-2016-0080-Figure9-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002369_ilt-04-2016-0080-Figure9-1.png", "caption": "Figure 9 (a) Two hollow cylinder of 61 per cent hollowness and (b) layered cylindrical hollow roller of 61 per cent hollowness", "texts": [ " It is clear from Table II that the percentage deviation is within 3 per cent for the solid cylindrical roller of the NU2206 bearing. These results are also shown in a graphical form in Figure 8. So, the experimental results obtained are giving accurate dimensions of the contact width. Thus, the footprint method can be used for determining the contact width for a layered cylindrical hollow roller and a flat plate. The layered cylindrical hollow roller was developed by assembling two hollow cylinders of the same percentage hollowness. A small hollow cylinder is embedded into another cylinder by tight fitting. Figure 9(a) and (b) shows both hollow cylinder of 61 per cent hollowness with layered cylindrical hollow roller. However, the model does not take into account the residual stresses because of the assembling of two hollow cylinders. Type of roller Applied load F (N) Theoretical half-contact width b (mm) Experimental half-contact width b (mm) Contact pressure p (N/mm2) von Mises stress VM (N/mm2) Solid roller 1,962 0.09056 0.092 1,149.4 689.64 2,943 0.111 0.112 1,406.6 562.64 3,924 0.128 0.13 1,626.36 902" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003606_s40997-019-00288-x-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003606_s40997-019-00288-x-Figure4-1.png", "caption": "Fig. 4 Definition of degrees of freedom, forces and moments (Raptis and Valavanis 2010) (with a little modification)", "texts": [ " In order to calculate each section\u2019s forces, different assumptions can be used which will change the complete model from a complete high-precision complex system to a simple model for basic applications. Based on definitions in flight dynamics, vertical displacement is known as heave and rotational movement around longitudinal, lateral and vertical axes is, respectively, named as roll, pitch and yaw. Forces and moments about these axes are (respectively) named as X, Y and Z for forces and L, M and N for moments (Fig.\u00a04). Since the number of control inputs is lower than the system DoFs, determining a stable operation point for the system is so hard without any augmenting system and actually for keeping helicopter in a specific situation, control inputs should continuously change and be tuned to desired values. Space states used in modeling include helicopter CG position, translational and rotational velocities in body axes, helicopter orientation Euler angles, main rotor flapping dynamics states and an extra state considered for modeling the effect of gyro rate feedback of internal PI controller" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000305_12.866387-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000305_12.866387-Figure1-1.png", "caption": "Figure 1. Gear virtual prototype dynamics model.", "texts": [ " The Pro/E has been used to establish the parameterized involute spur gear physical model and assembly model firstly. The teeth of the pinion and wheel are 40 and 85, and the tooth widths are 45mm and 30mm, respectively. The pressure angle of the gears is 20o. The Mech/Pro interface connecting the Pro/E with ADAMS has then been used to import the models into ADAMS. Finally, various of constraints have been defined and various of drives and loads have been imposed to the models for the dynamic simulation. Fig. 1 shows the normal gear virtual prototype model in ADAMS,, where the rotational joints has been created between the two gears and the ground body, and the load torque and rotational joint motion have been imposed on the centroids of the wheel and the pinion, respectively. In order to simulate actual gears meshing transmission more accurately, it is critical to set the simulation parameters accurately, such as the stiffness between the gears, force exponent, damping coefficient and penetration depth etc" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000004_icsmc.2008.4811594-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000004_icsmc.2008.4811594-Figure1-1.png", "caption": "Figure 1. Form of curvature energy function", "texts": [ " The normalized x direction force is, ))()(( 1 1 1 1 , ii ii ii ii e e xi pp xx pp xxKf (4a) Similarly, the normalized force in y direction can be obtained as, ))()(( 1 1 1 1 , ii ii ii ii e e yi pp yy pp yyKf (4b) 2008 IEEE International Conference on Systems, Man and Cybernetics (SMC 2008) 2057 To impose the curvature constraints on snake control point i, its preceding node and succeeding node exert pulling forces, ti-1 and ti+1, on it to reduce bending of two line segments. When the bending angle, i.e. the curvature, is small, , the forces are defined to be zero. Thus the corresponding bending energy can be defined as below with angle in the interval ],( : 2( ) ,| | 0, c curvature k E others (5) Where, R represents the angle where the potential becomes zero; kc is a positive coefficient for curvature energy. Fig.1 shows the form of this energy function. curvatureE others y signKf i ccurvature yi ,0 )|)(|( , (6a) others x signKf i ccurvature xi ,0 )|)(|( , (6b) Where int2 cc kK , is the angle from direction (pi->pi+1) to direction (pi-1->pi), sign( ) is a function which will return 1 if is positive or zero and -1 if is negative, and, ),( )),(sin( ),( )),(sin( )()( ))(1( )()( ))(1( ))arctan()(arctan( 1 1 1 1 2 1 2 1 1 2 1 2 1 1 1 1 1 1 ii ii ii ii iiii ii iiii ii i ii ii ii ii i ppd pp ppd pp yyxx yy yyxx yy x xx yy xx yy x (7a) ),( )),(cos( ),( )),(cos( 1 1 1 1 ii ii ii ii i ppd pp ppd pp y (7b) B" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000987_978-3-642-33795-6_17-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000987_978-3-642-33795-6_17-Figure5-1.png", "caption": "Fig. 5 The lag angle", "texts": [ " 4), Fni is the tension of a group of hinges to the hub, Fnix is the component of Fni in the X direction, Fniy is the component of Fni in the Y direction, W is the vertical loading, Fwi is the force from a group of hinges to the outer-wheel, Fwix is the component of Fwi in the X direction, Fwiy is the component of Fwi in the Y direction, ei is the lever arm of Fni, Md is the drive torque acting on the hub, M is the quality of the MET, J is the inertia moment from the wheels to the center axis, a is the acceleration of the MET, \u20ach is the angular acceleration of the MET, Fd is the driving force from the ground to the wheel, Fx is the horizontal force that the drive shaft acts on the MET, Mf is rolling resistance moment, R is the wheel radius. Because the hub and the outer-wheel are connected by hinges in the MET, in stress situations, the hinges are inevitable after the transition from a free bend to the pretension state and the process will produce a lag angle. According to the geometric relationship in Fig. 5, the lag angle a is solved in 4ABO. In the figure, R1 is the distance from the wheel center to the end of third hinge, r is the radius of hub, d is the length in the pretension state of hinges. R1 = R-D1-L1, D1 is the thickness of the wheel outer ring, L1 is a base length of the hinge and the elastic ring connected. From the cosine theorem: a = arccos[(R2 1 + r2 - d2\u00de=\u00f02 R1 r)] 180=p\u00bc 7:8 \u00f03\u00de where, R \u00bc 390 mm; D1 \u00bc 35 mm; L1 \u00bc 12 mm; r \u00bc 192 mm; d \u00bc 155 mm.The angle makes the wheel from stationary to start" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002619_j.mechmachtheory.2017.08.007-Figure10-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002619_j.mechmachtheory.2017.08.007-Figure10-1.png", "caption": "Fig. 10. CAD model of the Agile Eye 3-DOF rotational parallel manipulator.", "texts": [ " From (56) , the moving platform\u2019s constraint screw system can be decomposed as S r = G r 0 L r 3 , which belongs to a third- order special system. Accordingly, the motion system of the moving platform can be derived as { A \u2217 = ( C r \u2217) \u22a5 = 0 B \u2217 = \u2212b \u2217A \u2217 = 0 C \u2217 = ( A r \u2217) \u22a5 = I 3 \u21d2 S = G 0 L 3 (57) As a result, the moving platform\u2019s motion screw system also corresponds to a third-order special system, which comprises all infinite-pitch elements in various directions. And it means that the 3- P RC parallel manipulator only has three translational degrees of freedom. 5.2. The Agile Eye with 3-DOF rotational motions As shown in Fig. 10 , the Agile Eye parallel manipulator [38] consists of three identical R RR limbs equally arranged on the horizontal plane. In each limb, the axes of three revolute joints intersect at a common point. Moreover, those points in different limbs are coincident with each other. Let O be the common point of all those revolute axes, which is selected as the origin of the system inertial frame {S}. Then, the motion screw systems of the R RR limbs can be obtained as V i = \u23a7 \u23a8 \u23a9 A i = u i, 1 u T i, 1 + u i, 2 u T i, 2 + u i, 3 u T i, 3 B i = \u0302 rO C i = 0 \u21d2 S i, 3 = G i, 3 L i, 0 , i = 1 , 2 , 3 (58) where S i, j = [ u T i, j , ( \u0302 rO u i, j ) T ] T , i = 1 , 2 , 3 ; j = 1 , 2 , 3 " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003143_s12206-018-0739-y-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003143_s12206-018-0739-y-Figure1-1.png", "caption": "Fig. 1. 2(3PUS+S) parallel manipulator.", "texts": [ " Third, the eigenvalue of the stiffness matrix was adopted to describe the stiffness performance, and the overall stiffness model of the 2(3PUS+S) parallel manipulator was established based on the stiffness modeling method of the serial system. Finally, numerical analysis and virtual experiments were conducted. The 2(3PUS+S) parallel manipulator, which is composed of two 3PUS+S parallel manipulators, is the core motion mechanism of a hip joint simulator [17]. The two 3PUS+S parallel manipulators are driven by three linear modules (LN1, LN2 and LN3). Therefore, the two moving platforms (m1 and m2) can achieve identical motions. Each of the 3PUS+S type parallel manipulator possesses 3 rotational-DOF. Fig. 1 illustrates the topological structure and prototype of the 2(3PUS+S) parallel manipulator. The articular head and acetabulum are fixed on the moving platform. The articular head center, which coincides with the thrust ball bearing center, acts as the rotational center of the moving platform. Each linear module has two sliders in which their distance is fixed. The sliders are connected to the corresponding moving platform via a joint lever with a spherical joint at one end and a hook joint at the other end. The S-type intermediate branched-chain of the two 3PUS+S parallel manipulators is connected in series through a ball spline shaft. The intermediate branched-chain, which is used to install the artificial hip joint and balance the loading force from the hydraulic cylinder, is a passive branched-chain. A spring is used to balance the weight due to gravity of moving platform m1. In Fig. 1(a), aji and bji (j = 1, 2; i = 1, 2, 3) represent the fixed points of the spherical joint on the moving platform and the hook joint on the slider, respectively. Ai is the fixed point of the linear module. oj and O denote the centroids of triangles aj1aj2aj3 and A1A2A3, respectively. Absolute coordinate system OXYZ is fixed to the base platform at point O. The negative Xaxis passes through point A3, and Z-axis is perpendicular to the base platform and points toward the moving platform. Relative coordinate system ojxjyjzj is attached to moving platform mj at point oj, yj-axis passes through point aj2, and zj-axis is perpendicular to the moving platform" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000405_j.ijsolstr.2010.01.005-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000405_j.ijsolstr.2010.01.005-Figure1-1.png", "caption": "Fig. 1. Geometry of th", "texts": [ " These governing equations are degenerated to those of twisted rings and straight rods in Sections 7 and 8 by letting the tortuosity and curvature to zero, respectively. The Galerkin version of the e centerline helix. Chebyshev differentiation matrix with Clenshaw\u2013Curtis quadrature method of solution is presented in Section 9 and numerical examples and given in Section 10. A verification of results by ANSYS is given in Section 11. Finally, we give a conclusion in Section 12 and a Nomenclature in the Appendix B. 2. Geometry of a helical beam A helical beam is a beam having a helical curve as its centerline shown in Fig. 1. We follow Love (1944) to take \u00f0x; y\u00de as the crosssectional plane. For regular circular helix ~r\u00f0t\u00de \u00bc a cos t~i\u00fe a sin t~j\u00fe bt~k: \u00f01\u00de Differentiate the position vector with respect to t twice, one has ~r0\u00f0t\u00de \u00bc \u00f0 a sin t~i\u00fe a cos t~j\u00fe b~k\u00de; ~r00\u00f0t\u00de \u00bc \u00f0 a cos t~i a sin t~j\u00de: Since the arc-length s \u00bc R t 0 k~r0\u00f0x\u00dekdx \u00bc t ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 \u00fe b2 p , therefore, the speed v \u00bc k~r0k \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 \u00fe b2 p \u00bc s0 and s \u00bc vt. The curvature j \u00bc k ~r0 ~r00k k~r0k3 \u00bc kab\u00f0sin t~i cos t~j\u00de a2~kk \u00f0a2 \u00fe b2\u00de3=2 \u00bc a v2 : The tangent vector is given by T ", " A thick M\u00f6bius ring of rectangular cross-section is taken as an example to show the ability of the method in analyzing structures that have not been attempted before. AG 0 0 0 0 0 0 AG 0 0 0 0 0 0 AE 0 0 0 0 0 0 EI1 0 0 0 0 0 0 EI2 0 0 0 0 0 0 GJ 2 666666664 3 777777775 r00 q\u00bc0: S\u00bc 0 lAG AEjC 0 0 0 lAG 0 AEjS 0 0 0 AGjC AGjS 0 0 0 0 0 AG 0 0 0 GI1jC AG 0 0 0 0 GI2jS 0 0 0 EI1jC EI2jS 0 2 666666664 3 777777775 r\u00fe AG 0 0 0 0 0 0 AG 0 0 0 0 0 0 AE 0 0 0 0 0 0 EI1 0 0 0 0 0 0 EI2 0 0 0 0 0 0 GJ 2 666666664 3 777777775 r0: Appendix B. Nomenclature a; b; t 2 \u00bd0; T circular helix parameters in Fig. 1, a is the circular radius and 2pb is the pitch \u00f0x; y\u00de the cross-sectional plane \u00f0~i;~j;~k\u00de Cartesian unit vectors s arc-length of centerline of a circular helix ~r position vector at a point of the centerline of a circular helix ~r0\u00f0t\u00de derivative with respect to the argument v \u00bc k~r0k \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 \u00fe b2 p \u00bc s0 speed of the helix j curvature T ! unit tangent vector at a point of the centerline of a circular helix N ! unit normal vector at a point of the centerline of a circular helix B " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002635_s11771-017-3585-7-Figure9-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002635_s11771-017-3585-7-Figure9-1.png", "caption": "Fig. 9 Result of simulation I in VERICUT", "texts": [ " The Qin Chuan YK2050A Gear Grinding Machine is chosen as the processing equipment, which can meet the requirements of face gear grinding movement based on the worm wheel as mentioned above. The complete simulation environment (see Fig. 8) can be constructed by establishing a machine along with a face gear blank and taking the 3-D model of worm wheel involving errors obtained in section 4.1 as the processing tool imported into VEERICUT software [19] which is developed by CGTECH Corporation of America. Finally, by editing NC programs and implementing the simulation process, the outcome can be obtained as shown in Fig. 9. 4.2.2 Simulation II The method employed in simulation II is to grind the face gear by a theoretical worm wheel with actual installation position errors. The way to construct VERICUT simulation environment (see Fig. 10) is similar to the way presented in 4.2.1 section, and the differences are: the processing tool is a theoretical worm wheel without errors which is easy to get; the actual installation position error (tangential linear position error) of the worm wheel is increased, that is, the actual axis of the worm wheel offsets the theoretical axis 1 mm along the Z-axis direction (based on the coordinate of the machine in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001568_j.oceaneng.2012.07.003-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001568_j.oceaneng.2012.07.003-Figure1-1.png", "caption": "Fig. 1. Submersible with bow and stern hydroplanes.", "texts": [ " A smooth reference depth trajectory is generated by a fourth-order command generator of the form \u00f0s2\u00fe2z1o1s\u00feo2 1\u00de\u00f0s 2\u00fe2z2o2s\u00feo2 2\u00dehr\u00f0t\u00de \u00bco2 1o 2 2hn r \u00f050\u00de with initial conditions zeros, where zi40 and oi40. The target value hn r of the depth of the submarine is set to 10 or 30 ft. Since it is desired to keep y close to zero, the reference pitch angle trajectory is assumed to be zero. The closed-loop responses of the submarine including random force and moment for different values of uncertainty factor are obtained (Fig. 1). A. Adaptive control: slow command, hn r \u00bc 10, disturbance d\u00bc0, b\u0302\u00f00\u00de \u00bc 0:6b or 1:6b. 0 100 200 300 0 5 10 15 h[ ft] Time[sec] 0 100 200 300 \u22120.1 0 0.1 Q [d eg /s ec ] Time[sec] 0 100 200 300 0 50 100 ||\u03a8 fv || Time[sec] 0 100 200 300 \u221250 0 50 Time[sec] u c [d eg ] \u03b4 B \u03b4 S Fig. 7. Adaptive control: \u00f0z1 ,o1 ,z2 ,o2\u00de \u00bc \u00f01,0:1,1,0:1\u00de, no disturbance, fast response, 10 (d) Pitch angle y; (e) Control signal uc (dB, dS); (f) Tracking error h hr; (g) JCf vJ; (h) It is desired to steer the submarine to a depth of 10 ft" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003638_1464419319838773-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003638_1464419319838773-Figure2-1.png", "caption": "Figure 2. Angular contact bearing geometry and deflection:23 (a) geometry of the ith ball\u2013race contact, and (b) deflection of the ith ball\u2013race contact.", "texts": [ " Also, running speed of the system is assumed to be low and therefore centrifugal forces and gyroscopic moments of ball bearings can be ignored. Note that the i and j index represent leftand right-hand bearings, respectively. Assuming a fixed outer race, the angular velocity of the cage is assumed to be constant and equal to the following !c \u00bc !s 2 1 D d cos p \u00f06\u00de The local Hertzian contacts force and nonlinear deflection relationship for the ball bearing are expressed as follows23 Wi \u00bc K 3=2i \u00f07\u00de where K is the stiffness coefficient between the contacting surfaces and i is the total elastic deflection at the ith ball\u2013race contact. Figure 2 shows the ball total deflection i of the ith ball\u2013race contact. Since the outer race is assumed to be fixed, the location of the center of curvature of the outer race Oo will also be fixed. As shown in Figure 2, the initial axial preload (in the z direction) causes an axial displacement Zp for the free center of curvature of the inner race from Oi to (Oi)1. On the other hand, the external radial loading caused by the external forces (Fx and Fy) will dynamically displace (Oi)1 to a final position (Oi)2. Using Figure 2, the deflection due to the dynamics of the machine-tool spindle can be expressed as follows z \u00bc A sin o \u00fe ZL=R \u00fe \u00f0d=2\u00de y cos i \u00fe x sin i \u00f08\u00de r \u00bc A cos p \u00fe o cos p \u00fe XL cos i \u00fe YL sin i \u00f09\u00de From the triangle sides i, z, and r and by using the Pythagorean theorem, it is easy to conclude the following relation i \u00bc 2 z \u00fe 2 r 1=2 A \u00f010\u00de So, the deflection for the left and the right-hand bearing, i and j respectively, will be as follows i \u00bc A sin o \u00fe ZL \u00fe \u00f0d=2\u00de y cos i \u00fe x sin i 2n \u00fe A cos p \u00fe o cos p \u00fe XL cos i \u00fe YL sin i 2o1=2 A \u00f011\u00de j \u00bc A sin o \u00fe ZR \u00f0d=2\u00de y cos j \u00fe x sin j 2n \u00fe A cos p \u00fe o cos p \u00fe XR cos j \u00fe YR sin j 2o1=2 A \u00f012\u00de where ZL \u00bc Zp Z, ZR \u00bc Zp \u00fe Z, Zp \u00bc A sin p o = cos p and A \u00bc ror \u00fe rir D The contact angles for the left- and right-hand bearing, i and j respectively, are expressed as follows i \u00bc tan 1 A sin o \u00fe ZL \u00fe d=2 y cos i \u00fe x sin i A cos p \u00fe o cos p \u00fe XL cos i \u00fe YL sin i \u00f013\u00de j \u00bc tan 1 A sin o \u00fe ZR d=2 y cos j \u00fe x sin j A cos p \u00fe o cos p \u00fe XR cos j \u00fe YR sin j \u00f014\u00de By solving equations (15) and (16) by simultaneously using the iterative Newton\u2013Raphson method, the initial bearing preload contact angle p and the initial contact deflection o for a given preload Pr can be determined NbK 3=2 p sin p \u00bc Pr \u00f015\u00de o \u00bc A cos o cos p 1 \u00f016\u00de where A is the initial distance between the centers of curvature of the inner and outer races, and o is the unloaded contact angle and is calculated as follows20 o \u00bc cos 1 1 Cd Cd 2A \u00f017\u00de where Cd is the interference fitting of bearings and Cd \u00bc do di 2D" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003294_s40032-018-0492-0-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003294_s40032-018-0492-0-Figure2-1.png", "caption": "Fig. 2 Fluid domain meshing", "texts": [ " Edge size, mesh size and mesh method (hex and sweep) are very important parameters to have control over meshing. The numbers of layers used in radial direction for meshing fluid film thickness were seven. Sweep meshing was used for thinfilm region, and multizone method was used for the inlet semicircular portion. The mesh was recorded to avoid failure of meshing at higher eccentricity ratio. The current mesh had 211792 numbers of hexahedral cells with element size 0.40 mm. The meshing of the fluid domain is shown in Fig. 2. To ensure the mesh quality, skewness was monitored with maximum values of 0.9 and minimum value of 0.0254 to generate a very good quality of mesh. In FLUENT, parallel processing was selected with eight processors to accelerate the speed of calculations to achieve solution faster. A pressure-based solver was selected for steady-state calculation of static pressures, since the generated hydrodynamic pressure gives rise to reaction forces on the shaft. The cavitation was modeled by setting all negative pressures to zero as soon as they were generated with the help of user-defined function developed in C language" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001673_s0362119713020151-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001673_s0362119713020151-Figure1-1.png", "caption": "Fig. 1. Counting the direction of the joint angles. \u03b2, the angle of the hip joint; \u03b3, the angle of the knee joint; \u03b4, the angle of the ankle joint; (1) shoulder joint; (2) hip joint; (3) knee joint; (4) ankle joint; (5) metatarsophalangeal joints.", "texts": [ " The angle of the hip was measured between the lon gitudinal axes of the trunk and the upper leg at the ven tral body surface of the subject. The angle of the knee was measured between the longitudinal axes of the upper and lower legs on the dorsal side of the body. The angle in the ankle joint was measured between the lon gitudinal axes of the leg and the foot, at the anterior sur face of the lower leg and the dorsum of the foot. The double step length was determined by the displacement of the longitudinal coordinate of the Y marker on the ankle joint from one setting of the foot on the support to the next (Fig. 1). Kinematic characteristics of the double stepping cycle. The double stepping cycle consists of (1) the phase of the front push, which starts from the moment when the foot stands on the support and accounts for about 15% of the duration of a step; (2) the phase of the median (vertical) support, which starts from the moment when the plantar surface of the foot stands on a support (about 15% of the duration of a step), and ends with the sepa ration of the heel from the support (\u224845% of the dura tion of the double step); (3) the phase of the back push, which lasts from the separation of the heel of the take off leg from the supports (\u224845%) until the removal of the toes of the take off leg from the support (63\u201365%); and (4) the swing phase (including translation of the leg), which starts with the removal of the toes of the take off leg from the support (\u224863\u201365%) and ends with the con tact of the foot with the support (\u2248100%)" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002548_978-3-319-61134-1_5-Figure5.11-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002548_978-3-319-61134-1_5-Figure5.11-1.png", "caption": "Fig. 5.11 Devices based on wear debris accumulation in gap of permanent magnet core (a) and electromagnet (b, c): 1 magnetic system; 2 accumulated wear particles; MR and MR2 magnetoresistors; 3 permanent magnet; 4 induction coils; 5 current source; 6 Hall sensor; 7 magnet core; 8 electromagnet", "texts": [ " Capacitance of a capacitor with wear debris deposited between its plates is also used as an informative parameter in wear monitoring [56]. The analysis of accumulated wear particles is performed basing on measurement of optical signal by fiber optic system [57]. When the problem is to determine the maintenance necessity on the basis of the wear particle content in the oil, simple built-in devices based on particle accumulation can be used. An example is the device containing a permanent magnet, a pair of installed pole pieces, and two temperature-matched magnetoresistors MR1, MR2, which form the arms of a Wheatstone bridge (Fig. 5.11a) [58]. A non-ferromagnetic spacer is installed in the oil line and the measuring device is mechanically connected with a motor that is used to displace it. When the device is brought near the non-ferromagnetic spacer wear particles accumulate on the unit. This causes change of the magnetic flux, which leads to reduction of the flux density in the magnetoresistive sensor MR1 and increase in the sensor MR2. The bridge output voltage will increase linearly with particle accumulation. Upon reaching a certain level the linearity is disrupted, the motor is energized and moves the metering device away from the spacer on which accumulation took place", " This device can be used in relatively clean systems, in which the number of wear particles is critical. However, in measuring the particle content in the oil the particles whose size does not exceed 6 lm are not taken into account, since the magnetic flux gradient is not sufficient to capture them from the lubricant stream. As an example of device using the method of magnetic accumulation we refer to the sensor for detecting the content of ferromagnetic particles applied by IVECO FIAT [59]. The sensor registers the wear debris accumulation in a magnetic circuit clearance (Fig. 5.11b). Variation in magnetic field induced in clearance 1 with increasing accumulation of wear debris 2 suspended in a fluid is recorded. The magnetic circuit including clearance 1 is polarized by permanent magnet 3. Induction coils 4 connected to the auxiliary magnetic circuit produce a magnetic field opposite to that produced by magnet 3. Electric current in coils increases up to disappearance of the magnetic field in clearance 1. As a result, wear debris accumulated above the clearance are separated, clean and regenerate the sensor. Magnetic field of electromagnet can be also used for particle accumulation in the clearance of magnetic core 7 (Fig. 5.11c) [60]. Hall sensor 6 is installed in the clearance to monitor the accumulated particles. When the threshold level of Hall sensor output (which corresponds to limit level of mass of accumulated particles in the clearance) is reached, current in electromagnet 8 is switched off and the clearance cleaning occurs. This method is realized in Continuous Debris Monitor\u2014 CDM (Ranco Controls Ltd.). The ferromagnetic detector [61] also realizes the method of magnetic accumulation, which records the variation in the generator reference frequency with wear debris accumulation in a magnetic trap (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003115_lcsys.2018.2857512-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003115_lcsys.2018.2857512-Figure2-1.png", "caption": "Fig. 2. The cable\u2019s current and initial configuration.", "texts": [ " One end of the cable is fixed with the trolley and the other end of the cable is fixed with an eye-in-hand camera. The black block, of which the coordinate is brb=( bxb, byb)T in the base frame, is the object which is going to be grasped by the crane and which can be regarded as a point feature. u(t) is the input force to drive the trolley. d(t) is the disturbance on the trolley with the assumption that | ( ) |d t d . The variable \u0394 can be expressed as A Bx x where rA=(xA, yA)T, rB=(xB, yB)T is the displacement of the cable\u2019s end point A and B in the base frame respectively shown in Fig.2. The problem which is going to be solved is as follow. Problem. Without knowing the position of the object brb, design a proper input u(t) to drive the trolley to the desired position bxb and guarantee that the sway range satisfies the constraint |\u0394|< >>: \u00f04\u00de Finally, the tape spring kinematics is described by only four kinematic parameters attached to the rod line: \u2022 the translations u1 (s1) and u3 (s1) of the cross-section; \u2022 the rotation h\u00f0s1\u00de of the cross-section around e2 and \u2022 and the angle be\u00f0s1\u00de characterising the shape of the cross-section. We must notice here that the displacements u1\u00f0s1\u00de and u3\u00f0s1\u00de and the rotation h\u00f0s1\u00de are linked by the assumption (iv), that leads to: C \u00bc er3 OG;1 kOG;1k \u00bc sin\u00f0h\u00de 1\u00fe u1;1 jr \u00fe cos\u00f0h\u00de u3;1 jr \u00bc 0 with jr \u00bc kOG;1k \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f01\u00fe u1;1\u00de2 \u00fe \u00f0u3;1\u00de2 q : \u00f05\u00de The novelty of the model resides in the inextensibility assumption of the cross-section curve" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001988_604393-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001988_604393-Figure1-1.png", "caption": "Figure 1: Multibody system of the considered ROV with tethered cable.", "texts": [ " The rest of this study is organized as follows. Section 2 sets up the dynamic model of the ROV multibody system especially including the considered umbilical cable. A controller which is for the 3D path following is designed in Section 3, while Section 4 presents the experimental results. Conclusions are given in Section 5 to close this paper. 2. Dynamic Model of the ROV System 2.1. Modeling the Whole ROV Multibody System. The ROV is usually operating with the support vessel (mother ship) in the ocean; see Figure 1. The tethered cable not only provides power and communication media but also brings nonlinear drag forces upon ROV. In this study, the considered system is a multibody system including a flexible body, that is, the tethered cable, and a rigid body, that is, the ROV itself. The dynamic equation of the whole ROV multibody system according to [5] can be represented by M (q) q\u0308 + C (q\u0307) q\u0307 +D (q\u0307) q\u0307 + G (q) + \u0394d = Ttru + \ud835\udf0f\ud835\udc61, (1) where M(q) is the 6 \u00d7 6 mass matrix of the ROV, vector q = [\ud835\udc56, \ud835\udc57, \ud835\udc58, \ud835\udf11, \ud835\udf03, \ud835\udf13]\ud835\udc47 is a 6 \u00d7 1 pose vector of the ROV, C(q\u0307) is a 6 \u00d7 6 matrix of centrifugal and Coriolis terms, D(q\u0307) is the damping matrix,G(q) is the vector of gravitational forces and moments, \u0394d is a disturbance vector, and Ttru contains the forces and torques from thrusts, while \ud835\udf0f\ud835\udc61 is the drag effects from the tethered cable" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001628_j.ymssp.2012.08.013-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001628_j.ymssp.2012.08.013-Figure3-1.png", "caption": "Fig. 3. Housing\u2019s modal analysis.", "texts": [ " From the design of the bearings, it was possible to calculate the four excitation frequencies of each pair of bearings. The rotation of the roller produces four excitation frequencies, one caused by the spinning of the roller, one caused by its translation and two produced when the roller contacts the inner and outer rings [29,30]. The excitation frequencies are listed in Table 2. To help identify the frequencies displayed in the spectrum (Fig. 2), the natural frequencies of the housing were calculated with the finite element model (Fig. 3). Table 3 shows the fundamental modes. It is evident that the fifth mode coincides with the gear mesh frequency. Certain other frequencies were not identified; therefore, a time\u2013frequency analysis was conducted (Fig. 4). It is clear that the gearbox has a nonlinear behavior. It is evident that the dynamic behavior requires a dipper analysis; for that reason, a simulation model is constructed. For this work, a single reduction gearbox was simulated to illustrate the effect of the housing stiffness on dynamic behavior of nonlinear elements", " A compound effect is observed when the nonlinear waves travel between the gears and the bearings: the waves increase the dynamic load amplitude and add another periodic load. In this case, the life span increased by 25%. To confirm whether the housing is controlling the nonlinear synchronization, the housing stiffness was incorporated into the model. Three situations were simulated: in the first simulation, the housing stiffness is lower than the average bearing stiffness. In the second simulation, the housing stiffness is equivalent to the first mode of the actual housing; the data are taken from the finite element model (Fig. 3). In the third simulation, the housing stiffness is higher than the average bearing stiffness. Each simulation is analyzed with the same wavelet (Morlet), and the time\u2013frequency maps are constructed with the same parameters as the experimental data. Fig. 12 shows the time\u2013frequency map of the first simulation. The dominant frequency is due to the input unbalance force, and the dynamic response is steady during the time span. From this map, it is clear that the nonlinear effects are neglected. In practice, this condition is almost nonexistent" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002421_978-3-319-56099-1_6-Figure6.16-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002421_978-3-319-56099-1_6-Figure6.16-1.png", "caption": "Fig. 6.16 a Schematic of Nd:YAG laser-based repair system; and b deposition obtained by this system [43], with kind permission from Elsevier", "texts": [ " Pumping of Nd ions from the ground state to upper state, i.e., at 4th level is done by krypton arc lamp (also known as flash lamp) using light of wavelength 7200\u20138000 \u00c5. From 4th level, the ions become non-radiative which drops their energy to 3rd level. Therefore, the laser emission occurs in the 3rd level which is upper laser emission level and 2nd level which is lower laser emission level. This laser has better thermal efficiency than CO2 laser hence it can be used for depositing the material in powder and wire form. Figure 6.16a depicts schematic of Nd:YAG laser-based repair system with a powder feeder to supply deposition material in the powdered form. This type of laser can be used for small damages caused due to mishandling, defective material, reconditioning, poor inspection and quality control, setting of inappropriate parameters, and improper work environment. Figure 6.16b presents a typical material deposition obtained by Nd-YAG laser-based deposition system. Case Study Borrego et al. [31] used Nd:YAG laser to repair the damages such as wear and fatigue cracks (shown in Fig. 6.17a) caused due to high thermal\u2013mechanical loads in the molds made of P20 and AISI H13 steel. The cracked volume was cleaned mechanically and the cavity was filled with similar deposition material in the wire form using Nd:YAG laser-based deposition system. Figure 6.17b illustrates the surface after deposition and Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002493_0954410017715278-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002493_0954410017715278-Figure2-1.png", "caption": "Figure 2. Forces and moments analysis diagram: (a) lateral view; (b) back view.", "texts": [ " Based on the simulation tests, it is found that the velocity of ship bow airflow changes for the height above the ship deck. The ship bow airflow changes in large amplitude for the height below 10m. Especially, a symmetric vortex is produced for the height from the flight deck about 1m. The reason is that a vacuum lowpressure zone exists in the front of flight deck so that the back side air supplements it. Take-off process model of carrier-based aircraft Forces and moments analysis diagram of carrierbased aircraft in the running phase on the flight deck is shown in Figure 2. For the catapult-assisted take-off process, based on above motion models of the carrier-based aircraft, landing gear, steam catapult, flight deck, and ship bow airflow, a full nonlinear take-off process model of the carrier-based aircraft is established in Figure 3. Thus, the force and moment equations of carrierbased aircraft in the take-off process should be modified as _u \u00bc vr wq g sin \u00fe Fx \u00fe F 0x m _v \u00bc ur\u00fe wp\u00fe g cos sin \u00fe Fy \u00fe F 0y m _w \u00bc uq vp\u00fe g cos cos \u00fe Fz \u00fe F 0z m 8>>>>>>>< >>>>>>>: \u00f021\u00de _p \u00bc \u00f0c1r\u00fe c2p\u00deq\u00fe c3 L\u00fe L0 \u00fe c4N _q \u00bc c5pr c6 p2 r2 \u00fe c7 M\u00feM0\u00f0 \u00de _r \u00bc \u00f0c8p c2r\u00deq\u00fe c4\u00f0 L\u00fe L0\u00de \u00fe c9N 8>>< >>: \u00f022\u00de Here, F0x, F 0 y, and F0z are the projections of interactive forces in the body axis of coordinates, M0 and L0 are resultant moments of the forces, and F 0x \u00bc Tm cos cos Tm sin sin FS cos \u00fe Fs sin \u00f023\u00de F 0y \u00bc Fs sin \u00fe FS cos \u00f024\u00de F 0z \u00bc Tm cos sin \u00fe Tm sin cos FS sin Fs cos \u00f025\u00de M0 \u00bc FsL \u00fe FsR\u00f0 \u00delx1 \u00fe FsNlx2 FSL \u00fe FSR\u00f0 \u00delzm FSNlzn TmlT \u00f026\u00de L0 \u00bc FsL cos ly1 \u00fe FsL sin lzm FsR cos ly2 \u00fe FsR sin lzm \u00f027\u00de with Fs \u00bc FsL \u00fe FsR \u00fe FsN, FS \u00bc FSL \u00fe FSR \u00fe FSN" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001466_1.4006022-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001466_1.4006022-Figure1-1.png", "caption": "Fig. 1 Schematics of a rectangular fixed-incline-pad bearing", "texts": [ " This work derived a general solution which unifies these two existing groups of analytical solutions of fixed-incline-pad bearings, all in a summation form of an infinite series. All series member are the multiplication of two functions representing two coordinates, respectively. In this brief, it is shown that Hays\u2019 expression is actually equivalent to what Muskat et al. derived. The content in this work can be applied to sector-shaped pad bearings following Boswall\u2019s treatment, or can possibly be applied to other pad bearings. A fixed-incline-pad bearing is shown in Fig. 1 where an inclined pad is against a counterpart surface. Without losing generality, the inclined pad is assumed to be stationary and the counterpart moves at a speed of V with respect to the origin. Parameter s is the fixed incline height of the inclined pad, and parameters l and b are the length and width of the pad, respectively. Here, hydrodynamic lubrication is with an isothermal, incompressible, and Newtonian lubricant. The Reynolds\u2019 equation in the Cartesian coordinate (x0,y0) is written as @ @x0 h3 @p0 @x0 \u00fe @ @y0 h3 @p0 @y0 6gV @h @x0 \u00bc 0 (1) where g is the viscosity and p0 is the hydrodynamic pressure", " The author gratefully acknowledge financial support from the National Institute of Science and Technology (NIST) Advance Technology Program (ATP) Grant No. 70NANB7H7007, and Dr. Jean-Louis Staudenmann, ATP program manager. b \u00bc pad width, m Dn\u00f0x\u00de \u00bc function in the Michell\u2019s solution, Eq. (19) E \u00bc panx1\u00f0J01Y10 J10Y01\u00de H \u00f0s\u00de \u00bc Struve function of order I, K, J, Y \u00bc Bessel functions l \u00bc pad length, m L \u00f0s\u00de \u00bc modified Struve function of order h \u00bc film thickness, m h0, h0 \u00bc minimum film thickness, h0\u00bc h0/s m \u00bc slope in Sec. 5 p \u00bc fluid pressure: dimensionless in Secs. 3 and 4 s2 Vgl p0; dimensional in Sec. 5 s \u00bc incline height (Fig. 1), m V \u00bc speed, m/s x, y \u00bc Cartesian coordinates: dimensionless in Secs. 3 and 4; dimensional in Sec. 5 x0; y0; p0 \u00bc dimensional variables; the prime symbol is omitted in Sec. 5 g \u00bc dynamic viscosity, Pa s k \u00bc length-to-width ratio, k \u00bcl/b s \u00bc npkx [1] Cameron, A., 1966, Principles of Lubrication, Longmans, Green, New York. [2] Hamrock, B. J., 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York. [3] Dowson, D., 1998, History of Tribology, 2nd ed., John Wiley & Sons, New York. [4] Michell, A" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000976_978-90-481-9689-0_69-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000976_978-90-481-9689-0_69-Figure4-1.png", "caption": "Fig. 4 (a) Three volumes reached by the limbs of 3-RPR PPM, (b) W1 \u2229W2, (c) W1 \u2229W2 \u2229W3 (3D perspective view of the workspace), (d) top view of total workspace.", "texts": [ " Thus, in order to generate all the parallel plane regions produced by each limb for all orientations of the mobile 608 Planar Parallel Manipulators in a CAD Environment platform, a sweeping technique is applied in step 2. It consists in extruding the region generated in step 1, for a given platform orientation along the helical sweep path (see for example Figure 3b), created also in step 1. This second step is realized in the Generative Shape Design (GSP) CATIA workbench. The volume produced by one limb for all orientations of the mobile platform is obtained (see for example Figure 3c). This technique will be applied repeatedly for all the regions reached by the three limbs of the manipulator as it shown in Figure 4a. If the end-effector characteristic point EECP is chosen on the second revolute joint of the limb, the working volume associated to this limb is a cylinder in which the height represents the rotation angle of the moving platform and the base represents the translation workspace of the limb. Finally, in step 3 intersection Boolean operations are applied to obtain the common volume corresponding to the three-dimensional total workspace for the PPMs. Thus the total workspace W can be described as the intersection of three sets Wi associated with the three limbs (W = W1 \u22c2 W2 \u22c2 W3). The result is shown in Figure 4 for 3-RPR parallel manipulator. This step is realized in the Part Design CATIA workbench. The intersection of all three volumes is then the maximum workspace (total workspace). 609 K.A. Arrouk et al. The proposed method can be applied to several architectures of 3DOF PPMs as shown in Figures 5 and 6. In this section, the influence of the position of EECP on the workspace volume and total workspace shape is studied. The results obtained from the quantitative study confirm that there is no influence of the position of the EECP on the numerical value of total workspace volume" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003194_978-3-030-00365-4_22-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003194_978-3-030-00365-4_22-Figure1-1.png", "caption": "Fig. 1. Original (F and f) and canonical ( ~F and ~f ) reference frames.", "texts": [ " Consequently, several applications to the kinematic analysis and synthesis of planar mechanisms were carried out in [4\u20138] and more recently in [9], while re-proposed by Roth in [10]. They were also extended to the spherical and spatial kinematics, as reported in [11\u201313]. These parameters are defined invariants among any pairs of fixed and moving reference frames or coordinate systems, since related to the motion characteristics of the coupler link and thus, they are independent by the particular choice of the reference frames. For example, referring to the slider-crank mechanism of Fig. 1, the pairs of fixed F\u00f0O;X; Y\u00de and moving f(X, x, y) reference frames, were chosen along with the corresponding fixed and moving canonical reference frames ~F\u00f0P1; ~X; ~Y\u00de and ~f \u00f0P1;~x;~y\u00de which origin coincides with the instantaneous center of rotation P1 of the coupler link AB. In particular, the ~Y-axis is orthogonal at P1 point to the fixed centrode p and oriented toward the moving centrode that is not shown in figure. Consequently, the ~Xaxis is tangent to both centrodes at P1 point and oriented clockwise with respect to the ~Y-axis, while the moving canonical reference frame ~f is assumed as coincident with ~F at the referring configuration, as shown in Fig. 1. These canonical frames are very important for the kinematic analysis and synthesis of planar mechanisms, because the geometric loci, which are of kinematic interest, take a simple mathematical form, when expressed with respect to them. This is the case of Bresse\u2019s circles, the zero-normal and zero-tangential jerk circles, the cubic of stationary curvature and the Burmester curve. The position and the orientation of the moving frame f(X, x, y) is obtained though the position vector rX which can be expressed as rX \u00bc r cos d sin d\u00bd T \u00f01\u00de where r and d are the A0A crank length and the oriented counter-clockwise angle of A0A with respect to the X-axis, respectively", " The same rigid body motion can be also obtained by rolling the moving on the fixed centrode and giving the successive positions of I as the tangent point between them. The instantaneous geometric invariants an and bn are the n-order derivatives of the Cartesian-coordinates ~XI and ~YI of P1 with respect to the oriented angle # that ~f makes with respect to ~F during the coupler motion, by taking the form an \u00bc dn~XI d# n and bn \u00bc dn~YI d# n \u00f02\u00de where n is a natural number. For a starting configuration in which both canonical frames coincide each other, as shown in Fig. 1, the instantaneous geometric invariants up to the fourth order are given by the following expressions: a 0 \u00bc b 0 \u00bc a 1 \u00bc b 1 \u00bc a 2 \u00bc 0 \u00f03\u00de while b2, a3, b3, a4 and b4 are different by zero and take the following forms: b 2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2XX du2 \u00fe dYX du 2 \u00fe d2YX du2 dXX du 2 s \u00f04\u00de a 3 \u00bc 1 b 2 d3XX du3 \u00fe dXX du d2YX du2 dXX du d3YX du3 \u00fe dYX du d2XX du2 \u00fe dYX du \u00f05\u00de b 3 \u00bc 1 b 2 d3XX du3 \u00fe dXX du d2XX du2 \u00fe dYX du \u00fe d3YX du3 \u00fe dYX du d2YX du2 dXX du \u00f06\u00de a 4 \u00bc 1 b2 d4XX du4 dYX du d2YX du2 dXX du d4YX du4 \u00fe dXX du d2XX du2 \u00fe dYX du \u00f07\u00de b 4 \u00bc 1 b 2 d4XX du4 dYX du d2XX du2 \u00fe dYX du \u00fe d4YX du4 \u00fe dXX du d2YX du2 dXX du \u00f08\u00de Referring to Eq" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002437_978-3-319-55128-9_5-Figure5.9-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002437_978-3-319-55128-9_5-Figure5.9-1.png", "caption": "Fig. 5.9 NIST proposed standard benchmark part design", "texts": [ "4 lists these parameters and their potential effect on geometrical and mechanical characteristics of parts. By taking a subset of these parameters and focus on the experimental investigations, it is possible to obtain knowledge efficiently for a certain generic type of geometries (e.g. blocks, cylinders, thin-wall features) and optimize processes. National Institute of Standards and Technology (NIST) recently proposed a standard benchmark part that aims to provide both geometric and process benchmark [44]. As shown in Fig. 5.9, the part consists of multiple features that a represent relatively comprehensive set of GD&T characteristics, and some of the feature designs also considered unique issues with AM such as overhanging features, minimum feature sizes and extrusion/recession features. On the other hand, it does not include features for angular and size dependency evaluations. This benchmark part was primarily designed for powder bed fusion AM processes, while other designs might be potentially better suited for other AM processes" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001117_j.jmps.2011.10.008-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001117_j.jmps.2011.10.008-Figure1-1.png", "caption": "Fig. 1. (a) Slip-line field of a rigid spherical asperity (wear particle) plowing through a rigid-perfectly plastic surface and removing material by microcutting, (b) detailed view of plastic shear region showing a network of orthogonal a and b slip-lines, and (c) hodograph of the slip-line field (Komvopoulos, submitted for publication).", "texts": [ " Fang (2003) presented a slip-line model of surface machining with a round-edge tool; however, this model is suitable for macroscopic machining and, therefore, cannot be used to analyze cutting-mode deformation at the asperity/ wear particle scale. In the present analysis it is assumed that the dominant mode of friction is plowing and plastically deformed (sheared) material is removed by microcutting. A hard (rigid) asperity (wear particle) of radius of curvature R penetrates into a soft material to depth ds (Fig. 1(a)). For relatively shallow indentation, e.g., ds/Ro0.1, plane-strain deformation of the soft material is a reasonable simplification (Komvopoulos et al., 1986a). Plastic shear ahead of a hard asperity causes the plastically deformed (sheared) material to slide against the front surface of the plowing rigid asperity/particle at a relative velocity uc (Fig. 1(a)). The deformed medium is modeled as an isotropic, rigid-perfectly plastic material, moving toward the rigid asperity at a constant velocity u. The deformation field of the soft material is represented by a network of orthogonal shear lines, referred to as the a- and b-lines (Fig. 1(b)). Boundary BD is a free surface (i.e., zero surface traction) because separation of the material sliding against the rigid asperity occurs at point B; therefore, the a- and b-lines intersect BD at an angle of 451. The angle Z between an a-line and the tangent at any point along the contact interface BEG depends on the ratio of the interfacial shear strength s to the shear strength of the plowed surface k, i.e., Z\u00bc 1 2 cos 1 s k \u00f01\u00de where 0rs/kr1. The magnitude of the dimensionless shear strength ratio s/k reflects the interfacial adhesion characteristics, with the upper and lower limits corresponding to the ideal cases of adhesionless (s/k\u00bc0) and sticking (s/k\u00bc1) contact interfaces. For a slip-line field to be admissible, mass conservation and certain geometric, trigonometric, and kinematic conditions must be satisfied. Since the plowed material is modeled as rigid-perfectly plastic (incompressible), mass conservation yields D _V \u00bc lUuc \u00bc dsUu \u00f02\u00de where D _V is the material removal rate at the microcontact level, and l is the thickness of the removed material. The following relationships are deduced from geometry considerations (Fig. 1): Rcosf\u00fet\u00feds \u00bc R \u00f03\u00de t\u00bc lsin\u00f0\u00f0p=4\u00de\u00feb\u00de cos\u00f0\u00f0p=4\u00de Z\u00de \u00f04\u00de b\u00fef\u00feZ\u00bc p 2 \u00f05\u00de ds \u00bc R1\u00f01 cos\u00f0y b\u00de\u00de\u00fe lsin\u00f0y b\u00deffiffiffi 2 p cos\u00f0\u00f0p=4\u00de Z\u00de \u00f06\u00de R1 sin\u00f0y b\u00de\u00fe lcos\u00f0y b\u00deffiffiffi 2 p cos\u00f0\u00f0p=4\u00de Z\u00de \u00bc Rsinf\u00fe lcos\u00f0\u00f0p=4\u00de\u00feb\u00de cos\u00f0\u00f0p=4\u00de Z\u00de \u00f07\u00de where t is the pile-up thickness (Fig. 1(a)), R1 is the radius of curvature of arc IG (Fig. 1(b)), and f, b, and y are slip-line field angles (Fig. 1(a) and (b)). Fig. 1(c) shows the hodograph of the slip-line field shown in Fig. 1(a), where uDI is the relative velocity along boundary DI (Fig. 1(b)). In region BDF, consisting of a network of straight slip-lines (Fig. 1(a)), kinematic admissibility requires that \u00f0uB a\u00de 2 \u00fe\u00f0uB b\u00de 2 \u00bc u2 c sin2f\u00fe\u00f0uc cosf\u00feu\u00de2 \u00f08\u00de where uB a and uB b are the velocities at point B along a- and b-lines, respectively, obtained from a numerical scheme described elsewhere (Komvopoulos, submitted for publication). For a given velocity ratio uc/u, the slip-line angles b, f, y and the radius R1 were obtained in terms of s/k and ds/R by simultaneously solving Eqs. (1)\u2013(7). If the obtained slip-line field did not satisfy the velocity condition given by Eq. (8), a different value of uc/u was assumed, and the numerical procedure was repeated until a kinematically admissible slip-line field was obtained. Before proceeding with the friction analysis, it is appropriate to provide some justification for the complexity of the slipline field used in the present analysis (Fig. 1) compared to the frequently quoted model of Challen and Oxley (1979). As mentioned earlier, the assumption of perfectly sharp (wedge-shaped) asperities (or wear particles) is physically unrealistic at asperity length scales. The present model accounts for the removal of material (cutting) by an asperity (wear particle) with a rounded cutting edge. In addition, the fractal model of the rough surface (presented in the following section) is based on a power-law distribution of circular asperity/particle microcontacts; therefore, a slip-line field for a wedge-shaped plowing asperity cannot be used to analyze friction of fractal surfaces. Moreover, the present slip-line field provides a more accurate representation of the plastic flow of the soft material. In particular, because the slip-lines in region BIG are curved to satisfy the boundary condition along boundary BG (Fig. 1(b)), both the hydrostatic pressure (Henky\u2019s equations) and the slip velocity (Geiringer\u2019s equations) in region BIG demonstrate spatial variation, as opposed to the slip-line field of Challen and Oxley (1979), where the network of straight slip-lines used in that region yields a constant hydrostatic pressure and invariant slip velocity both in magnitude and direction. The coefficient of friction at a single fully plastic microcontact m can be expressed in terms of the resultant forces at boundaries BE and EG (Fig. 1(b)) as m\u00bc DFp x DFp y \u00bc DFBE x \u00feDFEG x DFBE y \u00feDFEG y \u00f09\u00de whereDFp x and DFp y are the resulting forces in the x- and y-direction, respectively. The normal and tangential stresses at the contact interface BEG were obtained from Henky\u2019s plasticity equations, using the Mohr circle and the known boundary conditions, i.e., stress-free surface BD and Eq. (1). DFBE x , DFBE y , DFEG x , and DFEG y were obtained by integrating the stress components acting along the corresponding contact interface (Komvopoulos, submitted for publication), i.e., DFBE x \u00bc Z f0 0 \u00bd1\u00fe2aN\u00fesin\u00f02Z\u00de kRsin\u00f0f aN\u00dedaN sR\u00bdsinf sin\u00f0f f0\u00de \u00f010\u00de DFBE y \u00bc Z f0 0 \u00bd1\u00fe2aN\u00fesin\u00f02Z\u00de kRcos\u00f0f aN\u00dedaN\u00fesR\u00bdcos\u00f0f f0\u00de cosf \u00f011\u00de DFEG x \u00bc Z f f0 0 \u00bd1\u00fe2f0\u00fe2\u00f0a3 a5\u00fea2\u00de\u00fesin\u00f02Z\u00de kRsinldl sRsin\u00f0f f0\u00de \u00f012\u00de DFEG y \u00bc Z f f0 0 \u00bd1\u00fe2f0\u00fe2\u00f0a3 a5\u00fea2\u00de\u00fesin\u00f02Z\u00de kRcosldl\u00fesR\u00bd1 cos\u00f0f f0\u00de \u00f013\u00de where angles f0, aN, l, a2, a3, and a5 are shown in Fig. 1(a). Angles a2, a3, and a5 can be obtained from geometric and trigonometric relationships (Appendix), whereas angle f0 is given by f0 \u00bc 2tan 1 l 2 ffiffiffi 2 p RcosZcos\u00f0\u00f0p=4\u00de Z\u00de \" # The hard and rough surface is assumed to be isotropic and self-affine, with profile z(x,y) given by (Yan and Komvopoulos, 1998) z\u00f0x,y\u00de \u00bc L G L \u00f0D 2\u00de lng M 1=2 XM m \u00bc 1 Xqmax q \u00bc 0 g\u00f0D 3\u00deq cosfm,q cos 2pgq\u00f0x2\u00fey2\u00de 1=2 L cos tan 1 y x pm M \u00fefm,q \" #( ) \u00f014\u00de where x and y are in-plane Cartesian coordinates; L is the profile length; G and D are the fractal roughness and the fractal dimension (2oDo3), respectively, both independent of spatial frequency in the range where the surface exhibits fractal behavior; g (g41) is a parameter controlling the frequency density in the surface profile, typically equal to 1", " The energy dissipated to remove material Ec can be expressed as Ec \u00bc Z a0 C a0 S DEc\u00f0a 0\u00den\u00f0a0\u00deda0 \u00f036\u00de where DEc is the energy dissipated at a fully plastic microcontact to remove material, given by DEc \u00bcDEp DEs, where DEs is the energy dissipated at a fully plastic microcontact to plastically shear the material. Energy terms DEe, DEp, and DEc can be expressed as DEe \u00bc \u00f0DFe x u\u00de T \u00f037\u00de DEp \u00bc \u00bd\u00f0DFBE x \u00feDFEG x \u00de u T \u00f038\u00de DEc \u00bc \u00bd\u00f0DFBE x \u00feDFEG x \u00de uc\u00fe\u00f0DFBE y \u00feDFEG y \u00de uc T \u00f039\u00de where T is the total time of sliding. Fractions of elastic energy xe, plastic shear energy xs, and material removal energy xc are defined as xe \u00bc Ee=Eex, xs \u00bc Es=Eex, xc \u00bc Ec=Eex \u00f040\u00de Using Eqs. (2), (18), (29), (30), (33)\u2013(40) and considering Fig. 1(a), the energy fractions defined by Eq. (40) can be expressed as xe \u00bc \u00f0s\u00f0D 1\u00de=2\u00f03 D\u00de\u00de\u00bd1 \u00f0a0C=a0L\u00de \u00f03 D\u00de=2 a0LR a0 C a0 S \u00f0DFBE x \u00feDFEG x \u00den\u00f0a 0\u00deda0 \u00fe\u00f0s\u00f0D 1\u00de=2\u00f03 D\u00de\u00de\u00bd1 \u00f0a0C=a0L\u00de \u00f03 D\u00de=2 a0L \u00f041a\u00de xs \u00bc R a0 C a0 S \u00bd\u00f0DFBE x \u00feDFEG x \u00de\u00f01\u00fe\u00f0ds=l\u00decosf\u00de \u00f0DFBE y \u00feDFEG y \u00de\u00f0ds=l\u00desinf n\u00f0a0\u00deda0R a0 C a0 S \u00f0DFBE x \u00feDFEG x \u00den\u00f0a 0\u00deda0 \u00fe\u00f0s\u00f0D 1\u00de=2\u00f03 D\u00de\u00de\u00bd1 \u00f0a0C=a0L\u00de \u00f03 D\u00de=2 a0L \u00f041b\u00de xc \u00bc R a0 C a0 S \u00bd\u00f0DFBE y \u00feDFEG y \u00desinf \u00f0DFBE x \u00feDFEG x \u00decosf n\u00f0a0\u00deda0R a0 C a0 S \u00f0DFBE x \u00feDFEG x \u00den\u00f0a 0\u00deda0 \u00fe\u00f0s\u00f0D 1\u00de=2\u00f03 D\u00de\u00de\u00bd1 \u00f0a0C=a0L\u00de \u00f03 D\u00de=2 a0L ds l \u00f041c\u00de From Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000431_1.3225921-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000431_1.3225921-Figure2-1.png", "caption": "Fig. 2. Model geometry at a collision with the next lower step.", "texts": [ " The system\u2019s kinetic energy T, potential energy V, and dissipative energy R are given by T = m 2 \u03071 2l2 cos2 1 + \u03071 2l2 sin2 1 + m 2 \u03071l cos 1 + \u03072l cos 2 2 + \u03071l sin 1 + \u03072l sin 2 2 , 1 V = mgl 1 \u2212 cos 1 + 2 \u2212 cos 1 \u2212 cos 2 + kt 2 2 \u2212 1 2, 2 and R = ct 2 \u03072 \u2212 \u03071 2, 3 where an overdot denotes differentiation with respect to the time t. The equations of motion may be obtained by solving Lagrange\u2019s equations see, for example, Ref. 14 d dt T \u2212 V \u0307i \u2212 T \u2212 V i + R \u0307i = 0, i = 1,2 4 for \u03081 and \u03082. The configuration of the two link system at a collision is shown in Fig. 2, with an impact occurring at point C. Because the collision is assumed to be perfectly inelastic, there will be energy dissipated at each collision see Ref. 15 . The 36 Am. J. Phys., Vol. 78, No. 1, January 2010 Downloaded 22 Jul 2013 to 129.174.21.5. Redistribution subject to AAPT lic collisions are assumed to take place instantaneously, so the geometry of the system is the same before and after a collision, that is, the system\u2019s potential energy doesn\u2019t change. There is a loss in kinetic energy, however", " We let N denote the torque and calculate the torque about point C taking into regard the entire system and the torque about point B considering the stance link alone and require NC = 0 5 and NB = 0 . 6 Because the sum of the externally applied moments is equal to the rate of change in the angular momentum NC= L\u0307C and NB= L\u0307B, with L the angular momentum , we conclude that L\u0307C=0 and L\u0307B=0. We let denote before the collision and + denote after the collision. Hence, the angular momentum of the system is conserved about point C as well as for the stance link alone about point B during the collision at a stair step, LC \u2212 = LC + 7 and LB \u2212 = LB + . 8 In terms of the coordinate system shown in Fig. 2, Eqs. 7 and 8 may be written as, respectively, rB/C \u2212 m \u03071 \u2212k\u0302 rB/A \u2212 = rB/C + m \u03071 +k\u0302 rB/C + + rA/C + mr\u0307A/C + 9 and 0 = rA/B + mr\u0307A/C + , 10 where, for example, rB/C \u2212 =\u2212l sin 2 \u2212\u0131\u0302+ l cos 2 \u2212j\u0302 is the position of B with respect to C before the collision, rB/C + = l sin 1 +\u0131\u0302 +\u02c6 \u2212 l cos 1j is the position of B with respect to C after the 36Ai-Ping Hu ense or copyright; see http://ajp.aapt.org/authors/copyright_permission collision, and k\u0302= \u0131\u0302 j\u0302. The mass at point A is fixed modeled as a pin joint before the collision and therefore does not contribute to the system\u2019s angular momentum during this time. The term r\u0307A/C + the velocity of point A after the collision where the point C is stationary after the collision is given by r\u0307A/C + = l \u03071 + cos 1 + + \u03072 + cos 2 + \u0131\u0302 + l \u03071 + sin 1 + + \u03072 + sin 2 + j\u0302 . 11 The stance angle \u03071 + and swing link angle \u03072 + can be expressed in terms of the pre-collision angles as 1 + = 2 \u2212 + 12 and 2 + = 1 \u2212 + . 13 This relation may be confirmed by referring to Fig. 2, which depicts the model at a collision, and observing that the stance link and the swing link switch roles at the instant shown such that the stance link is now in contact with the lower step and the swing link is just about to lift off from the upper step. Equations 9 and 10 yield two scalar equations. During its motion, a small portion of the total mass of a Slinky is in contact with a stair step. We assume for simplicity that the effect of the mass at point A see Fig. 3 is negligible when considering the entire system about point C in Eq", " The corresponding period is found to be 0.328366 s, consistent with empirical observations. We use the initial conditions in Eq. 16 and plot in Fig. 5 the corresponding stance link and swing link angles and angular velocities over three time steps. The solid lines represent the stance link and the dashed lines represent the swing link. The discontinuities we see in the plot of angles are due to the role-switching that takes place between the two links during a collision. To be consistent with the coordinates as defined in Fig. 2 , after a collision takes place, rad are added to the prior stance link angle and to the prior swing link angle. The discontinuities in the angular velocities are also due to the jump conditions of Eqs. 14 and 15 . Note that the angle of the stance link reaches a value less than /2. Physically, this scenario means that the stance link hits the edge of the step. It is more accurate to say that the model walks on a slope of constant angle rather than on the successively lower horizontal surfaces of stair steps" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002852_ascc.2017.8287413-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002852_ascc.2017.8287413-Figure2-1.png", "caption": "Fig. 2. AR.Drone 2.0/Parrot inc. [14]", "texts": [ " 1, there is some possibility of collision between agents if each drone is put any place as initial position. If the number of drones is a few, we can set the initial position of each agent not to collide each other. However it is difficult in the case that many number of drone are controlled. Hence the ability of collision avoidance is important. The effectiveness of the method is verified by applying to control method in the situation like this. The experimental quadcopter is AR.Drone 2.0 (Drone) of Parrot, Inc. Figure 2 shows the picture of Drone and the coordinate frame. The front side of Drone is x, right side is y and upward is z direction. Here we use the open source code called CV Drone to communicate control inputs to Drones by wireless LAN. This code can gets the control signals as inputs called Throttle 978-1-5090-1573-3/17/$31.00 \u00a92017 IEEE 1602 Level for each axis between \u00b10.5, and these input signals are translated to the angular velocity of the propellers in this Drone. Here drone is a system that it is difficult to apply the control input based on nonlinear dynamics because drone has black box inner feedback controller" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001988_604393-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001988_604393-Figure4-1.png", "caption": "Figure 4: The \ud835\udc57th microunit length of tethered cable in the water and its forces analysis.", "texts": [ " If we set kwind as the wind velocity relative to the cable, we have Fwind = 12\ud835\udc51\ud835\udf09\ud835\udc36wind\ud835\udf0cair\ud835\udc34 kwind kwind (6) as the wind effect on the \ud835\udc51\ud835\udf09 length tethered cable, where \ud835\udf0cair is the air density, the strength of local wind velocity above the sea surface can be expressed by kwind = V10(\ud835\udc511 \u2212 \ud835\udf09\ud835\udc6410 )1/7 (7) in which V10 is the wind speed at 10 meters above the sea surface, \ud835\udc511 is the cable height out of the water counting from\ud835\udc42\ud835\udc50 to thewater plane, and \ud835\udf09\ud835\udc64 is only the cable height out of the water counting from the considered point to the water plane; see Figure 2. Here \ud835\udc36wind is the drag coefficient in the air. If we focus on the \ud835\udc56th microunit length of tethered cable in the air; (see Figure 3), one has \ud835\udc47\ud835\udc56+1 \ud835\udc51\ud835\udf01\ud835\udc56\ud835\udc51\ud835\udc5d \u2212 \ud835\udc47\ud835\udc56 \ud835\udc51\ud835\udf01\ud835\udc56\ud835\udc51\ud835\udc5d + \ud835\udc39\ud835\udc56,wind = \ud835\udc5a\ud835\udc51k\ud835\udc61\ud835\udc51\ud835\udc61 \ud835\udc51\ud835\udf01\ud835\udc56\ud835\udc51\ud835\udc5d , \ud835\udc47\ud835\udc56 \ud835\udc51\ud835\udf09\ud835\udc56\ud835\udc51\ud835\udc5d \u2212 \ud835\udc47\ud835\udc56+1 \ud835\udc51\ud835\udf09\ud835\udc56\ud835\udc51\ud835\udc5d \u2212\ud835\udc4a\ud835\udc56,air = \ud835\udc5a\ud835\udc51k\ud835\udc61\ud835\udc51\ud835\udc61 \ud835\udc51\ud835\udf09\ud835\udc56\ud835\udc51\ud835\udc5d . (8) Here we consider as usual that the wind is horizontal only, and in this case in right horizontal, \ud835\udc47\ud835\udc56 and \ud835\udc47\ud835\udc56+1 are the two tension forces at the two ends of the \ud835\udc56th microunit length cable, \ud835\udc4a\ud835\udc56,air = \ud835\udc34\ud835\udf0c\ud835\udc61\ud835\udc54. Similarly, as shown in Figure 4, the tethered cable is in the water. Its dynamics in the water hold \ud835\udc47\ud835\udc57+1 \ud835\udc51\ud835\udf01\ud835\udc57\ud835\udc51\ud835\udc5d \u2212 \ud835\udc47\ud835\udc57 \ud835\udc51\ud835\udf01\ud835\udc57\ud835\udc51\ud835\udc5d + \ud835\udc39\ud835\udc57,\ud835\udc53 = \ud835\udc5a\ud835\udc51k\ud835\udc61\ud835\udc51\ud835\udc61 \ud835\udc51\ud835\udf01\ud835\udc57\ud835\udc51\ud835\udc5d , \ud835\udc47\ud835\udc57 \ud835\udc51\ud835\udf09\ud835\udc57\ud835\udc51\ud835\udc5d \u2212 \ud835\udc47\ud835\udc57+1 \ud835\udc51\ud835\udf09\ud835\udc57\ud835\udc51\ud835\udc5d \u2212\ud835\udc4a\ud835\udc57,water = \ud835\udc5a\ud835\udc51k\ud835\udc61\ud835\udc51\ud835\udc61 \ud835\udc51\ud835\udf09\ud835\udc57\ud835\udc51\ud835\udc5d , (9) where \ud835\udc4a\ud835\udc57,water = (\ud835\udf0c\ud835\udc61 \u2212 \ud835\udf0c\ud835\udc64)\ud835\udc34\ud835\udc54, and \ud835\udf0c\ud835\udc64 is the density of water. Here \ud835\udc47\ud835\udc57 and \ud835\udc47\ud835\udc57+1 are the two tension forces at the two ends of the \ud835\udc57th microunit length cable under water, and \ud835\udc39\ud835\udc57,\ud835\udc53 is the force due to the wave and current disturbances which usually by guest on June 23, 2016ade.sagepub.comDownloaded from only considers for the horizontal direction" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002502_s12283-017-0241-2-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002502_s12283-017-0241-2-Figure2-1.png", "caption": "Fig. 2 Flight path of a shuttlecock compared to the classical projectile motion", "texts": [ " Firstly, it possesses a unique transient period of instability where it must perform a \u2018\u2018turnover\u2019\u2019 upon being struck to become aligned with its direction of travel [1]. Moreover, the shuttlecock also exhibits an atypical flight trajectory, also referred to as the \u2018\u2018parachute trajectory\u2019\u2019, characterised by the rapid deceleration during flight to the extent where it would come to a near-vertical drop shortly after reaching its peak height, rather than taking the form of the classical parabolic flight path [2] (see Fig. 2). Although classified as a high-drag projectile due to its rapidly decelerating trait over an extremely short period of time, the badminton shuttlecock holds the current world record of possessing the highest initial velocity of 408 km/ & To-Ming Terence Woo s3473221@student.rmit.edu.au 1 School of Engineering (Aerospace, Mechanical and Manufacturing Engineering), RMIT University, Melbourne, Australia h (Sukumar [3]). However, it is also prone to breakage when subjected to repeated strikes during the course of a game; hence there has been an increase in the price of feathered shuttlecocks due to supply and demand" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001082_j.arcontrol.2013.09.003-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001082_j.arcontrol.2013.09.003-Figure1-1.png", "caption": "Fig. 1. (a) Profiles of state z1 after step disturbance parameterized by h1. (b) Those poi additional uncertain parameter h2. The grazing point is located at the extremum of the c (h1, h2).", "texts": [ " (32), is a point \u00bd h\u00f0i;j\u00deT ; t\u00f0i;j\u00de T ; i 2 I j; j 2 J 0, for which trajectories z reach the path constraint. Hence, 0 \u00bc w\u0302j\u00f0 z\u00f0i;j\u00de;p; h\u00f0i;j\u00de; t\u00f0i;j\u00de\u00de; z\u00f0i;j\u00de \u00bc u\u00f0 t\u00f0i;j\u00de; p; h\u00f0i;j\u00de\u00de; i 2 I j; j 2 J 0: \u00f037\u00de To guarantee that trajectories z just touch but never violate the path constraints, additional conditions have to be considered. Before introducing the mathematical formulations, let us motivate the ideas using a qualitative example. Consider a single state constraint (6) which is supposed to be a constant upper bound for the state z1 2 R, i.e., 0 6 z1,max z1. Fig. 1(a) shows an illustrative example of the transient behavior of state z1 after a step disturbance triggered at t = 0. The magnitude of the disturbance is parameterized by the uncertain parameter h1. The simple upper bound for z1; w\u0302 :\u00bc z1;max z1 P 0, is associated with a plane in the (h1, z1, t)-space that must not be crossed from below by the time response of z1 after the disturbance. As shown in Fig. 1(a), there is a critical value of h1 \u00bc h1 for which the bounding plane is tangentially touched but not yet crossed. The points where the time response of z1 touches the bounding plane tangentially is a socalled grazing bifurcation (Nordmark, 1991). On the other hand, the set of points where the bound is crossed, corresponds to a parabola-like curve in the (h1, t)-plane with its extremum located at the grazing point defined by \u00bd h1; t . In the presence of a second uncertain parameter h2 the parabola-like curve of the crossing points in Fig. 1(a) unfolds into a fold-like surface and the grazing point into a curve in the (h1, h2, t)-space as depicted in Fig. 1(b). The projection Mc of this curve onto the parameter plane spanned by h1 and h2 shown in Fig. 1(c) separates the region where the constraint is not violated from the region where uncertain parameters lead to time responses that cross the bound. In order to guarantee feasibility for all h 2 C; t P t0, the set of uncertain parameters C has to be restricted to the region where the constraint is not violated. In other words, grazing points cannot be located inside C, as shown in Fig. 1(c). From a mathematical point of view, the necessary conditions for a grazing point can be derived by taking into account that the trajectories z fulfill Eq. (37) and have a common tangent space with the hypersurface spanned by the active constraint w\u0302j at the point \u00bd h\u00f0i;j\u00deT ; t\u00f0i;j\u00de T ; i 2 I j; j 2 J 0, in the (z, t)-space (Gerhard et al., 2008). At the grazing point \u00bd h\u00f0i;j\u00deT ; t\u00f0i;j\u00de T , the tangent space of the active constraint w\u0302j can be computed using the orthogonality condition with its normal space, which is spanned by the gradient of the constraint w\u0302j with respect to differential states z and time t (Fleming, 1977, p" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002437_978-3-319-55128-9_5-Figure5.14-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002437_978-3-319-55128-9_5-Figure5.14-1.png", "caption": "Fig. 5.14 Complex support structures generated for laser powder bed fusion parts", "texts": [ " However, little decision support is available for the detailed design of these supports such as the support spacing and the contact area, and the design processes are still largely based on the designers\u2019 personal experiences. In many cases, in order to ensure the success of fabrication, the support structures are often over-designed, which often imposes significant challenges for the support removal and turns this process into a handcrafting type of work. For example, the support structures shown in Fig. 5.14 may require a series of manual operations such as cutting, machining, grinding and polishing in order to meet the end use specification, and the complex geometries of these support structures as well as their interfaces with the parts poses various design for manufacturing issues to these processes. Based on the geometries of the fabricated structures, it is often possible to reduce the amount of support structures required via the adjustment of orientation. However, the orientations that result in minimum amount of support also often result in very long fabrication times, since under these cases the largest dimensions of the parts are more or less aligned to the build direction, such as the example shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003076_0954406218784619-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003076_0954406218784619-Figure3-1.png", "caption": "Figure 3. The simplified geometric model of the hob assembly.", "texts": [ " This study was primarily conducted by using the hob assembly of a type of dry cutting gear hobbing machine. The hob assembly is composed of the spindle, hob, rolling bearings, direct-drive servo motor, back plate and so on. The picture and geometry model of the hob assembly are shown in Figures 1 and 2, respectively. And the typical working condition of this type of gear hobbing machine used in the present numerical study is detailed in Table 1. With necessary structural simplifications, the simplified geometric model of the hob assembly is shown in Figure 3. The gear hob and bearings are simplified as cylinders that have the same inner and outer diameters as the hob and corresponding bearings, respectively. Note that the spindle motor and the rear cover were not introduced in the developed model, but the heat generated by these components was added on the contact surfaces between spindle and motor. Figure 2. The geometry model of the hob assembly. Heat source and boundary condition are two essential conditions for the thermal performance analysis of the hob assembly", " According to the computing theory for this air flow pattern, the convection heat transfer coefficient of rotating surfaces in this paper can be defined by the following equations h \u00bc Nul L \u00f010\u00de Nu \u00bc CReb Pr 1=3 \u00f011\u00de Re \u00bc vL a \u00f012\u00de where Nu is the Nusselt number, is the air density, v is the velocity of the air, a is the dynamic viscosity of air and C and b are the constants, the values of which can be selected from Table 4. In addition to the outer surface of the sleeves, the taper sleeves and the cutter bar also rotate along with the spindle, and consequently the forced convection heat transfer occurs between the ambient air and these rotational parts of the hob assembly. They can also be defined by equations (10) to (12), and the locations of these parts are shown in Figure 3. The thermodynamic characteristics of air depend on its temperature. The temperature used to define the thermodynamic characteristics of air near the hob assembly is the mean temperature between air temperature and solid surface temperature, named qualitative temperature, which can be calculated by tq \u00bc tw \u00fe t1\u00f0 \u00de 2 \u00f013\u00de where tq is the qualitative temperature, tw is the solid surface temperature and t1 is the air temperature. The intensity of pressure of the compressed air is 0.5MPa. When the ambient temperature is 25 C, its density is equal to 5" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003989_tec.2019.2944424-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003989_tec.2019.2944424-Figure7-1.png", "caption": "Fig. 7. Space vector equivalent circuit of BDFIM including iron loss (complete model)", "texts": [ " > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 \ud835\udc45\ud835\udc56,\ud835\udc52\ud835\udc5e = 3\ud835\udc49\ud835\udc3f\u2212\ud835\udc3f 2 \ud835\udc43\ud835\udc56,\ud835\udc52\ud835\udc5e\u2044 and Fig. 5, the resistance of the CW side iron loss is obtained versus rotor speed varied in the range of \u00b140% around the natural synchronous speed. The calculated and measured results shown in Fig. 6 have a good agreement which verify acceptable accuracy of the presented analytical procedure. IV. REDUCED-ORDER DYNAMIC MODEL OF BDFIM INCLUDING IRON LOSS MODEL By connecting \ud835\udc45\ud835\udc56\ud835\udc5d \ud835\udc60 and \ud835\udc45\ud835\udc56,\ud835\udc52\ud835\udc5e across the magnetizing branches, the complete model of BDFIM including the iron loss is shown in Fig. 7. To derive a general model which is valid for all reference frames, two dependent voltage sources are placed series with the iron loss resistances. This model combines a well-known dynamic equivalent circuit of BDFIM excluding the iron loss with the conventional approach to model the iron loss in the space vector equivalent circuit [22]. From Fig. 7, in an arbitrary reference frame (\ud835\udf14\ud835\udc4e) the expressions for the voltages and flux linkages are obtained in the form: papppp jdtdIRV (11) crracccc NjdtdIRV )( (12) rrparrrr pjdtdIRV )(0 (13) pmprplpp ILIL (14) cmcrclcc ILIL (15) cp mcrmprrlrr ILILIL (16) ppp mprampri s ip ILjdtILdIR )( (17) ccc mcrrramcrieqi ILNjdtILdIR )()(, (18) ** .Im5.1.Im5.1 rmcrcrmprpe IILpIILpT cp (19) In Appendix, it is shown how (19) is derived. The BDFIM consists of three torque components. The first component is the synchronous torque which exists due to the indirect coupling of the two stator windings magnetic fields", " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 5 Note that after substituting the \ud835\udc4c model of inductances into equivalent circuit, the series voltage sources corresponding to the iron loss resistances can be shifted to the adjacent branches. To achieve the purpose, the above mentioned points are fulfilled in two steps as shown in Fig. 8. Applying KCL in Fig. 7 for nodes \u201ca\u201d and \u201cb\u201d and after some manipulations, \ud835\udc3c \ud835\udc5a\ud835\udc5d and \ud835\udc3c \ud835\udc5a\ud835\udc50 are obtained for voltage sources in Fig. 7 as: cpp ic r cr ip r crlr m II L L II L LL I .. (21) cpc ic r prlr ip r pr m II L LL II L L I .. (22) where \ud835\udc3f\ud835\udc5f = \ud835\udc3f\ud835\udc5d\ud835\udc5f + \ud835\udc3f\ud835\udc50\ud835\udc5f + \ud835\udc3f\ud835\udc59\ud835\udc5f . To develop the dynamic model for BDFIM, \ud835\udc45\ud835\udc56\ud835\udc5d \ud835\udc60 is placed immediately after the PW resistance. For our aim this placement is more convenient without loss of the performance accuracy, as noted in [8]. The reduced-order dynamic model for the BDFIM including the iron loss resistances is finally derived as shown in Fig. 9. Subscript \u201cth\u201d refers to the Thevenin\u2019s equivalent circuit seen from PW side", " As a result, this model can be considered as an attractive suggestion to study the BDFIM performance for various control strategies. APPENDIX In this Section, the detailed procedures are presented for deriving the torque equation (19). Substituting (11) and (12) into the space vector expression for active power, the total three-phase active input power can be written as follows: ***2 ***2 ** 3 )( 2 3 2 3 ccrrac c lcc m rccc ppap p lpp m prpp ccpp INjI dt Id LI dt Id LIR IjI dt Id LI dt Id LIR IVIVP c p (A-1) Using (17) and (18) and applying KCL to the nodes \u201ca\u201d and \u201cb\u201d [see Fig. 7], we have: ****2 pipp p p IILjIII dt Id LIR mpramrp m pri s ip (A-2) ****2 , )( cicc c c IILNjIII dt Id LIR mcrrramrc m rcieqi (A-3) 0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 0 0.5 1 1.5 2 Time (s) T e (p u ) 0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 0 0.5 1 1.5 2 Time (s) T e (p u ) 0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 0 0.5 1 1.5 2 Time (s) T e (p u ) 0885-8969 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 8 Applying KVL to the rotor loop in Fig. 7, we can write: rrpa r rlrr m rc m rp pj dt Id LIR dt Id L dt Id L cp )( (A-4) Substituting (A-2) to (A-4) into (A-1) and after some manipulations we can write the input power expression as: ** ** ** ** ** 2 , 2222 3 )( )( )( 2 3 rrrpar r rl ccrrac c lc ppap p lp imcrrram m cr impram m pr ieqii s iprrccpp IpjI dt Id L INjI dt Id L IjI dt Id L IILNjI dt Id L IILjI dt Id L IRIRIRIRIRP ccc c ppp p cp (A-5) This expression can now be broken down into its individual components as follows: Copper and iron losses 2 , 2222 2 3 cp ieqii s iprrccpp IRIRIRIRIR Change in field energy ** *** 2 3 r r rlc c lc p p lpm m crm m pr I dt Id LI dt Id L I dt Id LI dt Id LI dt Id L c c p p Rotational power *** 2 3 cc imcrrrccrrrrrp IILjNIjNIjp Therefore: cp mrcrcmrprp r rot e IILpIILp P T " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003843_iemdc.2019.8785408-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003843_iemdc.2019.8785408-Figure2-1.png", "caption": "Fig. 2. Motor configurations with the different thicknesses and regions of the motor. (a) slotless inner rotor, (b) slotless outer rotor.", "texts": [ " Section II provides a description of the motor configurations and of the winding. Section III explains the methodology and the criteria used for performing the comparative study. Sections IV and V detail the electromagnetic and thermal models respectively. Section VI presents and discusses the results. Finally, Section VII summarizes the main contributions of the paper. The motor is a 3-phase, n-pole slotless PM machine with a parallel magnetized PM. Two configurations are studied, the inner and outer rotor configurations, as depicted in Fig. 2. These are mainly characterized by the thickness of the different regions, the active length of the motor, and the magnetic properties of the PM. The winding is a PCB winding whose topology is described in Fig. 3. This topology allows both for a reduction in the phase resistance without changing the linked flux, and for a simplification of the winding connection compared to the traditional zigzag topology [4]. 978-1-5386-9350-6/19/$31.00 \u00a92019 IEEE 1311 The comparison between the inner and outer rotor configurations can be based on two different criteria, namely the motor constant and the nominal torque", " Based on the following hypotheses: \u2022 stator and rotor iron yokes have finite but constant per- meability, \u2022 the armature winding is open-circuit and therefore the magnetic field is just due to the permanent magnets, \u2022 all electrical conductivities are supposed to be zero, i.e. eddy currents are neglected, the Maxwell equations can be reduced to: \u22072Ai = 0 i = {I, R, A, S, E} (3) \u22072AM = \u2212\u03bc0\u2207 \u00b7M (4) where A is the vector magnetic potential, M is the magnetization vector in (A/m), \u03bc0 the permeability in freespace, and the superscript i refers to the region of the motor, illustrated in Fig. 2. In addition to the previous hypotheses listed above, no end effects are considered, i.e. the motor is assumed to have infinite axial length. It therefore arises that A has only a z-component. The general solutions of (3) and (4) can be expressed using the separation of variables. These solutions depend on a set of unknown coefficients that can be found by applying the boundary conditions as described in [5] and solving numerically a linear system of equations. The flux linked by a phase can then be computed using the vector potential through: \u03a8p(\u03b8) = \u222b Aa z(r, \u03d5, \u03b8) dz (5) Finally, considering a sinusoidal AC supply, the torque constant kT is given by: kT = 3 2 p\u03a8p (6) with p the number of pair of poles" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003378_012027-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003378_012027-Figure7-1.png", "caption": "Figure 7. Manufacturing process of hybrid tool (a-d) and a computed tomography image in one section (e).", "texts": [ " that by the end of the cooling time (19 s) ~9 \u00b0C lower temperature of the critical section could have been achieved with the new design than that of the original cooling system in the same section. Moreover, due to the conformal cooling the temperature distribution of the mold became much smoother. 5 1234567890\u2018\u2019\u201c\u201d The production of the tool insert with the new design was carried out by Direct Metal Laser Sintering, which is a multi-step process. As a first step, the tool is printed with the insert height and then stopped the process (Figure 7a). Then metal powder is removed from the hole and the insert is placed into that (Figure 7b). It is important that the top of the insert must be in the same plane with the last layer of the built part (Figure 7c) and then continue to build (Figure 7 d). To ensure the best filling with the insert, after reversing the tool it can be melted in the hole with a brazing process (Figure 7 e). The connection of the tool and the copper insert were examined by computed tomography and cross sectional optical microscopic images. After the powder deposition the upper part of the copper 6 1234567890\u2018\u2019\u201c\u201d insert is scanned by laser beam, so interesting to observe the interface of the two materials. In our experiments EOS M270 DMLS equipment was used with parameters applied for MS1 type maraging steel sintering. No porosity was detected in the region of steel-copper connection (interface area) by CT investigation (Figure 8" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002644_access.2017.2756852-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002644_access.2017.2756852-Figure2-1.png", "caption": "FIGURE 2. LOS guidance geometry for straight-line path.", "texts": [ " Simulation results in Section V validate the effectiveness VOLUME 5, 2017 21473 of the proposed approach, followed by the conclusion and future works in Section VI. II. PROBLEM FORMULATION A typical configuration of a fully submerged hydrofoil vessel is shown in Fig. 1 [2]. The T-shaped bow foil is equipped with two synchronous flaps. The aft foil has a pair of central flaps and two pairs of ailerons. The struts of the aft foil are equipped with rudders, which are used for roll and yaw dynamics together with the ailerons. The bow foil and the central part of the aft foil are for longitudinal motion control. A. KINEMATICS OF THE PATH FOLLOWING PROBLEM Fig. 2 [4] shows the geometry of the LOS guidance problem. For an FSHV located at the position (x, y), the cross-track error ye is defined as the orthogonal distance from the current location to the pedal point (xp, yp) on the path [4]. Similarly, the forward-track error xe is also defined. The path-tangential reference frame is rotated an angle \u03b3p using the rotation matrix R(\u03b3p) \u2208 SO(2) as[ xe ye ] = R(\u03b3p)T [ x \u2212 xp y\u2212 yp ] , (1) where \u03b3p is the path-tangential angle and R(\u03b3p) is defined as R(\u03b3p) = [ cos(\u03b3p) \u2212 sin(\u03b3p) sin(\u03b3p) cos(\u03b3p) ] [12]" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003864_s11071-019-05167-3-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003864_s11071-019-05167-3-Figure8-1.png", "caption": "Fig. 8 The trajectory of (29) with initial condition x(0) = (0.5, 0.2, 0.3)T", "texts": [], "surrounding_texts": [ "An exponential gain approach has been proposed to design the event-triggered controller in this paper to decrease the rate of triggering in event-triggered con- trol process. By introducing an exponential term, the new control gains became exponentially decreasing or increasing in the interval of two consecutive event times. Significantly, a novel event-triggered controller with exponential gain and a specific event-triggered scheme has been designed to stabilize the considered system in afinite time. In order to avoidZenobehaviors, a positive lower bound for the inter-execution has been obtained. Finally, two illustrative examples have been provided to show the effectiveness of the main results. In the future, based on the proposed ETM in this paper, it is interesting to investigate finite-time stabilization and control synthesis issues for other class of nonlinear systems with time delays. And how to improve the proposed exponential gain method and design eventtriggered controller are worthy to be studied, so as to further save the limited bandwidth and resources. Compliance with ethical standards Conflict of interest The authors declare that they have no conflict of interest." ] }, { "image_filename": "designv11_29_0003542_s12206-019-0114-7-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003542_s12206-019-0114-7-Figure1-1.png", "caption": "Fig. 1. The mobility vector and its components.", "texts": [ " The aim of this study is therefore to improve the accuracy of the original mobility method by considering some different features between the internal gear motor and the journal bearing. This is called hybrid mobility method. The basic principle of the mobility method can be interpreted as Booker [5]. The motion of the journal within a cylindrical housing can be regarded as a superposition of two motions which occur simultaneously; i.e., the motion of the unloaded rotating journal (the \u201czero-load whirl\u201d) and the motion of loaded nonrotating journal (the \u2018squeeze action\u2019). The mobility vector, M r , has two components, \u03b5M and \u03c6M , are illustrated in Fig. 1. \u03b5M Mcos\u03b2= and \u03c6M Msin\u03b2 .= - (1) The similarity between the construction of ring gear/housing and the journal/bearing allows applying the mobility method to analyze the dynamic behavior of the internal gear motor. In fact, the internal gear motor is more complex than a journal bearing in actual operation. The differences between the ring gear/housing and the journal/bearing are described through some features as follows: Self-supporting phenomenon: In order to lubricate for journal bearing, the external oil lubrication feeding into film thickness is required" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000690_icems.2009.5382859-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000690_icems.2009.5382859-Figure5-1.png", "caption": "Fig. 5. Vector diagram at very low speed.", "texts": [], "surrounding_texts": [ "to the stator frequency. Therefore, *\n0E k f= (5)\nwhere, 0k k= if * 00;f k k> = \u2212 if * 0f < ,\n* * *2p f\u03c9 \u03b8 \u03c0= = , 0k is positive constant.\nThe auto-boost voltage can be defined by ' 0b sV V E= \u2212 (6)\nIt is necessary to keep the system stable by introducing a first-lag low pass filter in the feedback loop because of the inherently positive feedback characteristic of the autoboost voltage. The auto-boost voltage command is computed by\n'1 1b bV V p\u03c4 = + (7)\nThe input voltage command is given by *\n0s bV V E= + (8)\nB. Compensation of Slip Frequency When the V/f controlled method is used, the slip causes an error between the desired speed and the actual one as load change. From Fig. 1, we have\n0 0 2\n*\nr\nE I\nMj L\n\u03c9 = (9)\n0 2T\nr\nr\nE I\nRM L s = \u239b \u239e \u239c \u239f \u239d \u23a0\n(10)\nFrom Fig. 2, in order to control according to the argument of 0E , the currents 0 , TI I are defined by\n( ) 2 0 0 , j j T TI I e I I e \u03c0\u03b1 \u03b1\u2212 = = (11)\nFrom (11), the following relation is obtained. * *\n0 00 0, 0 0 0 0, 0 0T T I I I s I s \u03c9 \u03c9> > < < > > < <\n(12)\nSubstituting (11) into (9) and (10), the slip frequency is calculated by\n'\n0 0\n, 2 r T r T sl r r R I R Is f L I L I \u03c9 \u03c0 = = (13)\nThe currents 0I , TI are written by d-q currents as\n0 sin cos1 cos sin3\nsd\nsqT\niI iI \u03b1 \u03b1 \u03b1 \u03b1 \u2212 \u23a1 \u23a4\u23a1 \u23a4 \u23a1 \u23a4= \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5 \u23a3 \u23a6\u23a3 \u23a6 \u23a3 \u23a6\n(14)\nIn order to stabilize the system, a first-lag low pass filter\nin feedback loop is introduced as\n'1 1sl slf f s\u03c4 = + (15)\nThe actual stator frequency *f can be calculated by\n* ** slf f f= + (16)\nwhere, **f is the frequency corresponding to speed command. Fig. 3 shows the block diagram of proposed method. From Fig. 1, the electromagnetic torque is obtained by\nC. Vector Locus According to Fig. 1, the vector loci of 0E , 0 , TI I as a function of slip make it easy to understand the characteristics of IM. From Figs. 1, 2, the relations of\n,sV 0 ,E 0 , ,T sI I I , ,\u03b1 \u03b8 are described. Defining s sV V= (real number) as the phase reference, internal induced voltage is written by\n0 2 2 2 2s s AB jACE V V\nB C B C = + + + (18)\nwhere, 2 rA R M\u03c9= , 2 2( )s r s r r rB R L s L L R M R\u03c9 \u03c3= + + , 2 2 s r r s rC R R L L L s\u03c9 \u03c3= \u2212 .\nTherefore, the phase angle of 0E is expressed as\n1tan ( )AC AB \u03b1 \u2212= (19)\nWhen the real part of 0E becomes minus, following condition is obtained.\n2\n2 s r r r\ns r\nL L R M R s R L \u03c3 + < \u2212 (20)\nWhen the slip is satisfied with (20) and 0\u03c9 > , because of 0C > , \u03b1 becomes larger than 90 .\nThe vector sI is described as\n2 2 2 2s s s DC EB EC BDI V j V C B C B + \u2212= + + +\n(21)", "where, r rD R L= , 2 rE sL\u03c9= .\nThe phase angle of sI is obtained by\n1tan ( )EC BD DC EB \u03b8 \u2212 \u2212= +\n(22)\nIn addition, from Fig.1, the vector of 0E is rewritten as\n0 ' ' s A jBE V X jY a jb jc += = + + + (23)\nwhere, 2 2' sA L M\u03c9 \u03c3= , 2' sB R M\u03c9=\n2 2 2 2{ ( ) }r s s sa L R L L M\u03c9\u03c3 \u03c9 \u03c3= + + , 2 sb R M\u03c9=\n2 2 2{ ( ) }r s s r Lc s R L R \u03c9 \u03c9\u03c3= + .\nFrom (23), deleting the term that includes s, the vector locus of 0E is derived as\n2 2 2 2 2' ' ' '( ) ( ) ( ) ( ) 2 2 2 2 s s s A V B V A BX Y V a a a a \u23a7 \u23ab\u2212 + \u2212 = +\u23a8 \u23ac \u23a9 \u23ad (24)\nFrom (24), the locus of 0E is proved as a circle which has no relation with the rotor resistance.\nD. Graphs of Vector locus\nThe vector loci of magnetizing current 0I , torque current TI and internal induced voltage 0E are shown in Figs. 4, 6 and 7 at the synchronous speed 0N of 30rpm, 300rpm, and 1800rpm respectively as a function of slip speed slN . The vector diagrams in motoring and regeneration mode are shown in Figs. 5 and 8. By using\nTI\nsI\n0E\n0 300rpmN = 80 ~ 80rpmslN = \u2212 1VsV =\nFig. 6. Vector locus at 300rpm.\n80 ~ 80rpmslN = \u2212 0 1800rpmN =\nTI sI\n0E\n1VsV =\nTI 0E\ns sR I\ns sj L I\u03c9\u03c3 sV 0I\n(a) 0 , 90slN \u03b1> <\nsI\nsV 0E\n0I\nTI s sR I\ns sj L I\u03c9\u03c3\n(b) 0 , 90slN \u03b1< <\nFig. 8. Vector diagram at high speed.\nthese diagrams, we can discuss the limited range of proposed method. In Fig. 4, the real part of 0E becomes minus if the slip speed is under -16rpm, and then cos\u03b1 which is computed from (4) is negative. However, this condition is not obtained easily in practical operation without speed sensor. This region which satisfied (20) occurs when the system is operated at very low speed and regenerative mode. In Figs. 6, and 7 we can see that | |\u03b1 is below 90 and the proposed method can easily compute cos\u03b1 when the slip speed slN is changed from -80rpm to 80rpm.\nIII. STABILITY ANALYSIS AND RESULTS By taking a small perturbation at a steady-state", "operating point, a linear model of the proposed system shown in Fig. 3 is derived by\np\u0394 = \u0394 + \u0394x A x B u (25)\nwhere, , , , , , , T\nsd sq rd rq r b sli i V f\u03c8 \u03c8 \u03c9\u23a1 \u23a4\u0394 = \u0394 \u0394 \u0394 \u0394 \u0394 \u0394 \u0394\u23a3 \u23a6x ,\n** , T\nLf T\u23a1 \u23a4\u0394 = \u0394 \u0394\u23a3 \u23a6u .\n1\n1\n2 2 2 2\n3 4 5\n6 7 8 9 *2\n3 32\n0 2\n10 0 2\n10 0 2\n0 0 0 10 0 0\n10 0 0 0\nrqr sq\nr s r s r s r s s\nrdr sd\ns r r s r s r\nr rq rq r r\nr rd rd r r\nrq rd sq sd\ns sq\nMM M ka i L L L L L L L L\nMM Ma i L L L L L L\nM\nM\na a a i a i\na a a\na a R i a a\nf\n\u03c8\u03c9\u03c9 \u03c0 \u03c4 \u03c3 \u03c3 \u03c3 \u03c3 \u03c3\n\u03c8\u03c9\u03c9 \u03c0 \u03c3 \u03c4 \u03c3 \u03c3\n\u03c9 \u03c9 \u03c8 \u03c0\u03c8 \u03c4 \u03c4\n\u03c9 \u03c9 \u03c8 \u03c0\u03c8 \u03c4 \u03c4\n\u03c8 \u03c8\n\u03c4\n\u03c4\n\u23a1 \u2212 +\u23a2 \u23a2 \u23a2 \u2212 \u2212 \u2212 \u2212 \u2212\u23a2 \u23a2 \u23a2 \u2212 \u2212 \u2212\u23a2 \u23a2\n= \u2212 \u2212 \u2212\n\u2212 \u2212\n\u2212\n\u2212 \u2212 \u23a3\nA\n\u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5\n\u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5\u23a6\nThe input variables are **f corresponding to the speed\ncommand and the load torque LT . By computing the eigenvalues of A obtained by (25),\nwe can study the stability of operating points. Figs. 9 and 10 show the root locus of the poles, in which motor speed is 300rpm, 1000rpm, and 1500rpm, in motoring and regeneration mode. The load torque is changed from -8Nm to 8Nm. From these figures, the system is stable for all points, because all poles are located in the left half of the s-plane along with the change of the load torque. Although the dynamic characteristic becomes worse as the speed decreases, the proposed system is stable and the stability depends on the inherent characteristic of IM.\nIV. SIMULATION AND EXPERIMENTAL RESULTS\nA. Experimental System The proposed control system is implemented by a DSP (TMS320C6713-225MHz) based PWM inverter. Because the dead time and the non-ideal features of IGBT influence the output voltage of the inverter, a compensating algorithm is developed for the experimental system. Steady-state and transient characteristics are tested experimentally for various operating points.\nactual motor speed rN , the auto-boost voltage bV and the slip frequency slf in motoring and regeneration mode, when the load torque is changed.\nIn Figs. 12 and 13, the speed command is 30rpm and 1500rpm respectively and the system is operated in" ] }, { "image_filename": "designv11_29_0001232_j.engfailanal.2013.03.009-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001232_j.engfailanal.2013.03.009-Figure2-1.png", "caption": "Fig. 2. root an", "texts": [ " When mated to a mirror-half, the SRGs provide a one-way, high contact area for the transfer of torque. The mating halves of the ratcheting assembly are pushed together by springs, allowing freewheel in one relative direction of rotation and firm engagement in the other. The SRGs, Fig. 1 (part 9) are placed inside the bike hub in two locations using splines that mate with either the driving cogs (part 10), or the driven wheel hub (part 12). SRGs have three major parts: a gear base, gear teeth, and gear splines (Fig. 2). When the driving cogs spin faster than the driven wheel, the SRGs engage and the rider can transmit power to the road. When the driven wheel hub spins faster than the driving cogs, the bicycle is allowed to coast or freewheel (Fig. 3). Initial inspection, coupled with Scanning Electron Microscopy (SEM) revealed fractures of five adjacent gear teeth on one half of the SRG, Fig. 4. While there is a vast amount of empirical data on the failure of spur-gears, bevel-gears, and worm-gears, there is no such database for SRG failures" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000741_robot.2009.5152782-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000741_robot.2009.5152782-Figure5-1.png", "caption": "Figure 5. A maneuver 3 and a backward maneuver 5 enable the robot to make a sharp turn indicated by the knot point P on a path. The shaded area indicates obstacles.", "texts": [ " If is too small so that the maneuver 1 and maneuver 2 patterns cannot be applied to the robot without violating the nonholonomic constraint, the patterns maneuver 3 and maneuver 4 (see Figure 4) can be used to make the turn by reversing the robot. The smaller is, the larger the angle is, and therefore, it is more likely that (4) will be satisfied. The two patterns show alternative ways of achieving the same result. Maneuver 5, also shown in Figure 4, is another alternative pattern to execute a sharp turn by reversing the robot. Although reversing the robot may not meet the requirement of certain turn by itself, it can be a necessary intermediate movement that leads to a correct turn eventually. Figure 5 shows an example. Note that each basic maneuver pattern can be used in two ways, with the robot driving either forward or backward. III. OUR ON-LINE PLANNING APPROACH Our on-line nonholonomic (ON) planner uses the novel maneuver patterns introduced above to find nonholonomic trajectories efficiently to reach a goal configuration based on the rough topological information of a sequence of knot points or positions (e.g., reading from a GPS navigator) and on sensing. It enables simultaneous planning and execution of robot motion in real-time" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001556_ifuzzy.2013.6825416-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001556_ifuzzy.2013.6825416-Figure1-1.png", "caption": "Fig. 1. Standard notation and sign conventions for ship motion description [17]", "texts": [ " Based on the error signal and its first derivative, the fuzzy system will tune the control signal automatically. This study intends to apply this control method for rudder roll stabilization with the consideration of a nonlinear ship model. II. SYSTEMS MATHEMATICAL MODEL A. Ship Model A model of ship has six degrees of freedom (DOF) in motion, consisting of translation motion (position) in three directions: surge, sway, and heave; and rotation motion (orientation) about three axes: roll, pitch, and yaw (see Fig. 1). The two reference frames shown in the figure are the inertial or fixed to earth frame O and the body-fixed frame O0. Regarding to the Society of Naval Architects and Marine Engineers (SNAME) standard notation, Fig.1 also gives the notation describing the position/orientation, force/moment, and linear/angular velocities in six DOFs of ship motion. Marine vessels dynamics can be described by a gen- eral model structure [18] as: vJ )(\u03b7\u03b7 = (1) dchvvRBvRB \u03c4\u03c4\u03c4 ++=+ )(CM (2) where Tzyx ][ \u03c8\u03b8\u03c6\u03b7 = is the generalized displacement vector, Trqpwvuv ][ = is the linear-angular velocity vector, )(\u03b7J is a transformation matrix that depends on the Euler angles ( )\u03c8\u03b8\u03c6 , MRB is the mass and inertia matrix due to rigid body dynamics, and CRB(v)v is the coriolis and centripetal forces and moments due to rigid body dynamics" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000017_tmag.2007.916241-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000017_tmag.2007.916241-Figure6-1.png", "caption": "Fig. 6. Different conducting position when WidB 2) identical substructures are connected to P vibrating central components. The central components can rotate at different constant speeds that can be calculated from the rotation speed of the reference frame {e1, e2, e3}, \u03a9, multiplied by a known scalar. In planetary gears, for example, the rotation speeds of the sun gear and the ring gear can be expressed by the rotation speed of the carrier multiplied by gear ratios [13]. In the following analysis, each central component has three translational vibrations (xc, yc, and zc) and three rotational vibrations (\ud835\udf01 c, \ud835\udf02c, and \ud835\udf07c) along e1, e2, and e3, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000610_s00466-010-0508-y-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000610_s00466-010-0508-y-Figure1-1.png", "caption": "Fig. 1 Generic 2-D frame element i (a) generalized stresses, (b) generalized strains", "texts": [ " This implies that the scalar product of generalized stress and strain vectors represents virtual work in the element concerned and is invariant with respect to rigid body motion. More explicitly, the stress resultant or generalized stress is obtained by integrating the assumed stress field across the section. Similarly, the associated strain resultant is computed by a suitable kinematic assumption associating each physical component of strains with displacements in global coordinates. For a generic self equilibrated 2-D frame element i in Fig. 1, the generalized stress vector si \u2208 3 contains the three (independent) two end moments (si 2, si 3) and one axial force (si 1). The corresponding generalized strain vector qi \u2208 3 then consists of the corresponding end rotations (qi 2, qi 3) and axial deformation (qi 1), which are explicitly taken as summation products of the generalized elastic strain vector ei \u2208 3 and the generalized plastic strain vector pi \u2208 3. The effect of shear force is ignored, and thus it does not contribute to the internal work" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000334_s11249-010-9628-y-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000334_s11249-010-9628-y-Figure2-1.png", "caption": "Fig. 2 Sectional 3D view of test cell assembly. 1 Brass contact with cantilever spring, 2 securing nut; 3 electrical insulating sleeve, 4 test disc, 5 heating oil chamber, 6 band heater, 7 negative electrode, 8 guard ring, 9 8 mm diameter bearing ball, 10 thermocouple, 11 cover", "texts": [ " The motivation behind this development was to allow the study of boundary film formation and growth, and their effects on friction and wear in a realistic tribological context. The objective of this paper is to introduce the new method, along with pilot test results using sunflower oil. The study represents the first attempts at monitoring the thickness of boundary films in situ between sliding steel surfaces over long sliding distances. The experimental setup is shown in Fig. 1. The setup is basically that of a ball-on-disc tribometer. The main difference is that the ball holder was modified to act as the capacitance probe (see Fig. 2). The rotating disc assembly is belt driven by an AC servomotor, giving a range of 1\u2013 1000 rpm at the disc. The capacitance and resistance measurements were made simultaneously using a GWInstek LCR 821 meter. COF was measured using strain gauges bonded onto the load cantilever arm. The sensitivity of the friction force measurement is about 0.632 N/V, and provides frictional measurement with an accuracy of 0.002 at 1 kg load. Wear was continuously monitored by measurement of the wear track width via a Dino-lite AM413ZT digital microscope fitted above the disc", " Temperature control was achieved by the use of a band heater (6) clamped around the assembly housing and a thermocouple (10) mounted in the heating chamber (5), where silicone oil serve as the heating oil to provide uniform heating. The lubricant cell was sealed from the heating chamber by an \u2018O\u2019 ring, to prevent cross contamination of the test lubricant with the heating oil. This setup allows the cell to be removed easily for cleaning after the test. To convert capacitance data to film thickness, the dielectric constant of the lubricant at ambient and contact pressure must be known. This can be measured using the same capacitance probe shown in Fig. 2. However, the guard ring of the capacitance probe was re-wired as the negative electrode, and the bearing ball was replaced with a spherical electrical insulator, such that there was a parallel gap of approximately 1 mm between the flat surface of the guard ring and the top side of the test disc. First, the capacitance of the air gap, Cair was measured, where eair is taken as 1.00059. The test lubricant was then slowly poured into the cell until the gap was fully flooded and the capacitance of the test lubricant is then measured" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001232_j.engfailanal.2013.03.009-Figure15-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001232_j.engfailanal.2013.03.009-Figure15-1.png", "caption": "Fig. 15. The solid deformable SRG created using Abaqus\u2019 3-D CAD package. Note that this part differs from that shown in Fig. 2 in that there are fillets at both the gear root and gear tip, and that the splines were removed.", "texts": [ " Since fractography showed that failure initiated at the root of the gears, we reduced the geometry of the part to the gear teeth and the gear base. This was accomplished by replacing the splines on the outside of the gear base with a smooth cylindrical surface. As we were interested in the stress concentrator at the gear root, the fillet due to machining was included in the model (64 lm). A fillet of the same radius was placed at the top of the gear to allow for successful mating of the two gears in the Assembly module of Abaqus (see Fig. 15). Based on test runs with simple loading configurations, we chose to use a mesh of 3-d fully integrated tri-linear elements that are highly refined in the region of interest. Linear element formulations presented the most efficient route to estimate the peak stresses at the gear root. In order to accommodate the strange contours of these gears, and maintain a high quality mesh, both wedge and hexahedral elements were used. Because the load is transmitted to the hub and, hence, the tire, through the splined edges on the outside of the SRG, a traction equivalent to the torque applied at the cogs is distributed over the area of the outer most diameter of the driving SRG" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000507_00368791011051062-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000507_00368791011051062-Figure1-1.png", "caption": "Figure 1 Fixed-pad thrust bearing", "texts": [ " After a quarter century, Gu\u0308mbel and Everling (1925) demonstrated that the Reynolds equations could be used in the design and calculation of slider bearings (Gu\u0308mbel, 1914). Falz (1926) put these equations in more relevant form for applications. After Falz\u2019s studies, many studies were published concerning the theory and application of hydrodynamics on slider bearings. Recently, it is possible to analyse pressure and temperature variations of the lubricant film in slider bearings, by using conservation equations which require numerical or graphical solution methods and have analytical solution under simplified assumptions only. Figure 1 shows a fixed-pad thrust bearing consisting essentially of a runner sliding over a fixed pad. The lubricant is brought into the radial grooves and pumped into the wedgeshaped space by the motion of the runner. Full-film, or hydrodynamic, lubrication is obtained if the speed of the runner is continuous and sufficiently high, if the lubricant has the correct viscosity, and if it is supplied in sufficient quantity (Shigley et al., 2004). Non-dimensionalization is preferred to put the equations into a more general form and to reduce the number of parameters which affect the phenomena" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001101_j.ijnonlinmec.2013.05.001-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001101_j.ijnonlinmec.2013.05.001-Figure1-1.png", "caption": "Fig. 1. Three-dimensional and end views of a clamped-clamped rod under edge thrust Px constrained inside a tube. (a) Point-line-point contact; (b) three-point contact; (c) two-point contact; (d) one-point contact. Dashed and solid lines represent free-of-contact and line-contact segments, respectively. Black dot represents point contact with the tube wall.", "texts": [ " For a constrained buckled beam under edge thrust, on the other hand, the intermediate steps between the first planar one-point-contact deformation and the final spiral shape are not known. One may wonder whether the deformation evolution for a buckled beam under edge thrust is similar to the one under end twist. This paper intends to find out the answer. The small-deformation theory similar to the one in Ref. [5] is adopted. Feodosyev [3] and Sorenson and Cheatham [4] have found that the final deformation of the compressed buckled beam is in pointline-point contact with the tube wall, as shown in Fig. 1(a). The total length of the elastic rod is l, and the bending stiffness is EI. The inner radius of the cylindrical tube is r. An xyz-coordinate system is fixed with origin at one end O. In Fig. 1 both ends of the rod are clamped and under the action of edge thrust Px. It is assumed that the left end O is space-fixed, while the right clamp D will move to the left a small distance e along the longitudinal direction (x-axis) under the edge thrust. In the point-line-pointcontact deformation as depicted in Fig. 1(a), the elastic rod is in point contact with the tube at point A with x\u00bc l1, and is in line contact with the tube starting from point B at position x\u00bc l2, where l24 l1. The dashed and solid lines represent segments of the deflection curve which are free of contact and in line contact with the tube wall, respectively. The y- and z-axes are defined in a manner so that the coordinates of point A are (x,y,z)\u00bc(l1, 1, 0). C is the middle point at x\u00bc0.5. All the variables described in Fig. 1 are dimensionless. The corresponding physical variables (with asterisks) can be recovered from the following relations: \u00f0xn; ln1; ln2\u00de \u00bc l\u00f0x; l1; l2\u00de; \u00f0yn; zn\u00de \u00bc r\u00f0y; z\u00de; Px n \u00bc EI l2 Px; en \u00bc r2 l e \u00f01\u00de The deformation pattern shown in Fig. 1(a) occurs when the edge thrust is large, and has been investigated thoroughly in Refs. [3,4]. We will not repeat their works here. Instead, we are interested in what happens when the edge thrust decreases. It will be shown that as the edge thrust decreases gradually, the point-line-point-contact deformation evolves to a three-pointcontact deformation, then to two-point, one-point, and finally returns to a straight configuration. When Px is reduced to a certain value, the l2 in Fig. 1 (a) approaches 0.5 and the segment of line contact in the middle shrinks to a point. This deformation pattern involves three contact points at x\u00bc l1, 0.5, and 1\u2212l1. Now point B converges to the middle point C. Whether this scenario is correct has to be examined theoretically. If a solution based on this assumed configuration indeed can be found, then the assumption is confirmed. For this deformation, the rod may be divided into four free-of-contact segments. From symmetry, we only need to consider one-half of the whole length, i" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003927_978-3-030-21755-6_7-Figure2.2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003927_978-3-030-21755-6_7-Figure2.2-1.png", "caption": "Fig. 2.2 The fitting of the VACF-spectrum (circles) with a help of asymptotic expansion (2.63) at 550 K", "texts": [ "15 ps corresponds to the dimer longitudinal vibrations, only observed for T < 400K; (2) the more large and deep oscillation is genetically connected with elastic transversal and longitudinal modes of the hydrodynamic velocity field. This range of negative values for the VACF disappears later, for T > 450K. In [14, 15, 24] it had been shown that the low-frequency asymptote for the spectral density of the VACF for T > 450K is determined by diffusion transversal modes and it is described by the expression: \u03c6 (D) V (\u03c9) = 3Dc [ 1 \u2212 4 3 \u221a 2\u03c0\u03c9\u03c4M ( 1 \u2212 3 2 \u03c9\u03c4M + 3 8 (\u03c9\u03c4M)2 ) + \u00b7 \u00b7 \u00b7 ] . (2.63) The full correspondence of the last to the VACF-spectrum for T > 450K is demonstrated in the Fig. 2.2. Near the triple point the important details of theVACF-spectrumare determined by elastic transversal and longitudinalmodes. In accordancewith [24] their contributions are determined by the formulas: \u03c6V (\u03c9) = 1 2\u03c0 \u221e\u222b 0 dtei\u03c9t ( \u03c6 (t) V (t) + \u03c6(l) s (t) ) , (2.64) where 2 Current Problems in the Quasi-elastic Incoherent \u2026 55 \u03c6(l) s (t) = 3 \u03c0 kBT mL \u221e\u222b 0 du u2 ( cos u \u2212 sin u u )2 e\u2212\u03c3\u03b8(u) u2t/r2L cos ( c u rL t ) (2.66) and p = 1\u2212u2, rL = 2 \u221a \u03bd\u03c4M is the suitable radius of the Lagrange particle (see [15, 24]), \u03c3 = 1 2 [ \u03bd + \u03bb(\u03b3 \u2212 1) ] , \u03bb = \u03c7/\u03c1CP, \u03b3 = CP/CV , where CP,CV are isobaric and isochoric heat capacities and \u03c7 is the thermoconductivity coefficient, \u03b8(u) is the step function" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002016_17452759.2013.812738-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002016_17452759.2013.812738-Figure3-1.png", "caption": "Figure 3. Dimensions (mm) of the reference bluff body.", "texts": [ " Therefore, this work also explores if the simplification in the CFD template for flow analysis around a shuttlecock, effectively a bluff body object, can be sufficient for early stage design work. The CFD template within the framework can be substituted by a more complete and advance flow simulation model in the later prototype refinement stage. However, such simulation models are usually much more demanding on computational power and will not be discussed here. The base profile of the reference bluff body, model A, consists of a cone attached to a cork, with dimensions as shown in Figure 3. This is in accordance with the gapless shuttlecock used by Verma et al. (2013). To evaluate the effect of gaps around the cone, 15 triangular cut-outs, extending 35 mm up the skirt, were formed on the two other CAD models. These two profiles, labelled B and C, were obtained by varying the width (X) and height (H) of the triangular gap while keeping the external dimensions consistent with profile A. The dimensions of the profiles are tabulated in Table 1. The various parameters that will be described were used in the flow simulation template" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003794_1.5112696-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003794_1.5112696-Figure5-1.png", "caption": "FIGURE 5. Methodology of measurement applied for the dimensional analysis: decomposition into simple elements (planes and cylinders)", "texts": [ " This technique uses a spherical probe to touch directly the part to define fundamental entities (plane, cylinder, etc.). The touch probe used for the measurements had a diameter of 2.5 mm. For these samples all the basic geometries were defined by planes (16) and cylinders (2). To define a plane 6 points were touched uniformly along the planes. To define a cylinder, 16 points were touched on 2 circles for the inner and outer diameter. The measures were repeated 3 times for all the samples (see Fig. 5). The surface quality was defined by a surface roughness meter SURFCOM 1400D-3DF. The diameter of the probe used was 2 \u00b5m. The ISO 4288 standard [17] was followed for each measurement. The arithmetic roughness Ra and the total roughness Rt values were recorded for each measured sample. Three measurements on the inner surface of the sample and three measurements on the outer surface were made. In addition, a visual observation of the details of the sample using a digital microscope was performed" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000764_09544062jmes1208-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000764_09544062jmes1208-Figure6-1.png", "caption": "Fig. 6 Configuration of an LGT recirculating roller bearing and section AA along the longitudinal direction", "texts": [ " Except for the linear and exponential profiles, the tangent directions of the straight line and the crowned profile at the intersection point are equal to zero. In this section, the deformation formula of two contacting elastic bodies with spherical surfaces is illustrated. According to Hamrock [18], the curvature sum Rxy and difference are 1 Rxy = 1 Rx + 1 Ry (14) = Rxy ( 1 Rx \u2212 1 Ry ) (15) where 1 Rx = 1 rCx + 1 rPx 1 Ry = 1 rCy + 1 rPy in which rCx , rCy , rPx , and rPy are the principal radii calculated in section 2.1. Since the plate deformation curve in the x-direction is concave (Fig. 6), rPx is negative, and the others are positive. In this study, the superposition method is used to find the stiffness of the crowned roller compressed by two plates. First, the stiffness of the non-crowned roller compressed by two plates is calculated, and the edge deformation of the plate is assumed to be a curved surface with two principal radii, rPx and rPy . Then, the crowned part compressed by two plates is simulated as two contacting elastic bodies with spherical surfaces. Hamrock [18] showed that the ellipticity parameter \u03ba can be written as a transcendental equation relating the curvature differences and the elliptic integrals of the first ( ) and second (\u03b5) kinds as \u03ba = \u221a 2 \u2212 \u03b5(1 + ) \u03b5(1 \u2212 ) (16) where = \u222b\u03c0/2 0 [ 1 \u2212 ( 1 \u2212 1 \u03ba2 ) sin2 \u03c6 ]\u22121/2 d\u03c6 \u03b5 = \u222b\u03c0/2 0 [ 1 \u2212 ( 1 \u2212 1 \u03ba2 ) sin2 \u03c6 ]1/2 d\u03c6 Finally, the maximum deformation at the centre of the contact can be written from the analysis of Proc", " [14], as follows Kn = Pn \u03b4 (18) where Ps is the load applied on the non-crowned part \u03b4 = ln ( 4H e\u22121/[2(1\u2212\u03bd1)][(1+(H/c)2)]1/2 ) (19) where = 2 ( Ps c ) ( E \u2032 \u03c0 ) (20) From Hertz\u2019s equation, the stiffness contribution Kc of the crowned part can be written as Kc = Pc \u03b4 (21) where Pc is the load on the crowned part. This load is generated from the crowned part compressed by two plates, which is simulated as two contacting elastic bodies with spherical surfaces. From the investigation conducted by Horng et al. [13], the deformation of point A, A, on the plate surface shown in Fig. 6 is \u223c 7/10 of the maximum plate deformation, y=0. Since it is difficult to find a theoretical solution for this deformation, an empirical form shown in equation (22) is used to obtain the deformation \u03b4c between the plate and crowned part of the roller \u03b4c = \u03b4r 2 + 0.7 y=0 = \u03b4 2 \u2212 0.3 y=0 (22) where y=0 is the plate deformation at y = 0, calculated using equation (9), and \u03b4r is the total deformation of the roller. According to equation (17), the load of the crowned part is obtained as follows Pc = \u03c0\u03baE \u2032 [ 2\u03b5R 9 ( \u03b4c )3 ]1/2 (23) Using the superposition method, the stiffness K of one crowned roller can be written as K = Kn + 2Kc = Ps + 2Pc \u03b4 (24) The stiffness shown in equation (24) is not an explicit form of the total applied force; thus, the total displacement \u03b4 is defined first. Using equations (19) and (23), one can obtain Ps and Pc. Finally, equation (24) can be used to evaluate the roller stiffness. In other words, one crowned roller is modelled as a spring and the spring constant can be calculated using equation (24). Rollers compressed between a carriage and a profile rail are simulated as springs with parallel connection, as shown in Fig. 6(a). Each discrete normal spring was modelled as a crowned roller compressed between two plates, as shown in Fig. 2. In this study, two plates are introduced to simulate the depth effect of a carriage and a profile rail. In an LGT recirculating linear roller bearing without an external force, the normal force is applied to each contact point of the raceways and the rollers in the load zone, with normal elastic deformation at each contact point. Thus, each contact point has the characteristics of a spring. Since the springs exist at an interval s of the loaded rollers, they are named \u2018discrete normal springs\u2019. The carriage is supported by the discrete normal springs in the load zone of each circuit of the recirculating rollers. The discrete normal stiffness is denoted by K , as shown in Fig. 6(b). When the LGT recirculating linear roller bearing is driven at a constant velocity, each contact point of the raceways and rollers constantly changes. Moreover, the total number of the rollers in the load zone varies. As a result, the location and number of the discrete normal springs change, and stiffness K also varies. These changes should be considered in the theoretical analysis of the rigid-body natural vibration of the carriage. However, it is very difficult to consider these changes from a theoretical point of view. In this article, discrete normal springs are replaced by distributed normal springs, which are continuously distributed along the length of the load zone of each roller circulation. Finally, the normal stiffness equation for LGT recirculating rollers with arbitrarily crowned profiles, denoted by KV , can be obtained as [5] KV = (4ZL sin2 \u03b1)K (25) where ZL is the average number of rollers in the load zone in one circuit of the recirculating rollers and \u03b1 is the contact angle shown in Fig. 6(a). From the practical applicative point of view, the stiffness equation for LGT recirculating rollers with arbitrarily crowned profiles can be used to calculate frequency expressions for the rigid-body natural vibration of a carriage for an LGT [21]. For convenience, natural vibration with the translational motion mode along the z-axis is called the vertical natural vibration JMES1208 \u00a9 IMechE 2009 Proc. IMechE Vol. 223 Part C: J. Mechanical Engineering Science at University of British Columbia Library on June 22, 2015pic", "comDownloaded from of the carriage, the natural vibration with the rotary motion mode around the y-axis is called the pitching natural vibration of the carriage, and the natural vibration with the rotary motion mode around the z-axis is called the yawing natural vibration of the carriage. The spring constant k per unit length of the distributed normal springs can be written as k = ZLK lL = KV 4lL sin2 \u03b1 (26) \u03c6, \u03b8 , and \u03c8 are the angular displacements of the carriage around the x, y, and z axes shown in Fig. 6(a), respectively, and the frequency fv of the vertical natural vibration of the carriage, the frequency fp of the pitching natural vibration of the carriage, and the frequency fY of the yawing natural vibration of the carriage are given by fv = sin \u03b1 \u03c0 \u221a klL M (27) fp = sin \u03b1 2\u03c0 \u221a kl3 L 3Jy (28) and fY = cos \u03b1 2\u03c0 \u221a kl3 L 3Jz (29) where M is the mass of the carriage and Jx , Jy , and Jz are the moments of inertia about the x, y, and z axes, respectively. LGT recirculating rollers with arbitrarily crowned profiles are shown in Fig. 1. Due to symmetry, rollers compressed between a carriage and a profile rail are simulated as springs in parallel connection, as shown in Fig. 6(b). Each discrete normal spring was modelled as the crowned roller compressed between two plates. Figure 2 shows this model and its dimensions. The boundary conditions of the model in Fig. 2 are: (a) Y -direction rollers along the leftmost surface, (b) X -direction rollers along the back surface, (c) the same Z-direction displacement applied on the top surface, (d) Z-direction rollers along the bottom surface, (e) contact elements between the roller and plate, and (f) free for other boundaries. For each crowned profile type, two values for the effective thickness H (20 and 100 mm), two values for the crowned length ds (0" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000224_9780470561232.ch4-Figure4.23-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000224_9780470561232.ch4-Figure4.23-1.png", "caption": "FIGURE 4.23. (n + 1) wires.", "texts": [ " By superposition the total flux through the flat surface between the interior edges of the two wires is the sum of the fluxes due to each current: \u03c8 = \u03c81 + \u03c82 = \u03bc0I 2\u03c0 ln d \u2212 rw2 rw1 + \u03bc0I 2\u03c0 ln d \u2212 rw1 rw2 \u223c= \u03bc0I 2\u03c0 ln d rw1 + \u03bc0I 2\u03c0 ln d rw2 = \u03bc0I 2\u03c0 ln d2 rw1rw2 since we must assume that d rw1, rw2 in order for the current to be uniformly distributed over the wire cross sections and for (2.14) to apply. Lines Composed of n + 1 Wires Consider the case of n + 1 wires of radii rwi that are parallel to each other as shown in cross section in Fig. 4.23(a). The (n + 1)st conductor through which the other n currents \u201creturn\u201d is denoted as the zeroth conductor. Figures 4.23(b) and (c) show the calculation of the per-unit-length self and mutual inductances of the line: lii = \u03c8i Ii \u2223\u2223\u2223\u2223 I1=\u00b7\u00b7\u00b7=Ii\u22121=Ii+1=\u00b7\u00b7\u00b7=In=0 = \u03bc0 2\u03c0 ln di0 rw0 + \u03bc0 2\u03c0 ln di0 rwi = \u03bc0 2\u03c0 ln d2 i0 rw0 rwi (4.93a) and lij = lji = \u03c8i Ij \u2223\u2223\u2223\u2223\u2223 I1=\u00b7\u00b7\u00b7=Ij\u22121=Ij+1=\u00b7\u00b7\u00b7=In=0 = \u03bc0 2\u03c0 ln dj0 dij + \u03bc0 2\u03c0 ln di0 rw0 = \u03bc0 2\u03c0 ln di0dj0 dijrw0 (4.93b) Lines Composed of n Wires Above an Infinite Ground Plane Figure 4" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003638_1464419319838773-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003638_1464419319838773-Figure4-1.png", "caption": "Figure 4. Schematic diagram of the waviness model.", "texts": [ " The relationship between the grinding force and the wear flat area has been previously investigated both theoretically and experimentally.5,24\u201326 The linear relationship between grinding forces as a function of wear flat area for AISI 52100 Steel can be represented as follows FH \u00f0 \u00de \u00bc 6:358\u00fe 1:666 0 5 2:5 13:006\u00fe 9:326 2:5 \u00f018\u00de FV \u00f0 \u00de \u00bc 16:818\u00fe 5:764 0 5 2:312 127\u00fe 64:4 2:312 \u00f019\u00de The waviness imperfections of a bearing can be simulated as a sinusoidal function to reflect the periodic nature of such imperfections. The magnitudes of these vibrations depend on the amplitude of the imperfection. Figure 4(a) represents a schematic diagram of the radial waviness on the inner and outer races. The radial waviness on the inner and outer races is modeled using equations (20) and (21), while the axial waviness on the inner and outer races is modeled using equations (22) and (23)22 pii \u00bc Xl\u00bcWO l\u00bc1 Ail cos l !i !c\u00f0 \u00det\u00fe 2 l j 1\u00f0 \u00de=Nb \u00fe il\u00bd \u00f020\u00de poi \u00bc Xl\u00bcWO l\u00bc1 Aol cos l !o !c\u00f0 \u00det\u00fe 2 l j 1\u00f0 \u00de=Nb \u00fe ol\u00bd \u00f021\u00de qii \u00bc Xl\u00bcWO l\u00bc1 Bil cos l !i !c\u00f0 \u00det\u00fe 2 l j 1\u00f0 \u00de=Nb \u00fe il\u00bd \u00f022\u00de qoi \u00bc Xl\u00bcWO l\u00bc1 Bol cos l !o !c\u00f0 \u00det\u00fe 2 l j 1\u00f0 \u00de=Nb \u00fe ol\u00bd \u00f023\u00de where pii and poi are radial waviness amplitudes of the inner and outer races and qii and qoi are axial waviness amplitudes of the inner and outer races in contact with the ith ball", " Also, Ail and Aol are the maximum radial waviness amplitudes and Bil and Bol are the maximum axial waviness amplitudes. In addition, angles il and ol are initial radial waviness phase angles and il and ol are initial axial waviness phase angles. Also, Nb, !c, !i, !o, l, and WO are the number of balls, cage angular velocity, inner race angular velocity, and outer race angular velocity, maximum value of the waviness order, and waviness order, respectively. Subscripts i and o stand for the inner race and outer race, respectively. Figure 4(b) shows a schematic representation of the ball radial waviness. In this representation, the phase angle of the ball waviness in contact with the outer race is assumed to be 180o ahead of the ball waviness in contact with the inner race.22 Therefore, the ball\u2019s radial waviness in contact with the inner and outer race is modeled as follows21 uii \u00bc Xl\u00bcWO l\u00bc1 Cl cos lwbt\u00fe il\u00f0 \u00de\u00bd \u00f024\u00de uoi \u00bc Xl\u00bcWO l\u00bc1 Cl cos lwb t\u00fe =wb\u00f0 \u00de \u00fe il\u00bd \u00f025\u00de where ui is the wave amplitude at any time, Cl is the wave maximum amplitude, wb is the spinning frequency of the ball, and il is the initial phase angle of the ball waviness" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000224_9780470561232.ch4-Figure4.4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000224_9780470561232.ch4-Figure4.4-1.png", "caption": "FIGURE 4.4. Circular loop.", "texts": [ ", l rw), and this simplifies to Lsquare loop \u223c= 2 \u03bc0 \u03c0 [ l sinh\u22121 l rw \u2212 l ln ( 1 + \u221a 2 ) + l \u221a 2 \u2212 2l ] \u223c= 2 \u03bc0 \u03c0 l [ ln ( 2 l rw ) \u2212 ln ( 1 + \u221a 2 ) + \u221a 2 \u2212 2 ] = 2 \u03bc0 \u03c0 l [ ln l rw \u2212 0.774 ] l = w rw (4.20) This tedious derivation will be obtained in a simple and straightforward manner using the concept of partial inductance in Chapter 5. 4.1.2 Circular Loop Next, we determine the loop inductance of a circular loop of radius a lying in the xy plane which is composed of a wire of radius rw, as shown in Fig. 4.4. Again we assume that the (dc) current is uniformly distributed over the cross section of the wire so that for the purposes of computing the flux through the loop surface, we can consider the current I to be contained in a filament at the center of the wire. The magnetic flux density is directed solely in the z direction over the loop, B = Bzaz, and is therefore perpendicular to the surface s that is surrounded by the wire. Once the B field over the surface s is computed, we next determine the total magnetic flux through the surface of the loop with a surface integral as \u03c8 = \u222b s B \u00b7 ds = \u222b a\u2212rw r=0 \u222b 2\u03c0 \u03c6\u2032=0 Bz r d\u03c6\u2032 dr\ufe38 \ufe37\ufe37 \ufe38 ds Note that the integral with respect to r is from r = 0 out to the inner edge of the wires at r = a \u2212 rw as with the rectangular loop", " Once this is completed, the self inductance of the circular current loop is again determined from L = \u03c8 I In Section 2.6 three methods for determining the B = Bzaz field over the loop surface were evaluated. First the Biot\u2013Savart law was the simplest method and gave the result in (2.73): Bz (r) = 2 \u03bc0Ia 4\u03c0 \u222b \u03c0 \u03c6=0 a \u2212 r cos \u03c6( a2 + r2 \u2212 2ar cos \u03c6 )3/2 d\u03c6 = \u03bc0Ia 2\u03c0 \u222b \u03c0 \u03c6=0 a \u2212 r cos \u03c6( a2 + r2 \u2212 2ar cos \u03c6 )3/2 d\u03c6 (2.73) Next, we obtained the B field over the loop surface from the vector magnetic potential of a current loop given in (2.59). That general result in (2.59) specialized for the problem of Fig. 4.4 for the field in the plane of the loop (z = 0) is A\u03c6 = \u03bc0Ia 2\u03c0 \u222b \u03c0 \u03c6=0 cos \u03c6\u221a a2 + r2 \u2212 2ar cos \u03c6 d\u03c6 (4.21) We obtained the magnetic flux density over the loop surface contained by the loop from B = \u2207 \u00d7 A = 1/r[\u2202 ( rA\u03c6 ) /\u2202r] az using the result in (4.21). The magnetic flux density in the plane of the loop (z = 0) is totally z directed (out of the page within the interior of the loop and into the page outside the loop) according to the right-hand rule and is Bz = 1 r \u2202 ( rA\u03c6 ) \u2202 r = \u03bc0I 2\u03c0 r \u222b \u03c0 \u03c6=0 a2 cos \u03c6 (a \u2212 r cos \u03c6)( a2 + r2 \u2212 2ar cos \u03c6 )3/2 d\u03c6 (4", "1: Lloop = 2 \u03c8left side (l, w, rw) + \u03c8top side (w, l, rw) I = \u03bc0 \u03c0 [ \u2212 (l \u2212 rw) sinh\u22121 l \u2212 rw w \u2212 rw \u2212 (w \u2212 rw) sinh\u22121 w \u2212 rw l \u2212 rw + (l \u2212 rw) sinh\u22121 l \u2212 rw rw + (w \u2212 rw) sinh\u22121 w \u2212 rw rw + rw sinh\u22121 rw w \u2212 rw + rw sinh\u22121 rw l \u2212 rw + 2 \u221a (l \u2212 rw)2 + (w \u2212 rw)2 \u2212 2 \u221a (w \u2212 rw)2 + (rw)2 \u2212 2 \u221a (l \u2212 rw)2 + (rw)2 \u2212 2rw ln ( 1 + \u221a 2 ) + 2 \u221a 2 rw ] (4.17) The remaining results in (4.18), (4.19), and (4.20) for a square loop and for loop side lengths greater than the wire radius are obtained from (4.17) and are identical to those obtained with this method. But the method of this section is much simpler since it avoids having to integrate B over the surface of the loop, thereby eliminating one integration. 4.3.2 Circular Loop The circular loop of radius a is composed of a wire having radius rw and shown in Fig. 4.4 and is illustrated for this problem in Fig. 4.11. Again we assume that the current is dc and is uniformly distributed over the wire cross section so that it can be represented by a filament on the axis of the wire. To obtain the magnetic flux through the loop enclosed by the wire surface using the vector magnetic potential method in (4.44), we first obtain the vector magnetic potential along the inner surface of the wire at r = a \u2212 rw. The vector magnetic potential for a circular current loop was obtained in Chapter 2 and given in (2" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003994_s00419-019-01609-x-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003994_s00419-019-01609-x-Figure2-1.png", "caption": "Fig. 2 Finite element model of the flexible beam", "texts": [ " . , Nx \u03c6yi (x) = cos(\u03b2i x) \u2212 cosh(\u03b2i x) + \u03b3i [sin(\u03b2i x) \u2212 sinh(\u03b2i x)] , i = 1, 2, . . . , Ny (10) where \u03b21L = 1.875, \u03b22L = 4.694 \u03b2i L = (i \u2212 0.5)\u03c0, i \u2265 3 (11) \u03b3i = \u2212cos(\u03b2i L) + cosh(\u03b2i L) sin(\u03b2i L) + sinh(\u03b2i L) (12) Substituting Eq. (8) into Eq. (2) yields the deformation displacement of point P{ ux = x (x)A(t) \u2212 1 2B T(t)H(x)B(t) uy = y(x)B(t) (13) where H(x) = RNy\u00d7Ny is the coupling shape function H(x) = \u222b x 0 ( \u2202 T y (\u03be) \u2202\u03be )( \u2202 y(\u03be) \u2202\u03be ) d\u03be (14) 3.2 Finite element method (FEM) As shown in Fig. 2, the FEM is adopted to discretize the deformation fields of a flexible beam. The beam is divided into n elements, and ux1 and uy of any point P within element j ( j = 1, 2 . . . n) are written as the linear interpolation of the deformation of the element node ux1 = N j,1(x\u0304)E j uy = N j,2(x\u0304)F j (15) where x\u0304 is P\u2019s Y-coordinate in the element coordinate system Oj \u2212 X jY j . It is assumed that the element j has a length of l j and that x\u0302 = x\u0304 l j , so that the shape function matrix can be written as N j,1(x\u0304) = [ N11 N12 ] N j,2(x\u0304) = [ N21 N31 N22 N32 ] (16) where N11 = 1 \u2212 x\u0302 N12 = x\u0302 N21 = 1 \u2212 3x\u03022 + 2x\u03023 N31 = l j (x\u0302 \u2212 2x\u03022 + x\u03023) N22 = 3x\u03022 \u2212 2x\u03023 N31 = l j (\u2212x\u03022 + x\u03023) (17) The deformation array of the element node is shown as: E j = [umx1 ukx1 ]T F j = [umy \u03b8m umk \u03b8k ]T (18) where \u03b8m = \u2202uy \u2202 x\u0304 \u2223\u2223\u2223\u2223 x\u0304=0 \u03b8m = \u2202uy \u2202 x\u0304 \u2223\u2223\u2223\u2223 x\u0304=l j (19) It is assumed that Cx j , Cy j are the positional matrices decided by the element number and that E and F are the overall longitudinal and transverse deformation arrays" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002700_s13538-017-0534-8-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002700_s13538-017-0534-8-Figure1-1.png", "caption": "Fig. 1 The two states of wettability that a droplet can assume on a periodic surface. a The Wenzel state, the drop penetrates the surface cavities. b The Cassie-Baxter state, the drop remains on the top of the pillars", "texts": [ "br 1 Departamento de F\u0131\u0301sica, Universidade Federal de Santa Maria, Santa Maria, Brazil Microfluidics for biotechnology, textile lubrication, and self-cleaning are some examples of applications on this field [1, 2]. The inspiration arose in nature, more precisely from the plant Nelumbo nucifera (the lotus), whose leaves have a natural hydrophobicity. The lotus leaf was studied by researchers to reveal its mechanism of water repellency [3\u20135]. Based on the surface structure of the leaf, similar artificial rough surfaces were produced. A drop of water on this type of surface can exhibit two states of wettability: (1) Wenzel state (see Fig. 1a), in which the drop of water penetrates the surface cavities [6], or (2) Cassie-Baxter state (Fig. 1b), in which the drop remains on the top of the pillars, as in the lotus leaf [7]. It is known that the contact angle of a drop placed on a repellent rough surface increases in relation to a smooth surface [3, 8]. The proposed wettability models are described by the Wenzel and Cassie-Baxter equations, respectively: cos \u03b8 = r cos \u03b8Y , (1) cos \u03b8 = fs (1 + cos \u03b8Y ) \u2212 1 (2) where \u03b8Y is the contact angle on the smooth surface of the same material, given by Young\u2019s equation [9]: cos \u03b8Y = \u03b3SG \u2212 \u03b3SL \u03b3LG " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000133_iecon.2009.5415081-Figure19-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000133_iecon.2009.5415081-Figure19-1.png", "caption": "Fig. 19. Dynamic Analysis of Yaw Moment", "texts": [ " In this experiment, the robot switches the support leg without moving forward. Experimental results are shown in Fig. 17 and Fig. 18. Fig. 17 displays the roll orientation without control while Fig. 18 displays the roll orientation with feedback control. Comparing these two cases, we obtained 40% decrease in peak-to-peak values. Another restriction factor during biped walking is upper body motion regulation. Especially, because of the swing leg motion, a certain amount of yaw moment should be compensated. In Fig. 19, dynamic yaw moment analysis is illustrated. During the single support phase, the swing leg moves forward with a certain amount of acceleration. The force which is based on this acceleration generates a moment with respect to the support foot sole center, point O in Fig. 19. This undesired moment may cause support foot to slip, which is a sort of dynamic instability. In our control block, we compensate this undesired yaw moment by waist joint swinging. Let \u03c4l, \u03c4b and \u03c4 are moments that are based on swing leg motion, waist joint and upper body translation motion, their summation respectively. They can be computed as shown below. \u03c4l = 2mld0x\u0308l (18) \u03c4b = \u2212Jb\u03b8\u0308waist \u2212 mbd0x\u0308b (19) \u03c4 = \u03c4l + \u03c4b (20) = 2mld0x\u0308l \u2212 Jb\u03b8\u0308waist \u2212 mbd0x\u0308b (21) In (18)-(21), mb is the upper body mass, x\u0308b is the upper body acceleration, ml is the swing leg mass, x\u0308l is the swing leg acceleration, Jb is the upper body inertia, \u03b8\u0308waist is the waist angular acceleration and d0 is the horizontal distance to the support foot center" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000683_s10764-010-9393-7-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000683_s10764-010-9393-7-Figure1-1.png", "caption": "Fig. 1 The simulated arboreal substrates used in our study: a horizontal ladder (a) and single pole (b). We made both substrates from scaffolding material, consisting of steel tubes 48.6 mm in outside diameter and right-angle couplers.", "texts": [ " Kumakura Laboratory of Biological Anthropology, Graduate School of Human Sciences, Osaka University, Suita, Osaka 565-0871, Japan e-mail: higurasi@hus.osaka-u.ac.jp When animals move quadrupedally in the branches of trees, they face different mechanical challenges, depending on the support they use. Assuming that substrates are small relative to the animals, rigid, level, and cylindrical, an animal that moves on a substrate perpendicular to its own craniocaudal axis may revolve around the support or pitch because of craniocaudal displacement of the body\u2019s center of mass (COM; Fig. 1a; Dunbar and Badam 2000). An animal that moves on a substrate parallel to its own craniocaudal axis may roll because of lateral displacements of the COM (Fig. 1b; Cartmill 1985; Dunbar and Badam 2000; Napier 1967). Nonhuman primates, which interact with trees habitually, rise to the challenges with prehensile hands and feet. Hands with mobile thumbs and feet with divergent big toes can exert an opposing torque to the pitch or roll motion around the support (Cartmill 1985; Lemelin and Schmitt 2007; Witte et al. 2002). We still know little about how changes in substrates affect hand and foot use during quadrupedal locomotion in nonhuman primates. It seems unlikely that the usage of hands and feet is independent of substrate", " Wunderlich (1999) quantified plantar pressures while 2 cercopithecine monkeys and an ape traveled on the ground and on a single elevated pole, and demonstrated similarities and differences in plantar pressure between the substrates. Studying these issues under a controlled experimental condition can shed light on how primates interact with their natural environment. To this end, we collected hand and foot pressure data while a Japanese macaque, a semiterrestrial anthropoid (Chatani 2003), walked on 2 simulated arboreal substrates of different orientations: a horizontal ladder (Fig. 1a) and a single horizontal pole (Fig. 1b). The ladder rungs could be likened to a lateral stem, as described by Dunbar and Badam (2000), and the single pole to a longitudinal stem. Wild, juvenile bonnet macaques (Macaca radiata) select lateral stems preferentially when they climb a tree for flower nectar (Dunbar and Badam 2000). The macaques avoid longitudinal stems, probably because there is relatively little possibility for them to execute mediolaterally stabilizing movements (Dunbar and Badam 2000). Bonnet macaques may resist the toppling pitch moment around the lateral stem by placing hands and feet widely on different branches", " We wrapped the mat with double-faced adhesive tape around the pipe placed at the center of the horizontal ladder and around the center of the single pole. Hereafter, we refer to the pipe to which the pressure-sensitive mat was fixed as the measurement pipe. The angular range of measurability was almost 360\u00b0, or 152.7 mm (the circumference of the pipe). Within this range were the entire lengths of the hand (86.3 mm) and foot (137.0 mm) of the subject. We obtained pressure data at 120 Hz while the Japanese macaque walked at her preferred speed on the horizontal ladder and single pole (Fig. 1). While we recorded the pressure, we also videotaped the Japanese macaque at 30 frames/s from a lateral view using 2 digital video cameras (DCR-HC 96; Sony, Japan). Third and fourth cameras (DCR-TRV 900 and 950; Sony) allowed simultaneous video recording of close-ups of the hand and foot. Following the topography of the hand and foot of other closely related species, such as the baboons studied by Swindler and Wood (1973), we identified the areas of the hand and foot that touched the substrate from close-up images" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002079_zamm.201000228-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002079_zamm.201000228-Figure7-1.png", "caption": "Fig. 7 Model NNC equality of velocities intensity.", "texts": [ " The second case, where the intensities of the velocities are equal, is described by the equation V 2 1 = V 2 2 \u2192 x\u03072 1 + y\u03072 1 \u2212 x\u03072 2 \u2212 y\u03072 2 = 0. (30) For the coordinates x, y, \u03be, \u03c6 the constraints have the form of \u03be \u2212 2l = 0, \u03c6\u0307(x\u0307 sin \u03c6 \u2212 y\u0307 cos\u03c6) = 0. (31) c\u00a9 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.zamm-journal.org ZAMM \u00b7 Z. Angew. Math. Mech. 91, No. 11 (2011) / www.zamm-journal.org 891 This problem, too, could be realized (according to (31)) in two ways: as a holonomic problem, out of which there follows a translatory displacement of the system: \u03c6\u0307 = 0 \u2192 \u03c6 = const \u2013 Fig. 7a, and, as a nonholonomic problem (special sleds of the Chaplygin type) \u2013 for its physical implementation it is necessary to position the edge in the middle of the rod, and alongside the axle of the rod \u2013 Fig. 7b. In both cases, for the selection of generalized coordinates x1, y1, x2, y2 the reactions R1 and R2 of the constraints are located at M1 and M2, bearing the mind that constraint is realized physically at the point M , when R = R1 + R2, Fig. 8. Also, we believe that the displacement is described according to the D\u2019Alembert-Lagrange principle, i.e., according to the equation Ri\u03b4q i = 0. (32) In the third case, where the velocities are perpendicular to each other, the nonlinear nonholonomic constraint has the form of The realization of this type of constraint is carried out by connection the particles by a light structure (\u201cpitchfork\u201d) which permits the distance M1M2 = \u03be = const to be varied" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000260_1.3078202-Figure19-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000260_1.3078202-Figure19-1.png", "caption": "Fig. 19 Calculated load on the drivin Fp and Fp are the loads due to the suction is located below. The total lo sure and contact force.", "texts": [ " These numerical results have been omputed by using Lund\u2019s method 6,12 combined with the reslution of two-dimensional generalized Reynolds equations with he finite element method. 52502-8 / Vol. 131, SEPTEMBER 2009 om: http://gasturbinespower.asmedigitalcollection.asme.org/ on 01/29/201 The first step is to calculate the load on the journal. A specific code has been developed to make this calculation. This program calculates the load on each gearwheel from the geometrical parameters number of teeth, modulus of gears, diameter, and width of gears, etc. and working conditions pressure and rotational velocity . Figure 19 shows the instantaneous load as the sum of the pressure contribution and the contact force. It can be observed that the load is larger on the driven gear. With the load, the equation of motion of the journal, mb 0 0 mb x\u0308 z\u0308 = FT cos FT sin \u2212 wx wz B1 is solved. In Eq. B1 , mb is the mass of the journal-gear set, FT is the load on the gear, and wi is the load due to the pressure distribution on the bearing. The force w on the journal due to the fluid film is linearized with Lund\u2019s method 6,12 . wx wz = wx 0 wz 0 + kxx kxz kzx kzz x z + bxx bxz bzx bzz x\u0307 z\u0307 B2 where wx 0 and wz 0 are the forces in the initial position, kij are the stiffness coefficients, and bij are the damping coefficients" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003123_978-3-319-96728-8_16-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003123_978-3-319-96728-8_16-Figure2-1.png", "caption": "Fig. 2. Online positioning correction (OPC).", "texts": [ " Thus, the movement of the robot towards the next cell is performed without considering such error, causing its propagation and, consequently, its accumulation along the path. OPC is based on the direction the robot must take to reach the next cell considering the path previously calculated by the CA rule. OPC is divided into two possible situations related to the direction of the next cell: cardinal and collateral points. For each situation, the method will use a different approach to make the correction calculus. They are illustrated in Fig. 2 and are explained following. The possible cardinal points of direction are north, south, east and west. The approach to made the correction calculus in such situation is illustrated in Fig. 2(a), where point (1) represents the center of the current cell, the several points (2) represent the center of the tentative cells to where the robot could move to and the several points (A) represent the possible actual positions of the robot within the current cell. From the coordinates of points (1), (2) and (A) corresponding to the current situation, the angle \u03b8 and the distance P are calculated. \u03b8 is the angle that the robot should rotate and P the distance that must be traveled for it to reach the center of the next desired cell (point (2)). Figure 2(b) illustrates the approach for the collateral points, i.e. northeast, southeast, southwest, northwest. It is similar to the approach explained for cardinal points. However, now we also need to calculate point (3), which is used to adjust the computation of the distance to be traveled through a translation operation. The \u03b8 angle is formed by the segment lines (A-3) and (A-2). As shown in Fig. 2(c), to determine the rotation angle \u03b8, it was used the equation of the line that connects (1) and (2). The distance P is given by the segment (A-2). The navigation model used in this work is based on CA rules and thus the environment is discretized in a lattice of cells. Therefore, When the robot moves from its current cell to an adjacent one, this is considered a discrete step of the robot\u2019s trajectory. The proposed correction is not applied at each step since the image acquisition and processing can make the model computationally expensive" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001782_pime_proc_1964_179_008_02-Figure19-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001782_pime_proc_1964_179_008_02-Figure19-1.png", "caption": "Fig. 19. Present design of the casing considered in Figs Id, 17 and 18", "texts": [ " In the new design a pad was cast as shown at C in Fig. 6 and the lifting eye was screwed to this pad. It was found, however, that this created faults at C due to the change of section, and to reduce this mass of metal the Proc Instn Mech Engrs 196445 surface was hollowed out as shown by the dotted line at C . This had only limited success in reducing faults. The use of electro-slag welding for producing this pad is considered later, but at the moment it is proposed to consider the alternative designs shown in Figs 16-18. For comparison, Fig. 19 shows a typical cast casing of the present design. VoI179 Pt I No 2 at Purdue University Libraries on June 4, 2016pme.sagepub.comDownloaded from 48 J. A. ROGERS AND R. C. BREWER Fig. 16 shows a typical casing of present design but with the casing split at A. This split could be made with or without the vertical flange at A and the design lends itself readily to semi-automatic welding. In contrast to Fig. 16, with its valve chest cast with the casing, Fig. 17 shows welding with a flange although the flange may not be necessary in some instances" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001573_00368791311303483-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001573_00368791311303483-Figure2-1.png", "caption": "Figure 2 A misaligned journal bearing", "texts": [ "1 Angle of journal misalignment in bearing caused by shaft deformation under load According to the deformation equation of a simply-supported beam (Timoshenko, 1972), the angle of journal misalignment in bearing caused by shaft deformation under load can be given by: gang \u00bc Pl2 16EsJ \u00f01\u00de where gang is the angle of journal misalignment in the bearing, P is the load acted on the centre of the shaft, l is the length of the shaft, Es is the module of elasticity of the shaft material, and J the inertial moment of cross-section of the shaft. The oil film thickness of the journal bearing is given by: h \u00bc h0 \u00fe dpb \u00fe dTb 2 dTs \u00f02\u00de where h0 is the oil film thickness when not considering the deformation of the bearing surface, dpb is the change of the oil film thickness caused by the elastic deformation of the bearing surface under oil film pressure, dTb is the change of the oil film thickness caused by the thermal deformation of the bearing surface, dTs is the radial heat expansion of the journal surface. As shown in Figure 2, due to the journal misalignment, the axis of the bearing is tilted, and the cross-section of the journal in vertical plane is an ellipse (the results of calculation show that the numerical scale of the difference between the half long axis of the ellipse and the journal radius is the same as the surface roughness of the journal bearing). The oil film thickness of the journal bearing is given by: h0 \u00bc 2R1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe \u00f0tggangcos\u00f0u2 c0 2 aang\u00de\u00de q \u00fe R2 \u00fe e cos\u00f0u2 c\u00de \u00f03\u00de where R1 is the journal radius, R2 is the bearing radius, c0 is the angle between the connecting line of the journal center and the bearing center and the coordinate z at mid-plane of bearing, and aang is the angle between the connecting line of the journal center and the bearing center and the journal rear center-line projection, e and c are eccentricity and angle between the connecting line of the journal center and the bearing center and the coordinate z at the cross-section having y coordinate, respectively", " Assuming that the circumferential temperature variation is negligibly small, the journal can be considered as an isothermal component within the bearing (Khonsari and Wang, 1991). The following integral condition termed \u201cnonet-heat-flow condition\u201d can be numerically satisfied by trial and error to obtain a steady-state journal temperature:Z 2p 0 kf \u203aT \u203az du \u00bc 0 and T jz\u00bch \u00bc T s \u00f09\u00de where Ts is the temperature of journal surface. The viscosity-temperature equation proposed by Reolands is used and CD30 oil is chosen in analysis: h\u00bchaexp \u00f0lnha\u00fe9:67\u00de \u00f01\u00fe5:1\u00a31029p\u00de0:68 T 2138 T a2138 21:1 21 \" #( ) \u00f010\u00de where ha is oil viscosity at Ta. As shown in Figure 2, the components of film force at x and z coordinate are found from: Study on thermoelastohydrodynamic performance of bearing Xiaoyong Zhao, Jun Sun, Chunmei Wang, Hu Wang and Mei Deng Volume 65 \u00b7 Number 2 \u00b7 2013 \u00b7 119\u2013128 Fx \u00bc 2 Z L 0 Z 2p 0 pR2sin u du dy; Fz \u00bc 2 Z L 0 Z 2p 0 pR2cos u du dy The film force F of bearing is then as follows: F \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F2 x \u00fe F2 z q \u00f011\u00de The lubricant flow-rate Q1 from the front-end plane of the bearing and the lubricant flow-rate Q2 from the rear-end plane of the bearing are given by: Q1 \u00bc 2 Z h 0 Z 2p 0 fy h3 12h \u00b7 \u203ap \u203ay y\u00bc0 \u00b7R2du dz0; Q2 \u00bc 2 Z h 0 Z 2p 0 fy h3 12h \u00b7 \u203ap \u203ay y\u00bcL \u00b7R2du dz0 The total end leakage flow-rate of the lubricant is then calculated by: Q \u00bc jQ1j \u00fe jQ2j \u00f012\u00de The frictional force on the journal surface can be computed from: F j \u00bc Z L 0 Z 2p 0 h 2 \u203ap R\u203au ffp \u00fe Uh h \u00f0ff \u00fe ffs\u00de R1du dy \u00f013\u00de where ffp, ffs and ff are shear stress factors" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002854_rpj-01-2017-0014-Figure23-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002854_rpj-01-2017-0014-Figure23-1.png", "caption": "Figure 23 Stacking operation and example results", "texts": [ " In order for good bonding, tests show that the dispensing head, or the slightly sticking out melt at the exit, needs to touch the existing deposition for a short period of time to melt local material so that new deposition can bond onto the existing deposition. Figure 22 Attaching operation and an example result (a) (b) Stacking is dispensing a freeform element on top of an existing deposition with continuous areas of bonding. Deposition over an existing ABS material is rather similar to the deposition of a first layer of material on the base stage. By raising the lower edge of the dispensing head off the surface beneath by a \u201clift-off\u201d distance, as illustrated in Fig. 23 (a), 0.5~1.0 mm used in tests, the new deposition \u201cfalls\u201d on top of the existing materials. Multiple layers of stacking appears to be smooth and parallel (Fig. 23 (b), (c)) and cross-sectioning examination shows no visible seams (Fig. 23 (d)). Stitching is dispensing a ribbon-shaped freeform element and bonding it to an existing deposition at one of its side edges. Stitching multiple ribbons side by side makes a thin-walled surface. The issue of the stitching operation was that the exit of the dispensing head has a side wall of a finite thickness that becomes a barrier between the existing deposition and the new deposition. When stitching is performed with material support underneath the depositions, the issue can be solved by making use of the swell phenomenon of the melt flowing out of the exit and proper positioning of the dispensing head relative to the existing deposition. Figure 24 (a) illustrates a preferred method of operation obtained after multiple tests. The dispensing head takes a \u201clift-off\u201d distance, of 0.0~0.5 mm, from the surface underneath, similar to the situation of Fig. 23 (a), and also a \u201ccut-in\u201d depth, of 0.3 mm measured from the edge of the dispensing head, into the side of the existing deposition. Thus, under the heat from the dispensing head, part of the existing deposition melts and joins the newly dispensed swelled melt just out of the exit to form good bonding. Fig. 24 (b) shows three ribbons stitched into a flat plane. Fig. 24 (c) shows two ribbons stitched together at an angle, which can be a basic operation for forming large curved surfaces. Notes: Lift-off distance between the lower rim of the dispensing head and the surface beneath 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002190_gt2013-95701-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002190_gt2013-95701-Figure7-1.png", "caption": "FIGURE 7. BEAM MODEL OF FINGER (GAP IS SHOWN MAGNIFIED)", "texts": [ " First to simplify loading scheme we apply all gas loads in relative to low pressure Lp terms. This, assuming pressures in the spacers cavities to be constant and equal to Hp and Lp correspondingly, allows us to consider only two gas loads: pressure in the gap determined by the Reynolds equation (1) and pressure in the plane of laminates contact which in general depends on pressure drop p\u0394 , contact pressure q and geometric parameters. Gas pressure in the gap acting on rigid lift pad is replaced by equivalent force g g gR R n= \u22c5 r r applied at the point gP (see Fig. 7). Value of lifting force gR is determined by integrating pressure distribution (see Eqn. (2)); gnr is a unit normal vector constructed at the point gP . Local coordinates of the point of equivalent load application are defined by 1 ( , ) inv g g D z z p z s dzds R = \u22c5 \u222b\u222b % , 1 ( , ) inv g g D s s p z s dzds R = \u22c5 \u222b\u222b % . (3) Pressure drop action (directly in the cut between fingers and through \u201caxial\u201d contact interaction between adjacent fingers) on rigid foot portion is accounted the same way, resulting in one more equivalent force f f fR R n= \u22c5 r r ", " This requires applying additional vector moment 0 g f g gM M M FP R= + = \u00d7 + uuurr r r r f fFP R+ \u00d7 uuuur r . The stick root (cross-section E) is fully constraint. Pressure drop action on flexible finger stick is accounted by distributed loads (force 0qr and, in general, moment 0mr ) applied over the length of the beam. Accounting contact interaction in beam model is not considered in this paper. So we assume 0q p \u03b2= \u0394 \u22c5 rr , 0 0m = rr . Here moving coordinates system \u03c4 \u03bd \u03b2< , , > rrr related with the beam axis in the undeformed state is used (see Fig. 7). As a first approximation we consider that there is no \u201cradial\u201d contact between fingers of the same laminate. Because ratio sc L of a cut width c to finger\u2019s length sL is small, then small deformation theory can be applied. Further small curvature of fingers is assumed. Internal forces 1 2Q N Q Q\u03c4 \u03bd \u03b2= + + rr rr and moments 2 1tM M M M\u03c4 \u03bd \u03b2= + + rr rr in all cross-sections of the beam are found from equilibrium equations which given for a beam with curved axis take form 1 0dN Q dS r \u2212 = , 1 0dQ N dS r + = , 1 1 0dM Q dS + = ; (4a) 2 0tdM M dS r \u2212 = , 2 2 0tdM M Q dS r + \u2212 = , 02 2 0dQ q dS + = , (4b) where S is a natural coordinate set on beam axis in undeformed state; ( )r S is a curvature radius of beam axis. Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 09/19/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 6 Copyright \u00a9 2013 by ASME Equations (4a) describe so called in-plane bending (displacements 1 \u03c4\u03b4\u0394 = , 2 \u03bd\u03b4\u0394 = , rotation angle 3 \u03b2\u03b8\u0394 = ), and ones (4b) \u2013 out-of-plane bending (displacement 4 \u03b2\u03b4\u0394 = , rotation angle 5 \u03bd\u03b8\u0394 = ) and torsion (rotation angle 6 \u03c4\u03b8\u0394 = ) of a curved beam (see Fig. 7). Though Eqn. (4) are given for fingers with arbitrary radius of curvature, in this paper we are interested in circular finger with ( ) constsr S R= = . Integrating Eqn. (4) and using boundary conditions ( ) 00Q Q= \u2212 r r , ( ) 00M M= \u2212 r r , we can obtain internal loads theoretically. Then the motion of end cross-section (F) of finger stick is calculated by using the Mohr\u2019s integrals [11] 1 1 1 1 0 s i i i i s s s s s s M M NN Q Qk R d E J E S G S \u03d5 \u03bd \u03b2 \u03d5 \u0394 \u0394 \u0394\u239b \u239e \u0394 = + +\u239c \u239f\u239c \u239f \u239d \u23a0 \u222b , 1,2,3i = ; 2 22 2 0 i iis t i s t s s s t s M M Q QM M k R d E J G J G S \u03d5 \u03b2 \u03bd \u03d5 \u0394 \u0394\u0394\u239b \u239e \u239c \u239f \u239d \u23a0 \u0394 = + +\u222b , 4,5,6i = , where corresponding unit forces and moments are denoted by index i\u0394 , ( )J \u22c5 , ( )k \u22c5 and sS are stick cross-section parameters, sE and sG are elasticity modules" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003470_s40815-018-0596-y-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003470_s40815-018-0596-y-Figure3-1.png", "caption": "Fig. 3 Reference contours for planar motion, a star outline, b circular outline, c four-leaf outline, and d window outline (unit: lm)", "texts": [ " Tracking error standard deviation (TESD), ESTD: ESTD \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xn k\u00bc1 \u00f0E\u00f0k\u00de EM\u00de2 , n vuut \u00f042\u00de To confirm the improved compensating control strategy, we use four contour shapes [10, 11], i.e., (a) star, (b) circular, (3) four-leaf, and (4) window outlines, to evaluate the performance of control system. With the use of this contour planning method, Hi, Vi and S denote the X-axis direction command, Y-axis direction command, and position increment, respectively. Table 1 lists the four kinds of trajectory planning, and Fig. 3 shows the reference contours. In the experiments, the learning parameters of three control method are selected as: (a) The conventional method (sgn) [2]: r1x \u00bc r1y \u00bc 0:08, r2x \u00bc r2y \u00bc 0:09, gD \u00bc 1, k1 \u00bc 10. (b) The conventional method (sat) [2]: r1x \u00bc r1y \u00bc 0:08, r2x \u00bc r2y \u00bc 0:09, gD \u00bc 1, k1 \u00bc 10, D \u00bc 0:05. (c) The proposed AFSMC method: r1x \u00bc r1y \u00bc 0:08, r2x \u00bc r2y \u00bc 0:09, r3x \u00bc r3y \u00bc 0:07, k1 \u00bc 10, Mf \u00bc Mg \u00bc 20, Mp \u00bc 80. These parameters are determined by empirical rules to achieve the better transient and steady-state response in simulation and experimentation conditions considering the requirement of stability", " Because of the self-tuning AFSMC control strategy, the system provides the better characteristics for curve contour in both axes. The experiment on the circular tracking trajectory is illustrated in Fig. 9c. The curve contour operation is more complicated than that of straight line movement. It is obvious that steady-state response is also better under the occurrence of system parameter variation. The position errors are 12.652 lm of ATE index and 6.70 lm of the associated TESD index. The four-leaf contour is plotted in Fig. 3c, with the motion divided into five parts. The R2 \u00bc 7:5 mm is the curve radius in the four-leaf contour. The experiments on the four-leaf tracking responses and associated four-leaf trajectory are illustrated in Figs. 10a\u2013c. The trajectory response is smooth even at a curve segment and corner point. The transient and steady responses show the improved compensating strategy of the developed system under parameter variations and external disturbances. The position errors are 16.965 lm of ATE index and 13.703 lm of the associated TESD index for four-leaf contour tracking. The window trajectory is designed in Fig. 3d, with the motion divided into eight parts. R3 = 10 mm is the radius of the curve in the window contour. The experiments on the window tracking responses and associated trajectory are illustrated in Figs. 11a\u2013c. The transient response is fast, and the steady-state error is alleviated. The developed adaptive dynamic system can perform asymptotically stable tracking of different moving trajectories with robust control performance. The position errors reach to 60.403 lm of ATE index and 32.572 lm of the associated TESD index for window contour tracking" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001668_j.measurement.2011.10.034-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001668_j.measurement.2011.10.034-Figure1-1.png", "caption": "Fig. 1. Fixed linear stage type (Type I).", "texts": [ " The parameters could be estimated in the case of ncnsnmnd P np \u00fe ndnt \u00f01\u00de The situation in Eq. (1) corresponds the calibration using calibrated artefacts. Meanwhile, when the centers of spheres are not calibrated, the coordinates of centers of spheres is regarded as zero. Then the number of parameters of transformation from coordinate system of physical constraints to world coordinate system is ncns. The parameters could be estimated in the case of ncnsnmnd P np \u00fe ndncns \u00f02\u00de The models of 2D planar parallel CMM are shown in Figs. 1 and 2. In this paper, the CMM in Fig. 1 is called as Type I, the CMM in Fig. 2 is called as Type II. In Fig. 1, three linear stages are fixed on world coordinate system. The end-effecter is connected with three linear stages with each rigid connecting rod. When the end-effecter moves to some position and rotates around a point of endeffecter, three linear stages move and their movements are measured. Type I CMM has 18 kinematic parameters including redundant parameters. The start points of the sliders are x1, x2, x3 and the direction vectors of those are v1, v2, v3. The length of rods are L1, L2, L3. The coordinates of the end-effecter are u1, u2, u3 in the end-effecter coordinate system" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002319_indiancc.2017.7846453-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002319_indiancc.2017.7846453-Figure1-1.png", "caption": "Fig. 1. Cart-Pendulum system", "texts": [ " Lemma 1: [8] The observer gain vector Lo is chosen such that AESO = A\u0303\u2212 LC\u0303m is a Hurwitz matrix, then the observer error e = [ (x\u0302\u2212 x) (x\u0302n+1\u2212 xn+1) ]T , for the ESO is bounded for any bounded g(t). Remark 3: The observer gain Lo and feedback control gain K are selected, such that AESO and ACL are Hurwitz matrices respectively, then the bounded stability of system (6) under the control law (10) for any bounded g(t) and f (x,d(t), t), is guaranteed [19] and the lumped disturbances can be eliminated from the output channel in steady state with the control law in (10) . A dynamic model of cart-pendulum system shown in Fig. 1, is described as follows: W (q)q\u0308+L(q, q\u0307)q\u0307+N(q) = F (12) where, q, q\u0307 and q\u0308 are the position, velocity and acceleration vectors respectively. The cart-pendulum system is described from (12) [15] as follows:[ Wc +Wp Wplcos\u03c6 Wplcos\u03c6 J+Wpl2 ][ x\u0308 \u03c6\u0308 ] + [ 0 \u2212Wplsin\u03c6\u03c6\u0307 0 0 ][ x\u0307 \u03c6\u0307 ] + [ 0 \u2212Wpglsin\u03c6 ] = [ u 0 ] (13) where Wc, Wp, l, g, J, x and \u03c6 are the mass of the cart, the mass of the pendulum, length of the pendulum, acceleration due to gravitational force, moment of inertia of the pendulum, linear displacement of the cart and angular displacement of the pendulum, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000571_1.3601179-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000571_1.3601179-Figure2-1.png", "caption": "Fig. 2 The Mohr circle in ihe xy plane w h i c h s h o w s the relationship between r, ct, 0 and axx, bx 0 > dy 0 (23) velocity gradient relations, equation (13) gives dx ( O = A (g() - s i n 2 The answer to the question just posed is that the determination is possible whenever the coefficient determinant in equation (23) does not vanish" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003734_978-3-030-20131-9_186-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003734_978-3-030-20131-9_186-Figure1-1.png", "caption": "Fig. 1: Elephant trunk robot [4] Fig. 2: Elephant trunk robot configuration", "texts": [ "eywords: Flexible robots, Forward kinematics, General routing Continuum robots consist of a set of flexible links whose movement is characterized by bending the links as opposed to rigid linked robots where the links are actuated at the joints. These robots deform and take shapes of smooth curves during actuation and mimic many biological systems [1]. This feature, along with the capacity to make them miniature and lightweight, has made continuum robots a topic of popular interest in robotics research (see [2] and [3]). One of the earliest continuum robots available in literature is the cable-driven elephant trunk robot (Rice/Clemson robot) shown in [4] (refer Fig. 1). The main part of the robot is a flexible backbone connected by a series of universal joints. On this backbone, a series of spacers is attached with equal spacing between them. The spacer consists of holes through which cables(tendons) can be routed from the base of the robot to the tip of the robot. The cables are fastened only to the topmost spacer of the robot so that when they are pulled from the base-end, the entire robot deforms and can take different shapes. An analysis of workspace of the robot can be found in [5]" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002842_jifs-169402-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002842_jifs-169402-Figure3-1.png", "caption": "Fig. 3. Static model of speed bump.", "texts": [ " This paper established the speed bump model and the triaxial truck dynamics model, based on the mathematical model to study vibration characteristics of the triaxial truck while the triaxial truck passes through a speed bump, and to analyze the reasonable distance between the speed bump and the weighing platform. The weighing platform of expressway generally uses the rubber hump speed bump. The surface profile of the rubber hump speed bump can be approximated thought as the arc, therefore the arc can be used to simulate the shape of the rubber hump speed bump Corr ec ted P roo f [15]. As shown in Fig. 3, it is the static model of the rubber hump speed bump. In the Fig. 3, A is the height of the speed bump, b is the width of the speed bump, o is the center of circle, r is the radius. When the vehicle passes through the speed bump with speed v, the dynamic incentive of the speed bump is xv(t), and the equation of motion is the Equation (9).( vt \u2212 b 2 )2 + (xv(t) + r \u2212 A)2 = r2 (9) r = (b2 + 4A2) 8A (10) According to the Equations (9 and 10), the dynamic incentive of the speed bump xv(t) can be expressed as: xv(t) = \u221a\u221a\u221a\u221a\u221a\u221a \u239b \u239c\u239d ( b 2 )2 + A2 2A \u239e \u239f\u23a0 2 \u2212 ( vt \u2212 b 2 )2 \u2212 ( b 2 )2 \u2212 A2 2A (0 \u2264 t \u2264 b/v) (11) The vehicle dynamics model is a complex spring damper mass system [16], when the vehicle passes through the speed bump, the vehicle vibration system receives the input of dynamic excitation, the vehicle system will generate vibrations under this dynamic excitation, and the degree of vibration is influenced by the vibration frequency, amplitude, strength, direction and duration of the force and other factors" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000146_jp807548s-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000146_jp807548s-Figure2-1.png", "caption": "Figure 2. (a) Sketch of the unstretchable bag described in the text, showing length L of the interior ridge and the length d of the flat section at the free boundary. A generic point P between the two vertices is indicated by a colored dot. The curvature boundary line is labeled by Y. (b) Top: view from the left side of the bag with d close to its maximum value, showing the bending angle R = \u03c0. Bottom: bottom view showing the shape of the boundary and the straight region of length d. (c) Top: end view with the smallest attainable value of R. Length (31/2)L/2 of the sides is shown. Bottom: bottom view of the corresponding free boundary. Distance u between the vertices is indicated. The radius of the two colored semicircles is the b parameter defined in the text. (d) Sketch of the unstretchable bag corresponding to panel c. The two induced vertices are labeled V.", "texts": [ " The sheet chooses that value of d that minimizes the total elastic energy. The bending energy in the two outer sectors favors small d. Small d makes the curvature in the outer sectors as small as possible. The bent regions have a conelike curvature C(r) \u223c 1/r and an associated bending energy (1/2)\u03ba \u222b r dr C(r)2 of order \u03ba log(L/h).12 This energy is asymptotically negligible in comparison with the ridge energy of order \u03baR7/3(h/L)-1/3.16 Evidently, any effect that decreases the bending angle R has a strong influence on the total energy. It is clear from Figure 2 that as the length d decreases from its maximum value L, the bending angle at the ridges decreases from \u03c0. Thus the optimal value for d is zero. The flat region becomes an isosceles triangle whose boundary vertex is equidistant from the two imposed cone vertices. Having decreased d to zero, it is possible to decrease R still further by spreading the boundary vertices further apart. This decreases R at the cost of extra bending at the boundary vertices and the four curvature boundary lines (marked by Y in the figure) connecting these vertices to the two interior vertices. Evidently, this spreading must increase until the cost of this high curvature is comparable to the ridge energy saved by reducing R. This means that the curvature at the curvature boundaries must become arbitrarily large compared to 1/L. Thus as h/Lf 0, the sheet must approach the shape of a tetrahedron which is flat everywhere except at the central ridge line and the four curvature-boundary lines Y, as shown in Figure 2d. Since we have chosen a height equal to 31/2/2L, the edges of this triangle all have length L and the bending angle R0 given by cos(R0/2) ) 1/31/2. Thus the energy incentive to reduce the bending angle of the central ridge has induced four other ridgelike structures terminating at the boundary. Our goal is to characterize the energy and sharpness of these \u201cinduced edges\u201d. We first analyze the energy of such an edge without allowing stretching. This energy diverges as its bending angle approaches R0 and the edge curvature diverges. Using this energy, we find the optimum curvature and energy of the edge. The induced edges described above are created by forcing from the central ridge; the ridge is external to the induced edges of interest. We thus simplify our treatment by replacing the central ridge with an external force acting to decrease the central angle R. Specifically, we exert equal and opposite point forces F at the induced vertices marked V in Figure 2d. Labeling the distance between the points V by u (Figure 2c), the energy associated with F is evidently Fu. We may now consider the shape of the induced edge in the unstretchable limit. Evidently, the length of the lower boundary imposes an upper limit on u: u < L. Being unstretchable, the surface near the induced edge is conical, That is, any point of the induced edge at a radial distance r from its vertex has a transverse curvature proportional to 1/r. This curvature depends on the polar angle \u03b8, the angular distance to the edge line. We thus denote the transverse curvature as c(\u03b8)/r", " The outer radius is the length L of the edge; the inner radius is of the order of the thickness; we denote it as a. Thus finally, Ec f (1/2)\u03ba log(L/a)cR0 We now determine c in terms of the main bending angle R. It is convenient to use the length coordinate u defined above and consider first the shape of the free boundary line of length 2L connecting the two vertices V. In the limit of interest, all but a small segment of this line is straight, and L - u \u2261 \u2206u is much smaller than L. The curved part of this boundary is approximately a semicircle of radius b at each vertex, as indicated in Figure 2c. In increasing \u2206u from 0, a segment of length \u03c0/2 b becomes bent to form one-half of the semicircle. The vertex is a distance b beyond the center of this quadrant. In order for the total length of the boundary to be unchanged, the vertex must move a distance \u2206u ) 2(\u03c0/2 - 1)b. The bending angle R is the complement of the apex angle of the triangle in Figure 2c; thus (1/2)u/((31/2)L/2) ) sin((\u03c0 - R)/2). Thus for R f R0, we can express \u2206u / (31/2L/2) ) cos((\u03c0 - R0)/2)\u2206R. This simplifies to \u2206u/L ) 2b/L (\u03c0/2 - 1)-1 ) 2-1/2\u2206R The curvature c is readily expressible in terms of the quadrant radius b. The semicircular boundary is the merger of two conical sectors, aimed at the two internal vertices. We ignore any possible elastic interaction between these two cones and simply presume that each quadrant forms the end of one sector. The quadrant, when projected along the radial direction, is an arc of principal curvature c/r" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003298_icelmach.2018.8506767-Figure22-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003298_icelmach.2018.8506767-Figure22-1.png", "caption": "Fig. 22. Contour plot of dxx vs. slip vs. vy (note vx = 0, so slip is analogous to \u03c9m)", "texts": [ " When the rotor\u2019s surface velocity matches the x velocity, the damping is minimized to produce more stable dynamics. The non-linear behavior means a more compute-intensive algorithm is required for re-calculating dxx during run-time, rather than a linear interpolation. Steady-state cruising and mild to moderate braking will keep the EDW in the stable region. Heavy acceleration and emergency braking will push dxx towards instability. Fig. 21. Plot of dxx and Fx vs. vx when (vy, vc) = (0,10) m/s The contour plot in Fig. 22 shows the relationship of dxx with respect to slip and vy. While slices with respect to slip are non-linear, slices with respect to vy are only weakly nonlinear and for control purposes may be approximated as linear. Reduced slip magnitude and larger vertical velocities affect the stabilization on dxx. During operation one would expect slip to be moderately large, which would lead to a near zero contribution on the x-axis dynamics from dxx. Fig. 23 confirms that while dxx vs. vy is not exactly linear, it could be approximated as linear within a subset of the operating region" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000204_978-90-481-9689-0_48-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000204_978-90-481-9689-0_48-Figure3-1.png", "caption": "Fig. 3 Force balanced configurations when: (a) \u03b3 = 0; and (b) \u03b3 = \u03c0 ; The position or value of two masses are determined for force balance.", "texts": [ " Still each of the four conditions of Eq. (3) must hold to have a force balanced mechanism. When \u03b3 = 0 or \u03b3 = \u03c0 , terms in Eq. (2) can be combined and as a result the four force balance conditions of Eq. (3) are reduced to just two conditions. For \u03b3 = 0 these two force balance conditions are m\u2217 1(l \u2217 1 \u2212 l\u22172)\u2212 (m3 + m\u2217 3)l1 +(m4 + m\u2217 4)l2 = 0 \u2212m3l3 + m\u2217 3l\u22173 + m4l4 \u2212m\u2217 4l\u22174 = 0 (6) and for \u03b3 = \u03c0 these two force balance conditions are m\u2217 1(l \u2217 1 + l\u22172)\u2212 (m3 + m\u2217 3)l1 \u2212 (m4 + m\u2217 4)l2 = 0 \u2212m3l3 + m\u2217 3l\u22173 \u2212m4l4 + m\u2217 4l\u22174 = 0 (7) Figure 3 shows the configurations for both \u03b3 = 0 and \u03b3 = \u03c0 . In this case the position or value of only two masses are determined for force balance, as opposed to the need of the position or value of three masses for the general configuration of Fig. 1b. 415 V. van der Wijk and J.L. Herder For a moment balanced mechanism, the angular momentum of all moving elements is zero [9]. The angular momentum of the mechanism of Fig. 1b can be written as HO = I1\u03b8\u03071 +(I3 + I4)\u03b8\u03072 + r\u22171 \u00d7m\u2217 1r\u0307\u22171 + r3 \u00d7m3r\u03073 +r\u22173 \u00d7m\u2217 3r\u0307\u22173 + r4 \u00d7m4r\u03074 + r\u22174 \u00d7m\u2217 4r\u0307\u22174 = ( I1 + m\u2217 1(l \u22172 1 + l\u22172 2 \u2212 2l\u22171 l\u22172 cos(\u03b3))+ m3l2 1 + m\u2217 3l2 1 + m4l2 2 + m\u2217 4l2 2 ) \u03b8\u03071 +( I3 + I4 + m3l2 3 + m\u2217 3l\u22172 3 + m4l2 4 + m\u2217 4l\u22172 4 ) \u03b8\u03072 +( m3l1l3 \u2212m\u2217 3l1l\u22173 + m4l2l4 \u2212m\u2217 4l2l\u22174 )( \u03b8\u03071 + \u03b8\u03072 ) cos(\u03b81 \u2212\u03b82) = 0 (8) with I1, I3, and I4 being the inertia of the crank and the two couplers, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001082_j.arcontrol.2013.09.003-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001082_j.arcontrol.2013.09.003-Figure4-1.png", "caption": "Fig. 4. (a) Two kinds of critical points can be detected: critical points located outside (1) or inside (2) the manifold Mrob. (b) Feasible points are located finding the closest critical point to Mrob or the critical manifold Mc(1) is pushed to Mrob. (c) In the presence of an other path constraint, a new critical point is detected.", "texts": [ " Each detected critical point adds a normal vector constraint and introduces new variables. In order to solve the NLP (47), the algorithmic solution strategy proposed by Gerhard et al. (2008) is briefly described in the next section. 4.4. Computational issues The strategy for the solution of the NLP (47) involves a four steps algorithm sketched in Fig. 3. Steps (i) and (ii) correspond to the location of the critical manifolds and initialization of normal vector constraints, while (iii) and (iv) involve optimization-based procedures. To illustrate the two first steps, Fig. 4(a) shows two cases to be analyzed: detected critical points are located outside or inside of the uncertain region C, which are illustrated by points (1) and (2), respectively. Once critical points are detected, feasible initialization points satisfying the normal vector constraints (47c) must be found using the procedures proposed by Gerhard et al. (2008) and sketched in Fig. 4(b): find the closest critical point to the robustness manifold, hc(1,1), or push the critical manifold Mc(j) to the robustness manifold Mrob to find a feasible critical point, hc(2,1). Fig. 4(c) illustrates the detection of other critical points when the problem is subject to a second critical manifold. Detection of critical points and initialization of normal vector constraints are implemented using the routines reported by Gerhard et al. (2008). For step (iii), NPSOL (Gill, Murray, Saunders, & Wright, 1986) is used to compute local solutions of the NLP (47), but any other gradient-based NLP solver could be used. This gradient-based solver requires the derivatives of the constraints (47b)\u2013(47d) and of the objective function (47a) with respect to the degrees of freedom of the NLP" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000045_cca.2008.4629597-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000045_cca.2008.4629597-Figure1-1.png", "caption": "Fig. 1. Sample base planar coil array and levitated magnet platform", "texts": [ " A maglev stage developed by Lai, Lee, and Yen [15] also uses a planar array of cylindrical coils to levitate disk magnets, however their system requires 15 magnets and 37 solenoid coils for stable levitation, as separate sets of coils and magnets are used to stabilize each axis of translation and rotation. Our current system levitates a single magnet using a limited number of coils, but the method can be extended without difficulty to arbitrarily large coil arrays and levitated platforms with multiple magnets to increase the planar motion range and lifting capacity, such as pictured in Fig. 1. The coils currently in use in the planar array are approximately 28 mm in diameter and 28 mm high, with 1000 turns of wire and copper cores for effective heat dissipation. Neodymium-iron-boron disk magnets 37.5 mm in diameter and 12.5 mm high with a mass of 125 g and a maximum 978-1-4244-2223-4/08/$25.00 \u00a92008 IEEE. 108 energy product approaching 50 MGOe are used for levitation. Each coil produces a combination of forces and torques in different directions on each magnet in its vicinity. The rotational symmetry of the coils and magnets simplifies the model of the forces and torques generated between them" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002812_imece2017-71685-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002812_imece2017-71685-Figure7-1.png", "caption": "Figure 7 Smaller induction coil used for a heat treating application http://www.pillar.com.", "texts": [], "surrounding_texts": [ "As previously mentioned induction coils can vary drastically in shapes and sizes and they rarely have a repeatable design. The physical design of the coils is purely dictated from electromagnetic thermal analysis design calculations. Everything from the thickness of the tube wall, to the spacing between windings, and the overall size and general shape of the part is all based off of the exact part or parts to be heated and what will work best. Coils can consist of one small unique shape or a large helical coil shape as shown in Figures 7 and 8. Due to this large variation in shape and size the ideal AM process used to create an induction coil may be different depending on what category a coil might fall into. The focus of this section will look at non-helical coils and also helical shaped coils. The overall accuracy is not an issue considering these parts are usually made by hand and the accuracy capability of even the least precise AM process is superior to that of a typical hand-made coil. 5 Copyright \u00a9 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/14/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use There has been successful attempts at creating fully dense high purity copper material using various AM processes including PBF, UAM, and DED [4,5,10,11]. Now the general capability of producing the material must be coupled with that particular AM processes ability to create unique geometries with minimal post-processing. Non-Helical Shaped Coils. The categories within AM best suited to produce the non-helical shaped coils would most likely be DED and UAM due to their ability to quickly create fully dense metal parts with internal channels. The specific DED process would utilize either an electron beam or laser heat source using a wire material delivery system. This allows for a more rapid build rate and these geometries are typically more blockish so it shouldn\u2019t overwhelm the geometrical capabilities of using wire feed. Two of the major drawbacks using wire feed is relatively poor surface finish and accuracy issues, however it is unlikely that either would affect an induction coils overall performance. The UAM process would be another good fit for creating non-helical shaped induction coils. As previously stated this process can quickly create complex shapes with internal channels. The geometries for these types of coils are unique, however they may have enough similarity in most cases in order to create an effective automation setup for this process which is often an issue. Helical Shaped Coils. When dealing with the helical shaped induction coils the AM category that would most likely lead to a high success rate for production would be PBF. Either fiber laser or electron beam would likely work well for this application; the most difficult challenge would likely be keeping the oxygen level low enough as to not affect the quality of the copper parts being printed. The PBF process is more capable of generating free-form shapes with even higher complexity and the powder would help to provide support for the minimal overhangs that would be encountered when creating helical shapes. One other important aspect of printing this geometry would be general print orientation or how what direction the part will be printed in. The DED process using a powder feed mechanism would also be a viable option for helical coils, however the build times may be quite a bit longer compared to PBF. The use of powder and also the number of axis on the machine would likely create a scenario were hollow helical structures could be created. The automation for controlling that process would most likely be quite complicated however. One primary advantage of the DED processes with regard to printing electrically conductive copper is the ability to provide an atmosphere with very little oxygen. Discussion. The more noticeable advantages of utilizing AM technology to directly produce induction coils compared to the current manufacturing method consist of reduced labor costs, a potential time savings that could be extremely substantial, and also an increased possibility on part geometry. Some of the advantages of implementing AM that are not as obvious consist of a design and manufacturing process flow that is entirely seamless. This would consist of designing the coil using a typical spreadsheet calculation program, which defines all of the geometry features. Having this information, a fully defined 3D CAD model could be generated by linking the spreadsheet dimensional information into the CAD file. The CAD file can then be used to analyze and validate the coil design using a CAE software, such as finite element analysis. Finally the CAD file can be used to directly print the coil. It is also worth noting that CAE software can furthermore be used to choose and validate the potential 3D printing parameters and processes to help ensure a successful print will be built. Another major benefit is that all of these factors added together can significantly reduce the time induction coils spend in the testing phase, which can take days to weeks, in order to ensure customer satisfaction will be met. This will further add significant cost and time savings." ] }, { "image_filename": "designv11_29_0002079_zamm.201000228-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002079_zamm.201000228-Figure3-1.png", "caption": "Fig. 3 Model NNC Maslov.", "texts": [ " It should be noted that in the basis of the constraint (6\u2032) (or in (8)) there is the holonomic constraint (1) since the variable appears in that holonomic constraint (non-stretchable rope) only. Therefore, any discussion on variation of the NNC and the reaction of the NNC on the grounds of constraints of the type (6\u2032) or (8), is in fact a discussion about those notions for holonomic constraints, considering that NNC (6\u2032) or (8) is in essence constructed on the holonomic constraint (1), [4]. The form of NNC in the model mentioned above (Fig. 3) is the same as in the preceding case \u2013 Fig. 2, i.e., z\u03072 = c2(x\u03072 + y\u03072). (9) An example of the NNC (it does not refer to the \u201ctype of constraints of the Chetaev type\u201d \u2013 according to the present authors) was given by Novoselov in [6], Fig. 4. This example represents the well-known friction redactor that transmits rotation form the shaft I to the shaft II. The angular velocities \u03c6\u03071 and \u03c6\u03072 are connected by the relation \u03c1\u03c6\u03071 = R\u03c6\u03072, (10) which represents a linear nonholonomic constraint. From the geometrical relation \u03c1 + x = L = const (11) www" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002082_0954409712473961-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002082_0954409712473961-Figure1-1.png", "caption": "Figure 1. The inner surface of the wheel hub is restricted in all directions. The contact force is applied as equivalent pressure proportionally split on two neighbouring elements. The contact area shifts one sector in each analysis step.", "texts": [ " The section on centrifugal and gyroscopic terms in the equation of motion discusses the treatment of gyroscopic and centrifugal terms, and then the economic approach for efficient load identification is discussed. In the section on numerical investigations, numerical investigations are presented for different load cases to study the performance of the algorithm, and to compare the methods, sensitivity to noise and regularization are explored. Finally, conclusions and an outlook to future research are given. A finite-element model of the passenger wheel with a radius of 412 mm is developed in ABAQUS-CAE for dynamic analysis in ABAQUS-standard, as shown in Figure 1. The material properties are chosen close to steel properties: Young\u2019s modulus E\u00bc 210 GPa, Poisson\u2019s ratio \u00bc 0.29 and density \u00bc 7800 kg/m3. The boundary conditions are applied such that the internal hub surface of the wheel is restrained in all directions. Eigenfrequencies and mode shapes obtained from frequency analysis of the finite-element model with the above properties correlates satisfactorily with the results of the experimental modal analysis performed on the passenger wheelset.10 The wheel is partitioned into 72 sectors (see Figure 1) that create 72 element surfaces on the wheel rim on which the contact pressure can be applied. The contact pressure shifts position around the wheel rim in analysis steps. The analysis is performed for one full cycle in 72 analysis steps (ABAQUS-Dynamic-Implicit). In the analysis, eight-node linear brick elements with reduced integration and hourglass control are used. Lewis and Olofsson11 suggested that the contact force between the wheel and the rail typically amounts to a pressure over an ellipsoid surface of 5\u201315 mm in diameter", " Since, in the present investigation, the important measures are the radial strains in a distance sufficiently far from the applied contact force, the contact surface can be larger than the recommended size, and the contact force can be represented by a uniform contact pressure without causing significant difference in the radial strains at the strain gauge positions. The typical element size on the wheel rim is around 40 mm, where the contact pressure is applied at each analysis step. As the force travels over several elements, it is important to have a smooth transition when the force switches elements. The contact pressure is applied on two neighbouring contact surfaces in each analysis step, as indicated in Figure 1. While the amplitude of the pressure on the first surface area a1 is linearly decreasing from 1 to 0, the amplitude of the second surface area a2 increases linearly from 0 to 1 over the step time. In the next analysis step, the two contact surfaces shift one sector, meaning that the surface with increasing amplitude in the previous analysis step has a decreasing amplitude in the new analysis step. In strain gauges, inducing a strain \" results in a change of electrical resistance R of the gauge. This electrical at FLORIDA INTERNATIONAL UNIV on December 24, 2014pif" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003900_ijvd.2019.103593-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003900_ijvd.2019.103593-Figure3-1.png", "caption": "Figure 3 The block diagram describing the proposed nonlinear observer", "texts": [], "surrounding_texts": [ "Theorem 1: If the nonlinear system of equation (1) satisfies Assumptions (1)\u2212(8), an adaptive observer (3) can be designed to estimate the unmeasured states as well as the unknown parameters \u03b8 using online neural network estimator in equation (3) Proof: The stability of the proposed observer is proven using the following Lyapunov candidate function: V = eTPe 2 + W\u0303T \u03b3\u22121W\u0303 2 (5) Hence, the derivative of V yields: V\u0307 = e\u0307TPe 2 + eTP e\u0307 2 + \u02d9\u0303WT \u03b3\u22121W\u0303 2 + W\u0303T \u03b3\u22121 \u02d9\u0303W 2 (6) Substituting the error equation and adopting the update law of the neural network weights found in equations (3) and (4) into equation (6) gives: V\u0307 = (Ace+BW\u0303\u03c3(x))TPe 2 + eTP (Ace+BW\u0303\u03c3(x)) 2 \u2212 (\u03b3\u03c3(x\u0302)\u03d5(y, u)TFe)T \u03b3\u22121W\u0303 2 \u2212W\u0303 T \u03b3\u22121(\u03b3\u03c3(x\u0302)\u03d5(y, u)TFe) 2 (7) rearranging equation (7) gives: V\u0307 = eT (AcP + PAc)e 2 + (BW\u0303\u03c3(x))TPe 2 + eTPBW\u0303\u03c3(x) 2 \u2212 (\u03b3\u03c3(x\u0302)\u03d5(y, u)TFe)T \u03b3\u22121W\u0303 2 \u2212W\u0303 T \u03b3\u22121(\u03b3\u03c3(x\u0302)\u03d5(y, u)TFe) 2 (8) After simplification of equation (8) yields: V\u0307 =\u2212 eTQe \u22640 (9) Therefore the observer is stable in the sense of Lyaponouv. The effectiveness of the proposed observed on state and unknown function is tested on a real word vehicle application." ] }, { "image_filename": "designv11_29_0001796_gt2012-68292-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001796_gt2012-68292-Figure1-1.png", "caption": "Figure 1. Computational Model and Impeller Mesh", "texts": [ " A Area, m2 BcC Constant of 189 C Clearance (mm) or damping coefficients (kN\u00b7s/m) Dc Impeller tip diameter (in) e Eccentricity (m) F Force, kN Hc Impeller tip width (in) HP horsepower M Margin (mm) or inertia (kg) K Stiffness (kN/m) n Node number N Rotating speed(RPM) P Static pressure, kPa Greek Letters \u03c9 Rotor rotating speed (rad/s) \u2126 Rotor whirling speed (rad/s) \u03c1 Density, kg/m 3 Subscript t Tangential xx,yy Direct xy,yx Cross-coupling CFD Modeling, Meshing, and boundary conditions As shown in Figure 1, a 360 degree impeller with front seal model was studied. This impeller is Solar's C51 compressor B2 impeller. A structured mesh for impeller was generated by using Tascgen, a mesh generator developed for Solar Turbines Inc.. The mesh size per impeller passage is 187395 (I*J*K=155*39*31). I is in the direction from inlet to diffuser; J is circumferential direction; K is from hub to shroud. The cavity mesh can be generated as unstructured or structured mesh. The unstructured mesh is mostly used for the seal calculations since it is relatively easier to generate for the complex geometry like the seals" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003154_j.jsv.2018.08.016-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003154_j.jsv.2018.08.016-Figure2-1.png", "caption": "Fig. 2. An example of a cyclically symmetric system with one vibrating central component and one non-vibrating central component.", "texts": [ " Because the system is brought into self-coincidence by rotations about the symmetry axis by integer multiples of the substructure spacing angle, the operator D relating q and F is invariant if q and F are simultaneously rotated by integer multiples of the substructure spacing angle. In the following discussion, this idea is illustrated when proving the properties of submatrices in D, which is achieved by analyzing the same symmetric system using different reference frame definitions. Meanwhile, it is also proved that the central components must have certain physical properties to be compatible with the full system symmetry. To illustrate the properties of Dss, Dcc, Dcs, and Dsc, an example system is given in Fig. 2. N equally spaced point mass substructures are connected to a vibrating central component. The substructures and the vibrating central component are installed on a non-vibrating rotor that rotates at constant speed \u03a9. The ith substructure has three translational vibrations: the radial motion ri along ei 1 , the tangential motion si along ei 2 , and the (out-of-plane) axial motion ui along ei 3 . Each pair of neighboring substructures are connected by springs kss and kss,a. Each substructure has mass ms, and it is isotropically connected to the non-vibrating rotor through springs ks, and connected to the vibrating central component through springs kcs,r, kcs,t, and kcs,a", "s(k) = 0, k = 2, 3,\u2026 ,N \u2212 2, (55) where the ith eigensolution, (\ud835\udf06(i)(k), ?\u0302? (i) s(k) ), is identical for all the N \u2212 3 selections of k. Therefore, all the eigenvalues consist of L pairs of eigenvalues with degeneracy N \u2212 3. Such analysis and conclusions about eigenvalue degeneracy also exist in Ref. [33], although that work considers the central components having in-plane degrees of freedom only. For systems with coupling between the substructures, the above eigenvalue degeneracy is not expected. The eigenvalue problem of the example system in Fig. 2 is solved with the parameters in Table 1. The imaginary parts of the eigenvalues are shown in Fig. 4 and Table 2. The number of substructure modes (k = 2, 3) for the example system with L = 3 and N = 5 matches the above derivation: there are L \u00d7 (N \u2212 3) = 6 pairs of substructure modes. The eigenvalues solved from the reduced eigenvalue problems match those from the full eigenvalue problem (Fig. 4). Fig. 5 illustrates two substructure modes (mode 10 and 11) of the example system. The central component has zero modal deflections, while the motions of all substructures are identical in magnitude" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003998_embc.2019.8856836-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003998_embc.2019.8856836-Figure1-1.png", "caption": "Fig. 1. Reference for the positions of the elbow", "texts": [ " The EMG system (FreeEMG, BTS) had a sampling rate of 1KHz with 16 bit resolution, and the angle of the elbow joint was acquired by the IMU at a rate of 1000 samples per second. 978-1-5386-1311-5/19/$31.00 \u00a92019 IEEE 5366 The volunteers were asked to apply the maximum force possible to flex the elbow while it was held in the 90o position, this procedure was necessary to determine the Maximum Voluntary Contraction (MVC). After this, each subject was asked to perform 5 flexion and extension movements starting from 50o and going up to 140o with a frequency of 0.5Hz. The positioning of the elbow is shown in figure 1. Finally, the subjects were asked to flex the elbow during 1 second and then hold the forearm at 140o for a further 1 second, to then extend the elbow also during 1 second and, then kept the forearm at 50o for 1 second. Continuous and intermittent motion tests were performed in three different situations: without load, with a load of 1.5 Kg and with a load of 3 Kg. Four procedures were used to process the EMG signals as in [5]: a second-order, high-frequency Butterworth filter with a cutoff frequency of 30 Hz was applied to remove motion artifacts" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003099_0142331218783242-Figure10-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003099_0142331218783242-Figure10-1.png", "caption": "Figure 10. Free-body diagram of 3-DOF helicopter.", "texts": [ " Furthermore, by comparing Figures 1\u20132 and Figures 7\u20138, the superiority of the proposed control method of this paper can be seen. Example 2 As shown in Figure 9, the instrument used in the experiments is a double-propeller helicopter, the Boeing CH-47. When the helicopter is at different heights, over different terrains or encounters different climates, the dynamics model of the helicopter system will experience greater changes. Based on this idea, we use a 3-DOF (three degrees of freedom) experimental helicopter to simulate the CH- 47\u2019s system dynamics model switch. Figure 10 shows a 3-DOF experimental helicopter produced by the company Quanser. In this part of the simulation, the elevation axis is used to simulate the Boeing CH-47 helicopter ascending and descending. Therefore, the elevation axis of the 3-DOF helicopter is considered, and the dynamic equation of the elevation axis is given below (Meza-Sa\u0301nchez et al., 2015): JY \u20acY= fC _Y kf sin (Y)+ cos (C)(Vf +Vb)+wY, \u00f075\u00de where Y and C indicate the elevation angle and pitch angle of the 3-DOF helicopter, respectively, JY = 0:91 kg m 2 is a moment of inertia of elevation axis, fY indicates the viscous friction level constant, kf represents the force constant of the motor/propeller combination, Vf and Vb indicate the voltage of the front motor and the back motor, and wY represents the external perturbation to the 3-DOF helicopter system" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002803_6.2018-1851-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002803_6.2018-1851-Figure1-1.png", "caption": "Figure 1: Vertical and forward mode of the Biplane-Quadrotor UAV", "texts": [ " The design is based on the IC engine powered quadrotor work carried out by Abhishek et al.12 at IIT Kanpur. While significant work has been done on the design and aerodynamic analysis of the quadrotor biplane configuration, systematic control design has not been carried out. The control design is critical as the Biplane Quadrotor configuration is statically unstable. Since it does not have any surface that generates restoring moments, therefore it requires autopilot for stabilization in both hover and forward flight modes. The schematic of the vehicle is shown in Fig 1. Much of the early work on hybrid UAVs was concerned with developing individual controllers for different flight regimes and mostly linear controllers for transition between them.13 However, the most challenging aspect of these hybrid UAVs is actually the transition from the hover mode to forward flight mode and vice versa while considering the nonlinear dynamics. Many previous approaches involved a stall and stumble profile aimed at tossing the airplane between two different domains and working with linearized approximations" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000677_1953563.1953571-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000677_1953563.1953571-Figure4-1.png", "caption": "Figure 4: 2-segment symmetries in a 8-size ring.", "texts": [ " 1: if the four robots do not form a final arrow and the configuration is distinguishable from Configurations (b) and (d) in Figure 2 then 2: if the largest segment has a size strictly less than four and is unique then 3: begin 4: if I am an isolated robot then 5: Move toward the unique largest segment by the smallest hole having me and an extremity of the segment as neighbors; 6: end 7: else 8: if the configuration contains a 4-segment then 9: begin 10: if I am not located at 4-segment extremity then 11: Try to move toward my neighboring node that is not an extremity of the 4-segment; 12: end 13: else 14: if the configuration contains an arrow then 15: begin 16: if I am the arrow tail then 17: Move toward the arrow head through the hole having me and the arrow head as neighbor; 18: end 19: else 20: if the ring-size is 6 then 21: See Figure 2, Configuration (a); 22: else 23: if the ring-size is 7 then /\u2217 there are two 2-segments \u2217/ 24: begin 25: if I am neighbor of the largest hole then 26: Move through my neighboring hole; 27: end 28: else /\u2217 the ring-size is 8 \u2217/ 29: if there are two 2-segments then 30: See Figure 4, Configurations (a) and (e); 31: else /\u2217 there are four isolated robots \u2217/ 32: See Figure 5, Configuration (a); THEOREM 1. Algorithm 1 is a probabilistic exploration protocol for 4 robots in a ring of 5 nodes. any initial configuration in rings of size 6 to 8 matches one of the following cases: (1) the configuration contains a 4-segment; (2) the configuration contains a 3-segment and one isolated node; (3) the configuration contains a 2-segment and two isolated nodes; (4) the configuration contains two 2-segments; (5) the configuration contains four isolated nodes", " In this case, it remains to show that the protocol correctly operates when the initial configuration contains either two 2- segments or four isolated nodes. Figures 4 and 5 describe the behavior of our protocol starting from a configuration that contains two 2-segments and four isolated nodes, respectively. These figures can be seen as an automaton: - Configurations are the states of the automaton. - Bold arrows between configurations represent possible transitions. (The transition \u03b3 7\u2192 \u03b3\u2032 means that any configuration indistinguishable with \u03b3\u2032 can be reached from any configuration indistinguishable with \u03b3.) - Configurations (a), (e) in Figure 4, and Configuration (a) in Figure 5 are initial states of the automaton. Any configuration that contains either two 2-segments or four isolated nodes in a ring of size 8 is indistinguishable with one of those configurations. - Below any configuration having no outgoing transition, we explain what robots have to do. In any configuration, we show how robots must behave using arrows: dashed arrows represents Try to move actions. When there are two possible directions for a robot, this means that if the robot is activated, the edge it will traverse is chosen by the adversary. First, we can observe that there is no ambiguity between the process described in Figures 4 and 5 and the rest of the protocol. We can then remark that starting from Configurations (a), (e) in Figure 4, or Configuration (a) in Figure 5, the system leaves configurations of Figures 4 and 5 only when the system reaches a configuration containing either a 3-segment and one isolated node or a 2-segment and two isolated nodes: Configurations (c), (d), and (g) in Figure 4 as well as Configurations (c), (l), (n), (o) in Figure 5. Let Cgood the set of all these configurations. From any configurations in Cgood, robots execute Lines 2- 18 in Algorithm 1 and by Lemmas 1 and 4, the exploration is achieved a finite expected time. Consider now a configuration \u03b3 in Figures 4 or 5 that is not in Cgood. In any configuration \u03b3, there is at least one robot that executes a Try to move if activated and every robot either stays idle or executes Try to move if activated. So, in any configuration, there is a strictly positive probability that only one robot moves despite the choice of the scheduler" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001510_vss.2012.6163470-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001510_vss.2012.6163470-Figure2-1.png", "caption": "Figure 2. Aerodynamic forces and moments on airfoil", "texts": [ " A simulation example is considered to illustrate effectiveness of proposed sliding mode controller. And finally a conclusion with an appendix for is given to explain variation of aerodynamic coefficients and flapping phenomena more clearly. II. NONLINEAR LONGITUDINAL AIRCRAFT DYNAMICS Consider a conventional aircraft configuration as shown in Figure 1 with a jet-engine/propeller just below wings. The aerodynamics lift (L) and drag (D) forces, pitch moment (M), (\u03b8) pitch angle, and angle of attack (\u03b1) on a S 978-1-4577-2067-3/12/$26.00 c\u00a92011 IEEE 7 wing are shown in Figure 2. For speed hold problem longitudinal nonlinear flight dynamics are considered by neglecting lateral effects may occur. Then let us build nonlinear model of aircraft by defining flow geometry of flow on an airfoil section: \u03b3 \u03b8 \u03b1= \u2212 (1) and aerodynamic forces and moments which occurs on airfoil are calculated as [9-11]: ( ) ( ) 21 2 D E b L E CD V cS CL \u03b4 \u03c1 \u03b4 \u23a1 \u23a4\u23a1 \u23a4 = \u23a2 \u23a5\u23a2 \u23a5 \u23a3 \u23a6 \u23a3 \u23a6 (2) ( )2 21 2Y M E bM V C c S\u03c1 \u03b4= (3) where \u03c1 is the air density, V is the free stream airflow velocity, c is the chord of the airfoil, Sb is the span of the airfoil, and CL, CD, CM are the aerodynamics coefficients explained in Appendix" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000269_s1068371210020057-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000269_s1068371210020057-Figure1-1.png", "caption": "Fig. 1. Sketch of winding arrangement in rotor grooves of turbogenerators T3FA 110 2U3 and T3FA 160 2U3.", "texts": [ " The main advantages of an ASTG over a synchronous generator are as follows: abil ity to work in modes of the deep consumption of reac tive power with the possibility of unloading form the functions of generators operating in parallel; increasing of the quality of dynamic process flows in the generator itself and the environment of the connected system; and increasing the reliability of the ASTG at the expense of its unlimited operating with one excitation winding in synchronous mode in the power diagram range of P = 105 MW, Q = 0 to P = 110 MW, Q = \u201335 MVA [5] or in asynchronous mode with short circuited excitation windings and simultaneous loading to 80 MW of active and \u201385 MVA of reactive power while maintaining the rated voltage on its wires [6]. The listed properties of ASTGs are due to the rotating magnetic current of the excitation winding regarding to the rotor body and are achieved in a system of automatic excitation winding current control. The appendix contains the main properties of all projects and samples of ASTGs (made by Electrosil) mentioned in the abstract. Based on the results of developing a T3FA 110 2U3, 160 MW ASTG, which is a project with a similar system of excitation windings (Fig. 1) and full air cooling, T3FA 160 2U3 (U = 15.75 kV, cos\u03d5 = 0.95) was created [5]. The power of Key words: asynchronized generators, asynchronized compensators, frequency converters. DOI: 10.3103/S1068371210020057 68 RUSSIAN ELECTRICAL ENGINEERING Vol. 81 No. 2 2010 ANTONYUK et al. the generator is increased at the expense of a propor tional increase in the stator voltage and the active length of the machine at the same diameter of the rotor body. However, at the moment of making a sup ply agreement, the customer suggested that the rated voltage coefficient be changed from 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003467_ica-acca.2018.8609836-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003467_ica-acca.2018.8609836-Figure3-1.png", "caption": "Fig. 3. Diagrama del cuerpo libre del conjunto motor/he\u0301lice.", "texts": [ " Esta pieza cumple con los criterios anteriormente citados y se adapta al servomotor fa\u0301cilmente. Posteriormente se ha realizado el ana\u0301lisis del esfuerzo de torsio\u0301n que actu\u0301a sobre el sistema de transicio\u0301n, el cual es necesario para garantizar el correcto funcionamiento del sistema de transicio\u0301n durante el vuelo. Se considera que los dema\u0301s esfuerzos se disipan en el fuselaje del UAV o son despreciables. El momento de torsio\u0301n se determina con el diagrama del cuerpo libre del rotor con la he\u0301lice como se muestra en la Fig. 3, en donde ~M representa el torque del servomotor de transicio\u0301n, ~Wm el peso del motor, h la longitud del motor, D el dia\u0301metro de la he\u0301lice, \u03c4t el a\u0301ngulo de transicio\u0301n y ~Fa la fuerza del arrastre. El mo\u0301dulo de la fuerza de arrastre puede calcularse como |~Fa| = 0,5 \u03c1 CD A V 2, (1) donde \u03c1 representa la densidad del aire, V la velocidad del viento incidente y CD el coeficiente de arrastre, con un valor igual a 1,17, teniendo en cuenta que el disco se proyecta sobre el plano de incidencia del viento" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003750_0954407019855908-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003750_0954407019855908-Figure1-1.png", "caption": "Figure 1. 3D illustration of the novel multispeed transmission. 3D: three-dimensional.", "texts": [ " Transmission principle of multistage transmission system and assembly modeling of face gears structure The study object is the core component of multistage transmission system, which is the key of realizing speed changing and principal innovation of the whole system. It is necessary to describe the structural characteristics and transmission principle to study the kinematic characteristics of multistage face gears comprehensively. The novel multispeed transmission consists of four master\u2013slave bevel gears, four cylindrical gears, multiple face gears, and four tumblers vertical orthogonal connecting with the output shaft, meshing a planetary gear combination to realize multistage speed, as shown in Figure 1. As shown in Figure 2, the driving bevel gear connects and rotates with the input shaft, and transfers movement and power by meshing with driven bevel gear. The driven bevel gear and cylindrical gear connect together and rotate around the tumbler. Face gears are ring-structures, which are meshing with the cylindrical gears and fixed by the adjusting mechanism. The tumbler is vertical orthogonal connecting with the output shaft. The master\u2013slave bevel gears are arranged in four pairs, and the cylindrical gears are arranged in four pairs to mesh with face gears, which form a planetary gear system to transfer the movement and power by driving the output shaft" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002342_s00339-016-0750-z-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002342_s00339-016-0750-z-Figure2-1.png", "caption": "Fig. 2 Geometrical scheme for the evaluation of energy of Si ions using laser-induced plasma as an ion source by Thomson parabola technique", "texts": [ " During the etching treatment, the purity and concentration of the NaOH solution were controlled regularly and refreshed after 4\u00a0h usage. After etching process, the CR 39 detector was removed from the etchant and then was rinsed with distilled water and was dried in air. After drying, the track density has observed under the optical microscope (Motic DMB Series). Figure\u00a01 shows two streaks of ions. One is the central nondeflected ion beam which consists of neutrals and the second one is the deflected beam of ions which consists of singly charged Si ions. Figure\u00a0 2 is a graphical representation of the Thomson parabola technique. For measurement of the energy of Si ions, the following equation was used [19]: In this equation, e (electron charge) = 1.6 \u00d7 10\u221219\u00a0 C, B (magnetic field strength) = 0.80\u00a0 mT, and M (mass of Si ion) = 4.6638 \u00d7 10\u221226\u00a0kg. R is radius of curvature of ions in the presence of magnetic field and is estimated using following equation [19]: (1)E = e2B2R2 2 M J. (2)R = r [ X + ( X 2 + 1 )1\u22152 ] where, r (radius of magnetic field) = 10\u00a0mm and X is determined by simple equation [19]: here, Y is the distance between detector (CR-39) and central point of magnet which is equal to 30\u00a0mm and d is the displacement of ion track on the surface of CR-39 found by digital optical microscope which is equal to 95\u00a0\u00b5m" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003205_gt2018-77058-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003205_gt2018-77058-Figure8-1.png", "caption": "Figure 8. DARWIN was recently enhanced to display location-specific POD curves at selected nodes in 3D FE models.", "texts": [ " The location-specific POD data are stored in a special node-based POD file. When the file is imported into DARWIN, it automatically creates an inspection region and assigns the location-specific POD curves to their respective nodes in the FE model. The user can then assign a timetable to the inspection region that applies to all nodes in the region. The DARWIN user interface provides visualization of the locationspecific POD curves that are imported from XRSim. It displays the complete location-specific POD curve for selected FE nodes (Fig. 8), and POD contours associated with a specified anomaly size over the entire FE model (Fig. 9). The integrated DARWIN/XRSim interface was applied to PDT and NDE inspection planning of an additively manufactured aircraft engine mount. Component geometry and stress contours associated with the major cycle are shown in Fig.10. Material data and anomaly information were not provided by the manufacturer, so example values were applied to the fracture risk analysis. An example anomaly distribution used in the demonstration is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001076_12.878228-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001076_12.878228-Figure1-1.png", "caption": "Figure 1: Cylinder with boundary conditions (left), cylinder deformed by indentation (right).", "texts": [ " We then perform numerical simulations of indentation experiments on an idealized cylindrical object in order to determine the parameterization of the new model. This mimics the approach that is usually taken in a laboratory in order to characterize an unknown material. An indentation of 10mm is performed at speeds of 1mm/s and 10mm/s. The cylinder is discretized with a hexahedral element mesh that contains 3264 elements and 14921 nodes. No-slip boundary conditions (encastre BCs) are prescribed on the bottom of the cylinder and pressure BCs are enforced in order to simulate the indentation (see Fig. 1). We use the commercial FEM program ABAQUS (Version 6.9-1) to perform the simulations and employ hybrid quadratic hexahedral elements to avoid volume locking. The coefficients for the simplified model that were obtained by a parametric study are listed in Table 2. Proc. of SPIE Vol. 7964 79642I-3 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 07/28/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx The influence of the model complexity and parameterization on the registration accuracy depends on the geometry and the boundary conditions" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001426_s11044-013-9367-6-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001426_s11044-013-9367-6-Figure1-1.png", "caption": "Fig. 1 Viscoelastic-legged rimless wheel", "texts": [ " Based on the observations, in this paper we investigate the potentiality and fundamental properties of passive dynamic walking (PDW) including DLS motion, which is not instantaneous. As the simplest model for PDW that generates measurable period of DLS, we introduce the model of a planar passive viscoelastic-legged rimless wheel (VRW) that consists of eight identical telescopic-legs incorporating viscoelastic elements. First, we observe the passive-dynamic gait of our experimental machine shown in Fig. 1, and discuss how the traditional collision model should be modified. Second, we develop the mathematical model based on the considerations, and numerically examine the potentiality of stable gait generation including DLS on a gentle slope with commonly-used physical parameters for bipeds. We also numerically analyze the fundamental gait properties and the change of GRF with respect to the viscosity. Furthermore, we mathematically reconsider the conditions for transition to DLS motion and specify the corresponding computational procedures. This paper is organized as follows. In Sect. 2, we summarize the experimental results of PDW of our VRW machine. In Sect. 3, we develop the mathematical model for numerical simulation following the experimental results. In Sect. 4, the validity of the model is investigated through numerical simulations. In Sect. 5, we discuss the conditions for transition to DLS motion. Section 6 concludes this paper and describes future research directions. The experimental VRW shown in Fig. 1 consists of eight identical telescopic-legs incorporating a coil spring. A force due to friction is also derived with the telescopic-leg action. A silicon cap is attached on the end point of the telescopic-leg frames to suppress bouncing at impact. This frame is extended to the end point (maximum length) by the elastic force and is then mechanically locked. The total mass is 4.610 [kg] and the diameter without leg contraction is 0.385 [m]. The telescopic-leg frames can be replaced with rigid-leg ones, and the VRW is also able to generate rigid-legged PDW without measurable period of DLS" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001117_j.jmps.2011.10.008-Figure9-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001117_j.jmps.2011.10.008-Figure9-1.png", "caption": "Fig. 9. Slip-line geometry used to determine angles a2, a3, and a5 in Eqs. (12) and (13) (Komvopoulos, submitted for publication).", "texts": [ " For adhesionless contact interfaces, both the global coefficient of friction and the fraction of energy dissipated due to the removal of material are approximately independent of normal load and roughness of the hard surface. 7. The fractions of energy dissipated due to plastic shear and material removal at fully plastic microcontacts decrease with increasing interfacial adhesion (shear strength). Appendix. Determination of slip-line angles a2, a3, and a5 Geometric and trigonometric relationships presented in this section refer to Fig. 9. A.1. Determination of a3, a1, and r3 The angle change from point I to point E along IHE is equal to the angle change moving along IFE, i.e., a1\u00fea3 \u00bc y\u00fef0 \u00f0A1\u00de Definitions r1 \u00bc \u00f0BF\u00de \u00bc \u00f0DF\u00de \u00bc \u00f0DI\u00de \u00bc \u00f0BD\u00de= ffiffiffi 2 p \u00f0A2\u00de r3 \u00bc \u00f0O3E\u00de \u00bc \u00f0O3H\u00de \u00f0A3\u00de r5 \u00bc \u00f0O5M\u00de \u00bc \u00f0O5H0\u00de \u00f0A4\u00de R1 \u00bc \u00f0O2I\u00de \u00bc \u00f0O2H\u00de \u00bc \u00f0O2H0\u00de \u00f0A5\u00de Triangle (O3O2H) \u00f0O3O2\u00de 2 \u00bc \u00f0O2H\u00de2\u00fe\u00f0O3H\u00de2 \u00f0A6\u00de +O3O2H\u00bc tan 1\u00bd\u00f0O3H\u00de=\u00f0O2H\u00de \u00f0A7\u00de +O3O2I\u00bc+O3O2H2a1 \u00f0A8\u00de Triangle (DO2I) \u00f0DO2\u00de 2 \u00bc \u00f0O2I\u00de2\u00fe\u00f0DI\u00de2 \u00f0A9\u00de +DO2I\u00bc tan21\u00bd\u00f0DI\u00de=\u00f0O2I\u00de \u00f0A10\u00de +DO2O3 \u00bc+DO2I2+O3O2I \u00f0A11\u00de Triangle (O3O2D) \u00f0O3D\u00de2 \u00bc \u00f0DO2\u00de 2 \u00fe\u00f0O3O2\u00de 222\u00f0DO2\u00de\u00f0O3O2\u00decos+DO2O3 \u00f0A12\u00de Triangle (OBD) \u00f0OB\u00de \u00bc R \u00f0A13\u00de \u00f0BD\u00de \u00bc l cos\u00f0\u00f0p=4\u00de Z\u00de \u00f0A14\u00de +OBD\u00bc 3 4p\u00feZ \u00f0A15\u00de +BDO\u00bc p2+BOD2+OBD \u00f0A16\u00de \u00f0OD\u00de2 \u00bc \u00f0OB\u00de2\u00fe\u00f0BD\u00de222\u00f0OB\u00de\u00f0BD\u00decos+OBD \u00f0A17\u00de \u00f0DB\u00de=sin+BOD\u00bc \u00f0OB\u00de=sin+BDO \u00f0A18\u00de Triangle (O3OE) \u00f0OE\u00de \u00bc R \u00f0A19\u00de +O3EO\u00bc p2Z \u00f0A20\u00de +OO3E\u00bc p2+O3EO2+EOO3 \u00f0A21\u00de \u00f0OO3\u00de 2 \u00bc \u00f0OE\u00de2\u00fe\u00f0O3E\u00de222\u00f0OE\u00de\u00f0O3E\u00decos+O3EO \u00f0A22\u00de \u00f0O3E\u00de=sin+EOO3 \u00bc \u00f0OE\u00de=sin+OO3E \u00f0A23\u00de Triangle (O3OD) \u00f0O3D\u00de2 \u00bc \u00f0DO\u00de2\u00fe\u00f0O3O\u00de222\u00f0DO\u00de\u00f0O3O\u00decos+DOO3 \u00f0A24\u00de Triangle (EHI) \u00f0EH\u00de \u00bc 2\u00f0O3H\u00desin\u00f0a3=2\u00de \u00f0A25\u00de \u00f0IH\u00de \u00bc 2\u00f0O2I\u00desin\u00f0a1=2\u00de \u00f0A26\u00de +EHI\u00bc p 2 a3 2 a1 2 \u00f0A27\u00de \u00f0EI\u00de2 \u00bc \u00f0EH\u00de2\u00fe\u00f0IH\u00de222\u00f0EH\u00de\u00f0IH\u00decos+EHI \u00f0A28\u00de Triangle (EBF) \u00f0BE\u00de \u00bc 2\u00f0OB\u00desin\u00f0f0=2\u00de \u00f0A29\u00de +EBF\u00bc Z\u00fe f0 2 \u00f0A30\u00de \u00f0EF\u00de2 \u00bc \u00f0BF\u00de2\u00fe\u00f0BE\u00de222\u00f0BF\u00de\u00f0BE\u00decos+EBF \u00f0A31\u00de Triangle (EFI) \u00f0IF\u00de \u00bc 2\u00f0DI\u00desin\u00f0y=2\u00de \u00f0A32\u00de +EFI\u00bc p 2 \u00fe y 2 \u00fe f0 2 \u00f0A33\u00de \u00f0EI\u00de2 \u00bc \u00f0EF\u00de2\u00fe\u00f0IF\u00de222\u00f0EF\u00de\u00f0IF\u00decos+EFI \u00f0A34\u00de Angle relationship +DOO3 \u00bcf02+BOD2+EOO3 \u00f0A35\u00de Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001688_0954406213477579-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001688_0954406213477579-Figure1-1.png", "caption": "Figure 1. Longitudinal section of a two-stage planetary drive with radial roller bearings mounted in tight spaces. An instance of customization is shown by the encircled bearings that miss the outer ring.", "texts": [ " The high degree of specialization developed has allowed high quality, high standardization and high variety to be achieved for these critical products while ensuring off-the-shelf availability and reasonably low purchase costs. Particular design instances (very large bearings, tight mounting spaces) can sometimes arise and require non-standard products that are available from the regular market only for inordinate amounts of time and money. In such cases, rolling bearings of simple geometry can be designed and manufactured by the end user itself to fit the specific needs at a fraction of the costs and delivery time requested by the specialized suppliers. Figure 1 shows a two-stage planetary gearbox, typically used for mining, lifting and earth-moving machines, in which space is at a premium for the insertion of the rolling bearings. The cylindrical roller bearings are geometrically simple and lend themselves to custom manufacturing as exemplified by the circled assembly. To conserve space, the four highlighted bearings miss the outer ring and the rollers are brought in direct contact with the bore of the satellite gear. Further space could be made available for bigger rollers by taking away the inner rings and letting them roll directly onto the centre pin" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001855_ifost.2012.6357708-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001855_ifost.2012.6357708-Figure3-1.png", "caption": "Figure 3. Shematic of Experiment", "texts": [ " Air, retained by polystyrene powder 978-1-4673-1773-3/12/$31.00 \u00a92013 IEEE particles, was the third component of the suspension. Air content in the exposed layer of the technological medium was 0.27 \u2013 0.30. Previous experiments shown that because of sedimentation [3], disperse phase content in the exposed suspension layer does not depend on the starter polystyrene concentration in the suspension. During the experiments single layers were formed by means of sintering of technological medium disperse phase particles. Schematic of the experiment see on Fig.3. According to the NC code laser beam scanned the technological medium surface. Scan patterns consisted from sets of four parallel tracks with equal spacing. The experiments were carried out all laser power P = 56.8 W and wavelength \u03bb = 1070 nm (output power stability is \u00b10.5%, CW mode of operation, random polarization state). Scan rate V has value of 400 mm/min, 800 mm/min, 1200 mm/min. laser beam concentration coefficient was k = 9.8e+5 1/m2. Hatch spacing s varied from 2.00 to 5.50 mm. Single layers were formed in series by 10 for every couple of parameters \u201cscan rate \u2013 hatch spacing\u201d" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002843_s11249-018-0983-4-Figure9-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002843_s11249-018-0983-4-Figure9-1.png", "caption": "Fig. 9 Photographs of the optical interferometry and fluorescence images. a Interferometry image. b Fluorescence image. c Labeled image. d Labeled image", "texts": [ "5\u00a0N for which the corresponding maximum Hertzian pressure was 0.43\u00a0GPa and the rotating speed was 70\u00a0mm/s. As shown in Chaps. 2 and 3, polyphenyl ether (5P4E) was used as Tribology Letters (2018) 66:40 1 3 40 Page 6 of 10 the lubricant and a pyrene concentration of 3.0\u00a0mass% was added as a fluorescence agent. According to Ref. [17], the pressure-viscosity coefficient of 5P4E is shown as 37.3\u00a0GPa\u22121 at 313\u00a0K. The tests were conducted at room temperature (295\u2013296\u00a0K). The test was conducted at least three times, and the results showed the repeatability. Figure\u00a09 shows photographs of the optical interferometry image obtained using green light (a) and the fluorescence image (b) of the lubrication film. In the figures, (c) and (d) show the contact area and horse-shoe region with a broken white line. The arrows show the lubricant\u2019s flow direction. Photographs (b) and (d) demonstrate that the fluorescence intensity decreased along the flow direction in the position between \u2212\u00a0200 and \u2212\u00a0100\u00a0\u03bcm; moreover, remarkable fluorescence was observed from \u2212\u00a0100 to 30\u00a0\u03bcm, corresponding to the parallel-film-thickness region as shown in photographs (a) and (b)", " In the spectrum at \u2212\u00a0200\u00a0\u03bcm, remarkable excimer emission at 475\u00a0nm was observed. This behavior was similar to the data for the viscous fluid at 296\u00a0K. The spectra at \u2212\u00a0100\u00a0\u03bcm showed no significant excimer emission peak compared with that at \u2212\u00a0200\u00a0\u03bcm. Moreover, the spectrum at the center was lower than that at the inlet and had identical behaviors to those at 243\u00a0K for the solid state. Figure\u00a011 shows the intensity ratio between the 478- and 450-nm peaks along the flow direction and the film profile at the central position of contact. The coordination is shown in Fig.\u00a09. The figure indicates that the intensity ratio steeply decreases to \u2212\u00a0100\u00a0\u03bcm at the contact inlet down to a value of about 1.08, meaning that the viscosity increased as shown in Fig.\u00a07. Moreover, changes in the intensity ratio between the positions of \u2212\u00a0100 and 25\u00a0\u03bcm were small, with the value ranging from 1.08 to 0.94. In particular, the ratio at the positions from \u2212\u00a050 to 25\u00a0\u03bcm was less than 1.0, meaning that the lubricant became a solid state. Figure\u00a011 also shows that the ratio steeply increased to about 100\u00a0\u03bcm at the exit up to a value of about 1", " Moreover, the state of the lubricant is suggested to become a viscoelastic solid according to \u03b1p [14, 17]. These results indicate that the solidification can be caused in the contact area because of high contact pressure causing the lubricant to become solid. This is shown by the fluorescence measurement results at positions from \u2212\u00a050 to 25\u00a0\u03bcm, which means the excimer emission decreases and the intensity ratio corresponds to that of the solid state because the state of the lubricant changes to a solid because of the contact pressure. (4) 0 = exp( p) In Fig.\u00a09, the intensity at front of horse-shoe area is the greatest, and this may be related to the higher contact pressure (pressure spike). Considering the results in this section, it is likely that the fluorescence behavior (in particular the intensity of 5P4E fluorescence) changes with pressure if the state is elastic\u2013plastic solids. A future research plan is to understand the effect of pressure on the fluorescence behavior of the solid state. However, the excimer decreases also in the solid state, as shown in Figs" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003618_j.matpr.2018.12.152-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003618_j.matpr.2018.12.152-Figure1-1.png", "caption": "Fig. 1. Scheme of measurement of microhardness (by Vickers)", "texts": [ ": +7-919-016-94-50 E-mail address: dgprivezencev@mail.ru 326 D. Privezentsev et al. / Materials Today: Proceedings 11 (2019) 325\u2013329 hardness of individual phases or structural constituents of alloys, or the difference in hardness of individual parts of these constituents [1,2]. The method is standardized (GOST 9450 - 76). As an indenter in the measurement of microhardness, a regular tetrahedral diamond pyramid with a vertex angle of 136\u00b0 is used most often, as in the case of Vickers hardness determination (Fig. 1.). This pyramid is smoothly pressed into the sample at loads of 0.05 - 5 H. The number of microhardness HV is determined by the formula 1.854 \u00b7 / This measurement is carried out using a microhardness meter, which can be divided into analog and digital. When using an analog microhardness meter (Fig. 2), the measurements are made as follows: The test material is fixed on a table, after which an indentation is performed to indent the material. This procedure is performed as many times as necessary" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002635_s11771-017-3585-7-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002635_s11771-017-3585-7-Figure6-1.png", "caption": "Fig. 6 Machining coordinate systems applied for face gear generation by worm wheel", "texts": [ " Thus, in order to completely envelop the whole surface of the face gear, a two-parameter method has to be utilized to grind the face gear by the worm wheel wherein two independent sets of parameters are provided: 1) a set of angles of rotation w f( , ) of the worm wheel and the face gear, and 2) a radial feed motion lw of the worm wheel. Parameters \u03c6w and \u03c6f, which are the angles of rotation of the worm wheel and the face gear, need to satisfy the following relation: f w w f/N N (14) where Nf and Nw are the number of teeth of the face gear and that of the worm wheel, respectively. Parameter lw of the radial feed motion is provided as collinear to the axis of the worm wheel. The face gear tooth surface is calculated as the envelope to the worm wheel surface, as shown in Fig. 6. Coordinate systems Sw and Sf are rigidly connected to the worm wheel and the face gear, respectively. Moreover, Sw0 and Sf0 are fixed coordinate systems. Ews is the distance from the axis of the face gear to the worm wheel. Therefore, the position of the face gear surface is determined as J. Cent. South Univ. (2017) 24: 1767\u22121778 1772 f s s w w fw w w w s s (1) s s w w f s f sfw f w (2) s s w w f s f sfw f w ( , , , ) ( , ) ( , ) ( , , , ) (( ) ( )) ( ) 0 ( , , , ) (( ) ( )) ( ) 0 R l l R f l R R R f l R R R l M (15) where the matrix fw w w( , )lM describes the coordinate transformation from Sw to Sf; the equation (1) s s w wfw ( , , , ) 0f l represents the meshing equation in the case that the radial feed parameter lw is constant and the rotation parameter \u03c6w is changeable" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002977_j.ifacol.2018.03.069-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002977_j.ifacol.2018.03.069-Figure2-1.png", "caption": "Fig. 2. Planar testbed used for the identification process.", "texts": [ " x\u0303m \u2212 xm(EA) ) T , (43) where x\u0303i is the measured and xi(EA) is the computed axial position for an external force IF H id = (\u2212fx 0 0 ) T (44) with the virtual work contribution (26). In the left diagram of Fig. 3, a clear nonlinearity in the measured stressstrain curve (red curve) can be observed, which can be reproduced much better by the Neo-Hookean material law (19) than by the linear Hookean law. Tab. 1 shows that the linear Hookean law overestimates the stiffness of the specimens. Shear test for identification of GA and EI For the shear test, a force in eIz-direction is applied at the tip of the ECM as depicted in Fig. 2 which leads to a bending deformation about the eIy-axis and a shear deformation along the eIz-axis. For all displacements increments, the Proceedings of the 9th MATHMOD Vienna, Austria, February 21-23, 2018 Bastian Deutschmann et al. / IFAC PapersOnLine 51-2 (2018) 403\u2013408 407 with N \u2032 = (\u22120.5 0.5 ) T and \u2206Le = ne+1\u2212ne. Moreover, the approximation (28) induces together with (31) also \u03b4x(\u03bd) = kel\u2211 e=1 \u03c7\u2126e (\u03bd)N(\u03bde(\u03bd))T (Ce x) T \u03b4q, \u03b4x\u2032(\u03bd) = kel\u2211 e=1 \u03c7\u2126e (\u03bd)N \u2032(\u03bde(\u03bd))T 2 \u2206Le (Ce x) T \u03b4q. (34) Providing the same computations for z and \u03b8, the virtual work of the internal forces (18) is approximated by inserting (33) and (34)", " (38) Using (32), the discretization of the virtual work of the tendon forces (24) is \u03b4W ext,t = (\u03b4qkel+1)TP\u03bb = \u03b4qTCLP\u03bb (39) with the tendon coupling matrix P = eIl,x eIr,x eIl,z eIr,z d(Ie H y )T Ie H z \u00d7 Iel \u2212d(Ie H y )T Ie H z \u00d7 Ier . (40) Using (35), (37) and (39) in the principle of virtual work (15), the infinite dimensional variational expression is reduced to the finite dimensional expression \u03b4qT ( f int + f ext,g +CLP\u03bb ) = 0 \u2200\u03b4qadm (41) which induces a nonlinear vector valued equation which can be solved numerically. 2.4 Identification of the stiffness parameters In this section, the experimental identification process is discussed in which the stiffness parameters EA, GA and Fig. 2. Planar testbed used for the identification process. EI for the constitutive laws (19) are identified. Two different experiments are carried out to excite independently the axial stiffness EA as well as the shear and bending stiffness GA and EI, respectively. The elastic parameters are incorporated in the FEMmodel being described by a nonlinear function. Thus, a nonlinear least square optimization is applied for the identification process using the \u201dlsqnonlin\u201d routine from MATLAB. Within this nonlinear optimization, the error function \u2206(\u03be) \u2208 IRm, is minimized to find the desired parameters \u03be \u2208 IRp, min \u03be ||\u2206(\u03be)||22, (42) where m, p \u2208 IR are the number of measurements and the number of identified parameters, respectively", " 3, a clear nonlinearity in the measured stressstrain curve (red curve) can be observed, which can be reproduced much better by the Neo-Hookean material law (19) than by the linear Hookean law. Tab. 1 shows that the linear Hookean law overestimates the stiffness of the specimens. Table 1. Left: Identified EA for Hookean and Neo-Hookean material laws. Right: Identified GA and EI. compression shear L [mm] EAnH [N] EAH [N] ft,max GA [N] EI [Nm2] 28 7448.94 8972.10 33 N 2405 2.993 40 7591.09 9071.84 66 N 2422 3.003 Shear test for identification of GA and EI For the shear test, a force in eIz-direction is applied at the tip of the ECM as depicted in Fig. 2 which leads to a bending deformation about the eIy-axis and a shear deformation along the eIz-axis. For all displacements increments, the Proceedings of the 9th MATHMOD Vienna, Austria, February 21-23, 2018 position and orientation are measured by a camera as well as the applied tendon force. The identified value EA = 7500[N] from the compression test is used within the shear test as an initial guess for the bending stiffness EI = 7500/A\u00b7I = 871080\u00b7I [Nm2] with second moment of area I. Here, \u03be = (GA EI ) T \u2208 IR2 and the error function for the identification is \u2206(\u03be) =( z\u03031 \u2212 z1(\u03be) \u03b8\u03031 \u2212 \u03b81(\u03be) ", "02. The points with relative error beyond the interval [\u22120.02, 0.02] are not displayed as located in a small range around zero (from \u22122[N] to 2[N] for the force and from \u22120.2[Nm] to 0.2[Nm] for the torque). This section will compare the two established models regarding there prediction accuracy and computation time. For the evaluation, we use experimental data from the planar testbed where a combined loading is applied, i.e. the mechanism is moved with two antagonistically arranged tendons, cf. Fig. 2. As the established models are static ones, the data is measured at poses in static equilibrium. The accuracy of the FEM model is mainly dependent on the identified material parameters provided that the assumptions about the geometry of the deformation and the Proceedings of the 9th MATHMOD Vienna, Austria, February 21-23, 2018 5 408 Bastian Deutschmann et al. / IFAC PapersOnLine 51-2 (2018) 403\u2013408 applied material laws match well. In Fig. 6, a comparison is shown between static poses of simulated and measured data" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001249_j.compind.2013.08.001-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001249_j.compind.2013.08.001-Figure8-1.png", "caption": "Fig. 8. Four types of predefi", "texts": [ " For example, a layer may comprise several materials, which means the layer has to be deposited by several actuators. Besides the geometrical and material information data from the transformed colour STL file, additional variables are added. For example, each material is assigned two variables to indicate deposition priority and speed, and each contour of the same material would be assigned a safety envelope. These additional variables will be used in the subsequent toolpath planning [26]. To facilitate synthesis of a virtual MMLM facility, a template library of four typical types of actuator, as shown in Fig. 8, has been built into VPRA. They can be directly loaded and reconfigured to synthesize a virtual facility for simulating an existing MMLM system or designing a new MMLM system. The first type is the XY-stage widely used in current LM systems. It is characterized by intuitive motion control, low cost, and high precision. In VPRA, multiple actuators of this type can be used to synthesize a composite XY-stage, called stage group [8], whose end-effectors can move independently. The second type is the gantry-style actuators" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000043_rspa.2007.0372-Figure9-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000043_rspa.2007.0372-Figure9-1.png", "caption": "Figure 9. Sketch of the coiled sheet for (a) R/SZe5, (b) R/SZ0.255, (c) R/SZe6, (d ) R/SZ0.240 and (e) R/SZe7.", "texts": [ " Force Q4 is perpendicular to the segment between points 0 and 1 in figure 8b, but the equivalent force has a radial direction in figure 6d. Hence, somehow the force Q4 must rotate between the values e3 and e4. To explain this rotation, we need to include the thickness of the sheet in the analysis, so that our approach is no longer valid in this case. Figure 8d shows the sheet shape for R=SZe5Z0:263. At this condition, a new contact is made between both detached segments. This contact adds a pair of point forces, so that there are now seven point forces, as figure 9b shows. We can use similar numerical analysis to obtain the shape of the sheet, although the technical difficulties increase. It is necessary to solve the equations for five different segments to obtain the unknown parameters. This solution is valid until Proc. R. Soc. A (2008) point 6 meets point 3 and presses directly against the wall. At this configuration R=SZe6Z0:250, the length of the sheet is eight times the diameter. The corresponding sheet shape is shown in figure 9c. For e!e6, the end of the inner detached segment rests over the part of the coil in contact with the tube wall. There are now six point forces over the sheet and a total of four segments. Further decreases of the radius make point 5 move along the wall and the curvature in point 4 decrease. The behaviour of the sheet at point 4 is very similar to the one observed for point 1 in figure 5. At the value R=SZe7Z0:224, the curvature at point 4 matches the curvature of point 1, so that a region of contact starts to develop for e" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002455_fitee.1500464-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002455_fitee.1500464-Figure1-1.png", "caption": "Fig. 1 Diagram of the longitudinal geometry profile and free body of an air-breathing hypersonic vehicle (Parker et al., 2007; Bu et al., 2016)", "texts": [ ", 2009; Fiorentini and Serrani, 2012; Li and Meng, 2015), the approach proposed makes the selection of controller parameters simpler. Notations: In the subsequent sections, 0m\u00d7n and Ip denote an m\u00d7 n zero matrix and a p\u00d7 p identity matrix, respectively. The symbols (\u00b7)max and (\u00b7)min denote the maximum and minimum values of \u2018\u00b7\u2019, respectively. For example, (Vr)max denotes the maximum value of the velocity reference trajectory Vr. The diagram of the longitudinal geometry profile and free body of an AHV in this study is depicted in Fig. 1. The longitudinal rigid dynamics are as follows (Serrani, 2013): V\u0307 = T cos\u03b1\u2212D m \u2212 g sin \u03b3, (1a) h\u0307 = V sin \u03b3, (1b) \u03b3\u0307 = L+ T sin\u03b1 mV \u2212 g V cos \u03b3, (1c) \u03b8\u0307p = Q, (1d) Q\u0307 = Myy Iyy . (1e) Herein V , h, \u03b3, \u03b8p, and Q denote the velocity, the altitude, the flight-path angle (FPA), the pitch angle, and the pitch rate, respectively; \u03b1 denotes the AOA, which is defined as follows: \u03b1 = \u03b8p \u2212 \u03b3; (2) g denotes the acceleration of gravity; m and Iyy denote the vehicle mass and the moment of inertia, respectively; T , D, L, and Myy denote the thrust, drag, lift, and pitching moment, respectively, whose curve-fit expressions are described as follows (Serrani, 2013): T = q\u0304S (CT,\u03a6 (\u03b1)\u03a6+ CT (\u03b1)) , (3a) D = q\u0304S ( C\u03b12 D \u03b12 + C\u03b1 D\u03b1+ C0 D ) , (3b) L = q\u0304S ( C\u03b1 L\u03b1+ C0 L + C\u03b4e L \u03b4e + C\u03b4c L \u03b4c ) , (3c) Myy = zTT + q\u0304Sc\u0304 ( CM (\u03b1) + C\u03b4e M \u03b4e + C\u03b4c M\u03b4c ) , (3d) where CT,\u03a6 (\u03b1) = C\u03b13 T,\u03a6\u03b1 3 + C\u03b12 T,\u03a6\u03b1 2 + C\u03b1 T,\u03a6\u03b1+ C0 T,\u03a6, CT (\u03b1) = C\u03b13 T \u03b13 + C\u03b12 T \u03b12 + C\u03b1 T\u03b1+ C0 T , CM (\u03b1) = C\u03b12 M \u03b12 + C\u03b1 M\u03b1+ C0 M " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000365_j.nonrwa.2009.02.024-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000365_j.nonrwa.2009.02.024-Figure1-1.png", "caption": "Fig. 1. The IVP (9): (a) classical solutions; (b) Filippov solutions.", "texts": [ " continuously differentiable) cannot be continued along the axis x = 0 because the derivative has a discontinuity in a small neighborhood of x = 0. The following ODE x\u0307 = 2\u2212 3 sgn(x), (9) has, for x 6= 0,the solutions x(t) = { 5 t + C1, x < 0, \u2212t + C2, x > 0, but, as t increases, these classical solutions tend to the line x = 0, where they cannot continue to evolve since the function x(t) = 0 does not verifies the equation. Thus, there are no classical (continuously differentiable) solutions starting from 0 (see Fig. 1a). Thus, one can see that the discontinuity does not necessarily implies the non-existence of solutions. To provide the possibility for the solutions to IVP (2) to be continued it is necessary to modify its right-hand side. The structure of the paper is as follows: Section 2 presents the set-valued IVP associatedwith IVP (2); Section 3 dealswith the existence of solutions to the set-valued IVP; Section 4 presents the main results of the paper regarding the uniqueness of the generalized solutions and Section 5 shows several examples" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002714_detc2017-67203-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002714_detc2017-67203-Figure5-1.png", "caption": "FIGURE 5", "texts": [ " This mobility allows point C to drift away from the target position and causes position uncertainty. In the discussion throughout this paper, the worst case scenario and hence the boundary of the uncertainty region is the concern. Assume that all joints have the same clearance. Each joint clearance is represented by a clearance link with the common length \u03b4R, which is the difference of the radii of the pin and hole of a revolute joint (Figure 2) [25]. By replacing each joint clearance with a clearance link of length \u03b4R, the eight-bar linkage in Figure 1(a) is remodeled as a 17-bar linkage (Figure 5(a)). Ting\u2019s rotatability laws lead to the following observation in the 17-bar linkage. 1. All clearance links in a leg may be connected in series following the principle of invariant link rotatability [28] as demonstrated by applying parallelograms to change the order of connection between nominal link and clearance links, as shown in Figure 5(b), in which all clearance links in a leg are grouped at Ai. After the grouping of clearance links, Figure 5(a) becomes Figure 5(c). Figure 5(a) and Figure 5(c) have the identical platform mobility. 2. Assume no any input error. For the given inputs \u03b8i, i = 1, 2, 3, the position of the input link MiAi and therefore the location of Ai can be determined unambiguously. Fix the joint at Ai, the linkage is remodeled to a 14-bar linkage, which insulates the geometric effect from input errors. 3. When Point C is at the target position for the given inputs, the effects of clearances or clearance links cancel each other as shown in Figure 5(d), in which the position and direction of each nominal link is identical to that of the instant structure in Figure 4(a). 4. Since the uncertainty associated to a target position is the concern, Figure 5(d) should be interpreted as the instant structure of Figure 4(a) or Figure 4(b) mounted on the three flexible links AiAi', in which each flexible link represents any possible combination of the three clearance links. Therefore Figure 5(d) is equivalent to Figure 6(a), in which Li is the length AiC obtained in Eq. (3) for the instant structure of Figure 4. For point C to reach a target position, Li and the location of Ai, i = 1, 2, 3, represent the deterministic aspect of the position, while the clearance links the uncertainty. 5 Copyright \u00a9 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/16/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 5. When point C is at an extreme position, i" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003427_s12666-018-1536-0-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003427_s12666-018-1536-0-Figure6-1.png", "caption": "Fig. 6 ASMEsection II-C specimen details a specimen center reference, b 8 passweld sequence, c test specimen dimensions and extraction location", "texts": [ " Though particle count is a little less in hybrid, the area distribution and the integrated density suggest comparable presence of acicular ferrite which has been vindicated earlier by the comparable micro-hardness. This iteration has been conducted to compare the effect of hybrid arc welding process on ductile-to-brittle transition of welded joints against conventional MAG welded joints. Transverse impact strength of the welded joint has been recorded and studied as per ASME section II-C and the ASTM E-23 procedural standards for the specimen making as documented in Table 5 and depicted in Fig. 6a. The conventional MAG has been carried out at 26 V for the 12 m/min of wire feed rate with welding speed of 0.36 m/ min. Similarly the hybrid process has been carried out with addition of TIG arc at 200A of current. In the multiple pass welds as shown in Fig. 6b, the required eight passes are laid with the inter-pass temperatures of 150\u2013160 C. Initially the welded specimens as shown in Fig. 6c have been tested for the radiography benchmark with gamma ray Ir192 isotope prior to the impact strength test specimen preparation for the assorted rounded indications as shown in Fig. 7a. As per ASME section V procedural standard with the source strength index of 23 and the exposure time of 3 min, the ASME section II-C 5A acceptance standard has been followed for the penetrometer image quality index of ASTM 1B 17 with AGFA-D7 film. The prepared \u2018Type A\u2019 specimens as shown in Fig. 7b have been maintained at sub-zero temperature in the acetone bath with the periodic addition of dry ice" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000610_s00466-010-0508-y-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000610_s00466-010-0508-y-Figure2-1.png", "caption": "Fig. 2 Initial and deformed configurations of frame element i", "texts": [ " Distributed loads, for example, are lumped on nodes simplified as concentrated forces. Spreading of plasticity through the depth of a cross-section is precluded, while the spread of plasticity along the member can be captured with suitably fine discretization in critical regions. The locations of possible hinges are a priori assumed, for instance, under concentrated loads, at the supports where yielding is likely to occur, etc. 2.2 Statics and kinematics Consider the generic self-equilibrated discretized 2-D frame element i in Fig. 2, where l and \u03b8 define the undeformed member length and the original inclined angle, respectively. Vectors ui \u2208 6 and Fi \u2208 6 denote respectively unconstrained nodal displacements and forces measured with respect to a global reference axis system. When the element is deformed, lc and \u03c1 indicate the deformed member chord length and the member chord rotation measured in a clockwise direction with respect to its initial position. Two fundamental ingredients of the structural behavior, namely the equilibrium between the nodal applied forces Fi and the element stress resultants si as well as the compatibility condition relating the member deformations qi to the nodal displacements ui , can be established", "g. D \u2261 diag(D1, . . . , Dn)). As is typical, the compatibility matrices C \u2208 m\u00d7d , C0 \u2208 m\u00d7d , C\u03c0 \u2208 2n\u00d7d and vectors f \u2208 d , fd\u2208 d , u \u2208 d are assembled using appropriate location vectors. 2nd-order geometry A simplified and common approach is to adopt a 2nd-order geometric assumption (see e.g. [6, 21]), for which the 1st-power quantities of the exact geometrically nonlinear formulation are retained. It is assumed that displacements from the undeformed state are geometrically small, such that in Fig. 2 \u03c1 is small so that cos \u03c1 \u2248 1; sin \u03c1 \u2248 \u03c1; \u03b4i n l; and lc \u2248 l. The equilibrium condition of each elastic member i in the deformed state is established by using the so-called geometric stiffness matrix Ki G \u2208 6\u00d76 [29] which accounts for change of configuration with loading. For a generic frame element i , a 2nd-order geometric nonlinearity formulation can be obtained by introducing an additional transverse force \u03c0 i f as well as its corresponding displacement \u03b4i f , as shown in Fig. 5. Clearly, this force \u03c0 i f and displacement \u03b4i f represent the configuration change of a member", " In small deformation theory, this can be simply expressed by the classical elastic stiffness relation of a typical frame element. However, when the effects of geometric nonlinearity are included, the elastic relations become nonlinear. Arbitrarily large deformation The destabilizing effect considered herein is the well-known P \u2212 \u03b4 effect [8,19], and the influence of axial forces on primary bending behavior can be described through stability functions. In addition, the effect of curvature shortening on axial deformation is captured through bowing functions. For the generic frame element i (Fig. 2) the elastic constitutive model relating stresses si to elastic strains ei , for arbitrarily large deformations, can be written in the following nonlinear form: si = Si ei + Ri b, (20) where Si = \u23a1 \u23a3 E A/ l 0 0 0 v1 E I/ l v2 E I/ l 0 v2 E I/ l v1 E I/ l \u23a4 \u23a6 , Ri b = \u23a1 \u23a3 Rb1 0 0 \u23a4 \u23a6 , in which Si \u2208 3\u00d73 is a symmetric (not necessarily positive semidefinite) stiffness matrix which contains the stability functions (v1, v2), Ri b \u2208 3 is a residual vector collecting nonlinear parameter Rb1 that represents the effects of bowing on the axial deformation, E is the modulus of elasticity, A is the cross-sectional area, and I is the second moment of area of the central elastic part" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000459_la901812k-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000459_la901812k-Figure6-1.png", "caption": "Figure 6. Brownian motion for myosin V.", "texts": [ " In this work the heads and actin are assumed to be frictionless, for the sake of simplicity, thus the horizontal forces illustrated in Figure 5 do not represent tangential friction. They are used to enforce an immobilization of the head when it docks. See Supporting Information A.4 for further details. 2.6. Brownian Motion. Random forces and moments in the model, representing Brownian motion, are implemented as Gaussian white noise. They act at and about the mass center of each body, as shown in Figure 6. See Supporting InformationA.5 for further details. 3. First-Order Model Division of eq (1) by the viscous damping coefficient yields 0\u2248 A\u00f0q\u00de::q\u00feb\u00f0 _q, q\u00de \u03b2 \u00bc \u0393cccB \u03b2 -D _q \u00f05\u00de \u0393cccB \u00bc \u0393contact\u00fe\u0393charge\u00fe\u0393conform\u00fe\u0393Brown \u00f06\u00de The argument behind the small mass assumption is that the mass terms divided by \u03b2 are sufficiently small to be omitted; this is clearly untrue for large accelerations. Regardless, 5 yields a first-order model where velocity is directly proportional to force _q \u2248 _q \u00bc D-1 \u0393cccB \u03b2 \u00bc D-1 aA \u03b2 \u0393cccB aA \u00f07\u00de assumingD is invertible" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002786_00207721.2017.1415390-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002786_00207721.2017.1415390-Figure1-1.png", "caption": "Figure 1, then", "texts": [ " Consider the class of single-input-single-output discretetime systems described by a\u0302 (z) y (t ) = zd b\u0302 (z) u (t ) + v (t ) , (1) where y(t ), u(t ) and v(t ) denote the output, input and external disturbance, respectively, t is the discrete time, d is the I/O delay which takes integer values greater than 1, a\u0302 (z) = 1 + a (1) z1 + \u00b7 \u00b7 \u00b7 + a (n) zn, b\u0302 (z) = b (0) + b (1) z1 + \u00b7 \u00b7 \u00b7 + b (m) zm Assumption 3.1: The polynomials a\u0302(z) and b\u0302(z) do not have the same unstable zeros, and n > m. The above assumption is almost without loss of generality in practice use and plays an important role in the development of the synthesis of a controller that minimises the tracking error. Consider the feedback system depicted in Figure 1, whereC is the controller and r is the reference signal. Assumption 3.2: The z-transform of the reference signal r\u0302 \u2208 Dr(a\u0302r), where Dr (a\u0302r) = {r\u0302 = b\u0302ra\u0302\u22121 r : a\u0302r \u2208 R[z] is known, but b\u0302r \u2208 R[z] is unknown}. The polynomials a\u0302r and b\u0302r are co-prime. Definition 3.1: Denoted by \u03b5 = r \u2212 y, the tracking error. If the plant is stable and the tracking error is bounded, then \u2016\u03b5\u2016ss = limsupt\u2192\u221e|\u03b5(t )| is defined as the steady-state tracking error. In this section, we provide, under Assumptions 3.1 and 3.2, a method for designing controllers such that the feedback system depicted in Figure 1 satisfies the following specifications: the feedback system is stable and minimises the worst-case steady-state tracking error, Jtrac = sup \u2016v\u2016\u221e\u2264wv \u2016\u03b5\u2016ss. The computation of formula of worst-case steady-state tracking performance is first provided for the systems free from external disturbances in Khammash (1995). The following result, aiming at systems with external disturbances, provides the formula of worst-case steady-state tracking performance in the same way. Result 3.1: If the reference signals satisfy r \u2208 l\u221e, where Gyr is the transfer function from r to y, and Gyv is the transfer function from v to y in the nominal system in The proof follows from Proposition 4 in Khammash (1995)", " With this controller, it is clear from Equation (7) that g\u0302 is a polynomial, thus G\u03b5rr = a\u0302s g\u0302b\u0302r \u2208 R [z] (9) FromEquations (6) and (8), it follows that q\u0302 \u2208 A. Thus, Equation (9) implies that with any controllers of Equation (2) with q\u0302 = h\u03020 + a\u0302\u2032 r k\u0302 b\u0302s , the tracking error settles down to zero in a finite number of control steps for any given reference input r\u0302 \u2208 Dr(a\u0302r). Therefore, for a given r\u0302 \u2208 Dr(a\u0302r), the problem of designing optimal tracking controller can be reduced to that of choosing k\u0302 \u2208 R[z] such that Jtrac = sup\u2016v\u2016\u221e\u2264wv \u2016\u03b5\u2016ss is minimised. From Equations (2), (8) and Figure 1, we have the following transfer functions: Gyv = y\u03021 \u2212 zdb\u0302q\u0302, (10) G\u03b5r = a\u0302 ( y\u03021 \u2212 zdb\u0302q\u0302 ) (11) It follows from Equation (9) that \u2225\u2225 ( 1 \u2212 Gyr ) r \u2225\u2225 ss = \u2016G\u03b5rr\u2016ss = \u2225\u2225\u2225a\u0302sg\u0302b\u0302r \u2225\u2225\u2225 ss = 0 Then, from Result 3.1, and Equations (10) and (11), the worst-case steady-state tracking error can be written as Jtrac = wv \u2225\u2225Gyv \u2225\u2225 A (12) D ow nl oa de d by [ G ot he nb ur g U ni ve rs ity L ib ra ry ] at 0 4: 06 1 3 Ja nu ar y 20 18 Thus, from Equations (12) and (10), it follows that the problem of minimisation of Jtrac is reduced to the same l1 optimisation problem, \u03bc = inf q\u0302\u2208A \u2225\u2225Gyv \u2225\u2225 A = inf q\u0302\u2208A \u2225\u2225\u2225y\u03021 \u2212 zdb\u0302q\u0302 \u2225\u2225\u2225 A " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000085_robot.2009.5152184-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000085_robot.2009.5152184-Figure2-1.png", "caption": "Fig. 2. Ray-shooting problems in robotic grasping depicted in the wrench space. (a) Non-force-closure grasp that can be determined in finite iterations. (b) Non-force-closure grasp determined without iteration. (c) Force-closure grasp determined with finite iterations. (d) Contact force optimization and grasp quality evaluation, where our ray-shooting algorithm requires infinite iterations w.r.t. w1, finite iterations w.r.t. w2, and no iteration w.r.t. w3.", "texts": [ " The full row rank of [ ]1 2 m=G G G G\" ensures that int cW is not empty. Moreover, it can be proved that cw given below lies in int cW : 1 1 1 1 ( ) 1 1 m m TT T c i i nii i im m= = = \u00d7 =\u00aa \u00ba\u00ac \u00bc+ + \u00a6 \u00a6w n r n w (13) where [ ( ) ]T T T ni i ii= \u00d7w n r n is the normal contact wrench. For the nontrivial case of c \u2260w 0 , let ( , )c cz W\u2212w be the intersection of bd cW with the ray ( )cR \u2212 w , which can be obtained by the ray-shooting algorithm. If ( , )c cz W\u2212 =w 0 , then bd cW\u22080 and the grasp is not force-closure [Fig. 2(a) and (b)]; otherwise 0 lies strictly between ( , )c cz W\u2212w and cw , which implies that int cW\u22080 [Fig. 2(c)]. Fig. 2(a)\u2013(c) also indicates that the ray-shooting algorithm often requires only finite iterations in the force-closure test. Particularly, when a grasp is not force-closure [see Fig. 2(b)], perhaps no iteration is needed, since ( ) 0W cch \u2212 =w and 0 =b 0 in Step 1 and 0( , ) 0cd W =b in step 2. B. Contact Force Optimization The goal of contact force optimization is to compute the minimum contact forces if , 1, 2, ,i m= ! within the friction cones for generating a required resultant wrench reqw . A contact force if within the friction cone can be written as a positive combination of iJ finite primitive contact force vectors in iU , denoted by ijs , 1,2, , ij J= ! : 1 iJ i ij ij j \u03bb = =\u00a6f s with 0ij\u03bb \u2265 for 1,2, , ij J= ", " In fact, the points ij iU\u2208s will be determined prior to ijw (see Section IV-D), so that if can be computed by (14). Note that, along with the variation of reqw , the computed ijs are varying and can be any points of iU . Hence the above contact force computation is essentially different from the method linearizing the friction cone [5], in which ijs are fixed at some points of iU . In addition, the required number of iterations of the ray-shooting algorithm is dependent of the direction of reqw , as described in Fig. 2(d). C. Grasp Quality Evaluation Force-closure is an important property of grasps, but it says nothing about the goodness of a grasp. Then the methods for quantitatively evaluating the grasp quality are needed. One of the advanced methods is based on the required wrench set [10], whose result is independent of the choice of coordinate frame and unit. Let reqW denote a required wrench set. Then the grasp quality index q is defined in terms of the minimum contact forces for generating all wrenches in reqW as req req 1 min ( , ) max ( ) max c W W z W q \u03c3 \u2212 \u2208 \u2208 = = w w w w w " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001730_green.2011.5754884-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001730_green.2011.5754884-Figure1-1.png", "caption": "Figure 1. PM TFW", "texts": [ " Moreover, Eddy cu what increases the power losses the winding and PMs. In paper [13] authors p magnetic shunts. There a thorou distribution in the generator is maximize the power of particula paper the authors analyze the per 1kW PMTF generator with i magnetic shunts. PARAMETER A scheme of the generator is show gative influence an ] which are placed however, increases es lower power to rrents are induced and temperature of roposed laminated gh analysis of flux done in order to r generator. In this formance of a small nternal stator and ION AND DESIGN S n in Fig. 1. The G 978-1-61284-714-6/11/$26.00 \u00a92011 IEEE inner stator attached firmly to the sh three rings of magnetic poles, each phase. The magnetic poles are Udistributed evenly around the stator placed inside of the stator slots (see Fig rotor also has three rings that match th Each ring has two rows of PMs. To in linkage of the coils magnetic shun axially between the stator poles (see effectiveness of the magnetic shunts i [13]. In order to obtain 3 phase sinus displaced by 120 degrees, magnet pairs armatures have a 15 degrees shift as it 3", " It is much one produced by the single phase s cogging torque reduction can be exp shift of magnet pairs on the rotor for e Fig. 3). at rated current of ual if the aire stator poles he same rotor the generator and with outer wer to volume outer stators nerator power e outer stator cur in all PM used by the th stator teeth. the interaction . 12 shows the ase generator del without shunts the 3-phase lower than the tructure. This lained by the ach phase (see Magnetic shunts, apart f negative magnetic field comin magnets, also reduce a cogg generator. This is shown in Fig. 1 torque calculated in 3-phase m shunts is presented. Summarizing, one can say th the generator with electromagn small. Since the cogging torque and vibration this feature of this very important, in particular if th to be mounted on the roof of applications of the generator for described in the next section. IV. GEARLESS WIND POWE AGREGATE Gearless wind power generat many papers [1-4]. Their ad generators driven by the wind gear is not only in higher effici but also in lower capital cost. The considered generator wi additional advantage" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000043_rspa.2007.0372-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000043_rspa.2007.0372-Figure6-1.png", "caption": "Figure 6. Sketch of the sheet for e3!R=S!e2. (a) R/SZe2, where the curvature at the midpoint is 1/R. The detached region has a shape as shown in figure 2. (b) The contact point at sZS transforms into a region of contact that spans an angle 4. Here, 4Zp/4, (c) 4Zp/4 and (d ) 4Z p/2. The two ends of the strip make contact at the line yZ0. The total angle of contact with the tube is 4Z1.9 (z1098) and R/SZe3.", "texts": [ " In contrast with the first case, the curvature at the midpoint decreases and the angle f0 increases as the radius is further decreased. Our solution is valid while the curvature of the midpoint is larger than the curvature of the tube. When they become equal, a region of contact is developed between the sheet and the wall. This region separates two similar detached regions that obey exactly the same boundary conditions that we used to obtain the universal shape in \u00a72. Therefore, the sheet geometry is represented by two segments with universal shape connected by an angular region f (figure 6b) in contact with the tube. We readily obtain the values f0Za, f1Zb and q0ZP that we found in \u00a72. There are a pair of point forces in each detached region and a distribution of forces at the contact region, as figure 6b shows. As the radius of the sheet decreases, the detached segments keep their shape and the region of contact expands. This solution is valid until point 3 meets point 0 in (x, y)Z(R, 0), as is shown in figure 6d. Since the detached segment spans an angle b, we conclude that the solution remains valid until the angular sector f equals the angle (2pK2b). It yields a value R/SZe3Z0.328. Finally, figure 7 summarizes the behaviour of the quantities ff0;f1; q0; q1g for the events described in this section. Proc. R. Soc. A (2008) For S/R!e3, the endpoint at sZ2S touches the end at sZ0. There are five point forces along the sheet, as figure 8b shows. These forces point perpendicular to the surface of contact, i", "1) and applying the constraints defined above. Our solution satisfies the compatibility condition f2Zf3, so that this shows that both detached segments can be connected through a segment in full contact with the wall. There is no solution of this kind for e4!R/S!e3, where e4Z0.323. This can be explained by the fact that the solution for e3!e cannot be continuously connected with the solution for e!e4. Force Q4 is perpendicular to the segment between points 0 and 1 in figure 8b, but the equivalent force has a radial direction in figure 6d. Hence, somehow the force Q4 must rotate between the values e3 and e4. To explain this rotation, we need to include the thickness of the sheet in the analysis, so that our approach is no longer valid in this case. Figure 8d shows the sheet shape for R=SZe5Z0:263. At this condition, a new contact is made between both detached segments. This contact adds a pair of point forces, so that there are now seven point forces, as figure 9b shows. We can use similar numerical analysis to obtain the shape of the sheet, although the technical difficulties increase" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002081_iecon.2012.6388931-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002081_iecon.2012.6388931-Figure4-1.png", "caption": "Fig. 4. NCE mode 2", "texts": [], "surrounding_texts": [ "often completely surrounded by a material. In contrast to that, medium-power machines often use a complicated mechanical structure from various iron and plastic parts to stiffen the geometry and to take up the relatively strong electromagnetic forces, shown in figure 1 [2].\nI. INTRODUCTION\nA very important component of a turbo-generator, which definitely still shows potential for improvement is the stator end winding. This is primarily used for guiding the current in the non-active part of the machine, i.e. the part of the machine which is located outside the laminated core. Due to the advances in cooling, forging and high-voltage insulation technology, the unit output of synchronous generators have been constantly increased. A particularly strong increase in unit output was in the sixties and in the seventies of the last century. There also was an increase in short-circuit power and an increase of switching operations in the grid at about the same time [3]. The combination of these different factors led and is still leading to an increased number of cases of serious damage in the stator end winding regions, caused by the occurring electromagnetic forces. With recent developments, such as the liberalization of the electricity market, or a greater share of renewable energies in electricity production, this problem is exacerbated because the power plant operators are sometimes forced to operate their machines with widely varying active and reactive power. Observations have shown that these variables may exert an influence on the performance of the stator end winding structure. Although it is the desire to address this problem through structural changes in the stiff ening elements, a consistent and complete solution could not yet be drawn. The main reasons for this are certainly mostly the complexity and variety of possible embodiment of the geometry in this area. The sometimes large differences in the structural realization mainly result from the different classes of machine performance and the associated electromagnetic forces on the stator end winding basket. For machines of smaller capacity, the stator windings are often manufactured free-floating and for machines of the highest performance class, the conductors in the stator end winding region are\nt=O\n978-1-4673-2421-2/12/$31.00 \u00a92012 IEEE 1781\nt = 2ms t = 3ms\nt = 8ms t = 9ms\nFig. l. Electromagnetic forces\n< \"\n0.75 \ufffd \ufffd \" 2 0.5 2 \"0 \" N \ufffd 0.25 E i\no", "II. MODES OF VIBRATION\nUsing the modal analysis, the natural frequencies and mode shapes of a mechanical structure are beeing evaluated in a technically relevant frequency range. This can be done in two different ways:\n\u2022 On the one hand there is computational modal analysis. For solving this problem you need a profound knowledge\nabout the geometry and the material properties but no measurements from the physical object. First you have to build a physical model with reduced properties. This keeps simulation time short. Then you have to choose sensible degrees of freedom and constraints. The result of this operation is a mathematical model which consists\nof differential equations. \u2022 On the other hand there is an experimental operation\nwith tests at the physical object by induced forces. There is no need of a profound knowledge mentioned above, but it is a must have to acquire the test object. The principle is to measure the deviation and the oscillations after inducing a motion with a shaker or a hammer. By using the fast Fourier transformation you can migrate the path, speed and acceleration signals from discrete time range to discrete frequency range. This generates a spectrum with value and phase for every stimulation. Every single spectrum has amplitude exaggerations which are characteristic for the pulse response and thus for the transfer function. The analyzer can generate the natural frequencies from all transfer functions.\nThe end winding area of a large synchronous generator can be stimulated to several oscillations similar to the a ring or a frustum. The natural oscillations from both can be found in the end winding area for deeper frequencies. It is possible that conductors oscillate separately or in groups around the perimeter or in radial direction. The oscillations in radial direction can be damped with blocks between the conductors. There is no major difference behavior between the connecting side of the end winding area and the non-connecting side. Both oscillation types mentioned above exist contemporary because of the strong joint between the conductors, the slots and the support rings.\nIn the critical frequency range are natural modes with a maximum of 6 nodes. There are examples in table I for the connecting and non-connecting side of the generator.\nThe non-connecting end winding area is symmetrical and the oscillation nodes are even spaced. The zero mode is marked with an amplitude which has a constant ramp in axial direction. There is no deformation near the slots while the maximum is at the end of the conductors. Around the perimeter are equidistant support measures which cause local mismatches for the bending stiffness. This can be seen in the oscillations. The contour lines of the deformation vector are not parallel to the axis, they are part of a sinus function with six periods.\nIn opposite of this there exist oscillations in axis direction for the first mode. Printing this motion in a three-dimensional plot in addiction to the axial and radial coordinates will cause a sinus function with only one period. There is only one node in axial direction similar to the zero mode with a higher deformation. The influence of the inhomogeneous bending stiffness is declining.\nWith raising nodes around the perimeter the influence of the locally mismatching bending stiffness declines more and more (see figures 4 and 5). The contour lines of the deformation vector become like a normal scaled sinus function.", "At the connecting side of the machine there are very unsym metrical oscillations caused by the unsymmetrical geometry. This is illustrated in figure 6 with the second mode of the connecting side. The oscillations are stronger at the positions of terminal conductors with a higher mass. The modes have a permanent position in contrast to the symmetrical side. At the symmetrical side the modes can move, theoretically. This abnormal behavior can be observed for the 4-node oscillation and declines for higher nodes (see figure 7).\nThe above mentioned nodes have the commonalities that there is only one oscillation node at the slot and an rising amplitude with a rising distance to the bundle of laminations. This behavior exists mostly at end windings where the con ductors are strongly jointed with the support measures. There exists more than one node in axial direction for machines with levitated end windings. The first node lies again next to the slots but the second node can be at several positions. It is possible that there are only little deformations at the end of the bars but high deformations in the middle between laminations and end. For this type a measurement only at the end of the bars will have no conclusiveness. In figure 8 is a 4 node oscillation illustrated with a frequency of II = 39 Hz. Figure 9\nshows the same end winding area with a 4 node oscillation and two nodes in axial direction with a frequency of 12 = 83 Hz.\nDepending on the shape of the force field, it is possible that mode shapes with multiple nodes in the axial direction can be more easily excited as a corresponding mode shape with only one node in the axial direction.\nIII. EXCITABILITY BY ELECTROMA GNETIC FORCES\nAs mentioned above there exist several natural modes of the end winding area near the single or double operating frequency of the generator. This is rated different for miscellaneous natural modes. A method is explained in the following which allows calculating a standard for rating the probability of stimulating a special mode. For this it is necessary to get a term for the force that takes effect on the system. By dividing the system in k parts the vector F for the axial force components looks like\n1 Fax,J (t) ) Fax,2 (t)\n{Fax (t)} = :\nFax,k (t)\n(1)\nUnder the condition that only the Lorentz forces have to be considered here and that these consist of a constant and a sinusoidal component, equation (1) becomes the following expression:" ] }, { "image_filename": "designv11_29_0002619_j.mechmachtheory.2017.08.007-Figure13-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002619_j.mechmachtheory.2017.08.007-Figure13-1.png", "caption": "Fig. 13. CAD model of the Exechon parallel manipulator.", "texts": [ " As a result, the motion screw system of the manipulator\u2019s moving platform can be obtained as \u23a7 \u23a8 \u23a9 A \u2217 = ( C r ) \u22a5 = x x T + v v T B \u2217 = \u2212b \u2217A \u2217 = 0 C \u2217 = ( A r ) \u22a5 = z z T \u21d2 S 3 = G 2 L 1 (67) According to (67) , it is known that the moving platform of this specific 3- P RS parallel manipulator also has two rotational and one translational degrees-of-freedom. The difference is that the direction of translation is fixed along the z -axis of {S}, without changing at different configurations. Further, the center of instantaneous rotation axes is always coincident with the origin of {T}, namely the spherical joint S 3 . Therefore, the moving platform can rotate about the origin of tool frame, but without generating any parasitic motion. 5.5. The Exechon parallel manipulator with 2R1T motions As shown in Fig. 13 , the Exechon parallel manipulator [41] constitutes of two U P R limbs which are assembled on the same plane and one S P R limb on the perpendicular plane. The inertial and tool frames, namely {S} and {T}, are structured as shown in the figure. The motion screw system of the U P R limbs can be represented as S i, 4 = span { S i, 1 , S i, 2 , S i, 3 , S i, 4 } \u21d2 V i = [ A i A i B T i B i A i B i A i B T i ] + [ 0 0 0 C i ] , i = 1 , 2 (68) where S i, j , j = 1 , 2 , 3 , 4 are the twist associated with the universal, prismatic and revolute joints, respectively S i, 1 = [ x \u02c6 rA i x ] , S i, 2 = [ v \u02c6 rA i v ] , S i, 3 = [ 0 p i ] , S i, 4 = [ v \u02c6 rB i v ] \u21d2 \u23a7 \u23a8 \u23a9 A i = x x T + 2 v v T B i = \u0302 rA i x x T + \u0302 rC i v v T C i = p i p T i + 1 2 l 2 i q i q T i , i = 1 , 2 (69) where u 1 = u 2 = x and v 1 = v 2 = v relate to axes of universal joint" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002473_b978-0-12-813489-4.00004-0-Figure4.2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002473_b978-0-12-813489-4.00004-0-Figure4.2-1.png", "caption": "Figure 4.2 Comparison of File Sizes. (A) 49 kB, (B) 8 kB, and (C) 141 kB.", "texts": [ " ASCII format allows the user to debug the file if there are any errors encountered but comes at the expense of a larger file size. In contrast, comparable binary STL files are smaller in size. For example, to store a numeric value of 10,000 in a computer, it would take about 6 bytes of storage space to store in ASCII compared to 4 bytes of storage space in binary. STL file size increases with the number of facets. A high resolution model will generate a larger STL file than a low resolution model. Fig. 4.2 illustrates the difference in file sizes of a cylinder that was designed in a CAD software program, and then converted to an STL file for AM fabrication. To accurately represent the cylindrical shape, a high resolution STL file would consist of numerous triangle facets to approximate the curved surface of the cylinder, which can be seen as a dense black cylinder on the right of the figure. On contrary, if the tolerance of the curvature is not crucial, a low resolution STL file can be used. This results in a reduction from 141 kB (high resolution) to 8 kB (low resolution)" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002623_icma.2017.8015868-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002623_icma.2017.8015868-Figure1-1.png", "caption": "Fig. 1. Structure of a tilt-wing", "texts": [ " However, since the direction of the rotor shaft and that of a shaft for attaching the fixed wing are different each other, this UAV may expect that the performance of VTOL will be decreased by downwash. In this research, it is aimed at developing a tilt-wing for tilt rotor type UAVs that integrates a rotor and a wing so that it can be tilted simultaneously to prevent its VTOL performance from decreasing by downwash. This paper describes the design and production of a tiltwing, and some experiments are conducted to check how the tilt-wing affects the VTOL performance. In addition, the overview of a tilt-wings-mounted Quadrotor is described. Fig.1 shows the structure of a tilt-wing. The tilt-wing consists of a servo motor, a brushless DC motor, and a wing frame. This servo motor is mounted to control the angle of attack of the wing and a rotor separately on the right and left. The wing frame is hollowed for reducing the weight, and integrally manufactured from ABS resin by using a 3D printer. Fig.2 shows an airfoil profile used for the tilt-wing. This airfoil profile is called NACA2410, which was designed by National Advisory Committee for Aeronautics (NACA)" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001311_ias.2012.6374017-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001311_ias.2012.6374017-Figure5-1.png", "caption": "Fig. 5. Vector diagram of a PLPF representing both (\u03c61, \u03c62) and ( \u03c6\u0302 ) : (a) > 0 (b) < 0", "texts": [ " 4 shows the gain and phase compensators necessary to ensure that a PLPF acts as a pure integrator only at the operating frequency. The value of k is selected as 1 to make the analysis simple. As shown in Fig. 4, when e = e1or2, a PLPF should be compensated by G1or2 and exp(\u03c61or2). But, in the sensorless system, the gain and phase compensators are determined by e\u03c9\u0302 . Therefore, in fact, a PLPF is compensated by G\u0302 and exp( \u03c6\u0302 ) instead of G1or2 and exp(\u03c61or2). Then, a pure integration fails and it results in the stator flux error, which in turn causes the synchronous speed error in (16). Fig. 5 clearly depicts that the synchronous speed error ( ) as (17) is related to the phase lag error ( ) as (18). ee \u03c9\u03c9\u03c9 \u02c6\u2212=\u0394 (17) )\u02c6( 2 )sgn( sEee \u03b8\u03b8 \u03c0 \u03c9\u03b8 \u2212\u2212\u22c5\u2212=\u0394 (18) where e\u03b8\u0302 is the angle of the estimated stator flux, sE\u03b8 is the angle of the back-emf. To analyze the relation between and , it is assumed that \u03c9e = \u03c9e1 and > 0. In Fig. 5(a), the additional phase lag as \u03c61 in (19) is necessary so that 1s\u0302\u03bb is orthogonal to Es [5]. However, actually, \u03c6\u0302 in (20) larger than \u03c61 is added and the phase lag of 1s\u0302\u03bb is larger than 90\u00b0. On the other hand, it is assumed that \u03c9e = \u03c9e2 and < 0. In Fig. 5(b), \u03c62 in (19) should be added to maintain the ortho- gonal relation between 2s\u0302\u03bb and Es. But, actually \u03c6\u0302 less than \u03c62 is added and the phase lag of 2 \u02c6 s\u03bb is less than 90\u00b0. It is obvious that > 0 for > 0 and < 0 for < 0. \u22c5 \u0394+ \u2212\u2212\u22c5\u0394+\u2212= \u2212\u22c5\u2212= \u2212 |\u02c6| \u02c6 2 )\u02c6sgn( 2 )sgn( 1 2121 e e e orLPFeor k tan \u03c9 \u03c9\u03c9\u03c0 \u03c9\u03c9 \u03c6 \u03c0 \u03c9\u03c6 (19) \u22c5\u2212\u2212\u22c5\u2212= \u2212 ))\u02c6( 1 ( 2 )\u02c6sgn(\u02c6 1 ee sgn k tan \u03c9 \u03c0 \u03c9\u03c6 (20) 2 21 \u02c6 |\u02c6| 1 \u0394+ \u22c5 += \u03c9\u03c9 \u03c9 e e or k G (21) 21\u02c6 kG += (22) where \u03c6LPF1or2 is the phase response of the transfer function of a PLPF, G1or2 is the required gain compensator in order that the gain of s1or2 is same as 1/| e| and G\u0302 is the gain compensator which is actually compensated in the system" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000844_robot.2010.5509937-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000844_robot.2010.5509937-Figure4-1.png", "caption": "Fig. 4. (a) An example work space, (b) its configuration space, and (c) its reduced configuration space (defined below). The s-axis is horizontal, the \u03b8-axis is vertical. Configuration-space obstacles are drawn dashed in light gray, the forbidden push range is drawn in dark gray.", "texts": [ " A configuration-space obstacle C\u03b3 consists of the configurations where the pusher intersects obstacle \u03b3. A forbidden push range FPRi consists of the configurations where the object is on the interior of path section \u03c4i and the pusher is outside the push range. By C\u03b3,i we\u2019ll mean the restriction of C\u03b3 to configurations with the object on path section \u03c4i. The forbidden space is then the union of k(n + 1) shapes: n obstacles and one forbidden push range for each of the k path sections. An example is shown in Fig. 4(a)\u2013(b). Theorem 1: The configuration space for each path section has complexity O(n) (i.e. the boundary of the forbidden space consists of O(n) vertices and constant-complexity curves between them), and thus the total configuration space has complexity O(kn). Proof: Since a path section \u03c4i has constant complexity, so do FPRi and C\u03b3,i for all \u03b3 \u2208 \u0393. We will prove that\u22c3 \u03b3\u2208\u0393 C\u03b3,i has complexity O(n). It then follows that FPRi \u222a\u22c3 \u03b3\u2208\u0393 C\u03b3,i, the forbidden space for one path section, also has complexity O(n), yielding O(kn) in total", " The combined sweep area of the object and pusher for this length-d \u201cprefix\u201d of the path section fits in a disk of diameter d + 2ro + 4rp = O(ro), and can thus intersect at most O(\u03bb \u00b7 ro 2/\u03b42) obstacles, where \u03b4 is the length of the shortest obstacle. Assuming constant \u03bb and \u03b4 = \u03a9(ro), the configuration space for this prefix has constant complexity. The complexity of the remaining \u201csuffix\u201d of the path section can be \u03a9(n), though, so the complexity of the configuration space can still be \u03a9(kn). However, for this suffix we can replace the O(n)-complexity shape \u22c3 \u03b3\u2208\u0393 C\u03b3,i by the O(1)-complexity shape that forces the pusher to remain in the object\u2019s sweep area. This yields the reduced configuration space (see Fig. 4(c)), which admits a push plan if and only if the original configuration space does, but has lower complexity and can be computed more quickly: Theorem 3: Assuming constant \u03bb and \u03b4 = \u03a9(ro), the reduced configuration space has complexity O(1) per path section (i.e. O(k) in total), and can be computed in O((k + n) log(k + n)) time using O(k + n) space. Proof: From the above discussion it follows that the reduced configuration space for one path section has O(1) complexity. Computing all C\u03b3,i and FPRi section-bysection and obstacle-by-obstacle would still take \u03a9(kn) time, though" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000431_1.3225921-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000431_1.3225921-Figure1-1.png", "caption": "Fig. 1. The model of a Slinky with two degrees of freedom.", "texts": [ " Redistribution subject to AAPT lic We modified the Slinky by lumping coils together: We fastened three groups of 24 coils together, leaving four coils free between adjacent lumps. Upon launching this modified Slinky down the stairs in the same way as before, we observed the same behavior with a couple of exceptions, that is, we observed that the motion was faster, with the time of one step now of the order of 10\u22121 s. Also for an arbitrary launch, the modified Slinky took just a few steps before tumbling off the stairs. Our empirical observations led us to model the Slinky\u2019s motion by the two degrees-of-freedom system shown in Fig. 1. The model is comprised of three point masses, each of mass m, connected by two massless rigid links of length l. The choice of this model follows directly from our observation that the motion of the modified three lumped-coil Slinky is qualitatively the same as the actual Slinky, including the fact that the overall length during motion stays approximately constant. Each \u201clink\u201d of our model represents half the length of the total Slinky. A linear torsion spring, with stiffness coefficient kt, is placed at the junction of the two massless rigid links", " The collision is also modeled as being perfectly inelastic because the end of the swing link \u201csticks\u201d to the surface of the step, that is, there is a fixed pivot there after the collision occurs. Between collisions the dynamics of the model is of a double pendulum with a stationary pivot and with a torsion spring and damper at the second joint. We define the angles of the stance and swing links as 1 and 2, respectively, 35\u00a9 2010 American Association of Physics Teachers ense or copyright; see http://ajp.aapt.org/authors/copyright_permission measured from the vertical parallel to the direction of gravity , as shown in Fig. 1. The system\u2019s kinetic energy T, potential energy V, and dissipative energy R are given by T = m 2 \u03071 2l2 cos2 1 + \u03071 2l2 sin2 1 + m 2 \u03071l cos 1 + \u03072l cos 2 2 + \u03071l sin 1 + \u03072l sin 2 2 , 1 V = mgl 1 \u2212 cos 1 + 2 \u2212 cos 1 \u2212 cos 2 + kt 2 2 \u2212 1 2, 2 and R = ct 2 \u03072 \u2212 \u03071 2, 3 where an overdot denotes differentiation with respect to the time t. The equations of motion may be obtained by solving Lagrange\u2019s equations see, for example, Ref. 14 d dt T \u2212 V \u0307i \u2212 T \u2212 V i + R \u0307i = 0, i = 1,2 4 for \u03081 and \u03082. The configuration of the two link system at a collision is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003772_j.mechmachtheory.2019.06.015-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003772_j.mechmachtheory.2019.06.015-Figure4-1.png", "caption": "Fig. 4. Real-time protective clearance between rotor and neck bush.", "texts": [ " According to Hunt-Crossley impact force law [21,46] , the impact force between the rotor and neck bush can be obtained F nb i = { k nb \u03b4 10 9 r i ( 1 + 3 2 \u03b1 \u02d9 \u03b4r i ) \u03b4r i > 0 0 \u03b4r i \u2264 0 (10) where typical value of \u03b1 for steel-steel contacts ranges from 0.08 to 0.32 s/m; k nb is the contact stiffness between the rotor and the neck bush, and it can be calculated by the Palmgren formula [47] ; \u03b4r i is the penetration between the rotor and the neck bush. \u03b4r i > 0 means that the rotor contacts with the neck bush. Fig. 4 shows the real-time protective clearance ( \u03b4r i ) between the rotor and the neck bush. It can be obtained that \u03b4r i is the distance between point A \u2019 and point B at this moment, which can be calculated by \u03b4r i = \u2212( \u03c1z i \u2212 z i \u2212 r i / tan \u03b8d ) sin \u03b8d (11) where \u03b8d is the value of the taper of the conical surfaces on the rotor and the neck bush; \u03c1z i is the real-time axial clearance between the rotor and the neck bush. \u03c1z i = { \u03c1a \u2212 z i i i = 1 \u03c1a + z i i i = 2 (12) where z i i represents the axial displacement of the neck bush in each RAIAB" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002411_s00170-017-0378-y-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002411_s00170-017-0378-y-Figure8-1.png", "caption": "Fig. 8 Manufacturing processes of LM rail", "texts": [ " The trough surrounding the die cavity can no longer be sketched as a circle alone; however, it can be designed to take any shape to achieve the optimal product situation. The shape of the trough is similar to that of a ladder; the left side near the die edge is higher than the right side. Figure 7 illustrates a trough cavity on which the workpieces are laid. Table 3 lists the billet data for the experiment. Workpieces with a diameter and thickness of 40 mm and 25 mm, respectively, were laid on the trough for experiments. A negative clearance size (\u22125%) for the punch diameters was applied in the experiments. Figure 8 illustrates the steps of the manufacturing processes from the billet to the product. The detailed descriptions of the experimental procedures are as follows: Step 1: Workpieces with a diameter and thickness of 40 and 25 mm, respectively, were laid on the container for experiments. No lubricant was required for the workpieces, punch, or die. Step 2: A punch with a negative clearance (\u22125%) descended to touch the surface of the workpieces in the hole of the ram. Step 3: The ram was used to press the workpieces into the trough cave" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002635_s11771-017-3585-7-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002635_s11771-017-3585-7-Figure7-1.png", "caption": "Fig. 7 Theoretical models of face gear and worm wheel involving errors: (a) Face gear; (b) Worm wheel", "texts": [ " Further, comparison can be made between the theoretical face gear tooth surface involving errors and the tooth surface acquired by one of the above mentioned simulation process (here the simulation result of the first group is taken), which completely verifies that the results of both theoretical derivation and simulation process are identical. Taking tangential linear position error as 1 mm and using the parameters listed in Table 1, the error surface discrete points of the face gear and the worm wheel can be calculated. Then, the separate theoretical model can also be obtained by importing those discrete points into CATIA software, as shown in Fig. 7. J. Cent. South Univ. (2017) 24: 1767\u22121778 1773 4.2 Face gear ground in VERICUT for simulation 4.2.1 Simulation I The method adopted in simulation I is to grind the face gear by a worm wheel involving errors. The Qin Chuan YK2050A Gear Grinding Machine is chosen as the processing equipment, which can meet the requirements of face gear grinding movement based on the worm wheel as mentioned above. The complete simulation environment (see Fig. 8) can be constructed by establishing a machine along with a face gear blank and taking the 3-D model of worm wheel involving errors obtained in section 4", " (2017) 24: 1767\u22121778 1774 within the range of allowable error. Therefore, this result indicates that grinding the face gear blank by a worm wheel involving errors is equivalent to grinding the face gear blank by a theoretical worm wheel with actual installation position errors, which proves in turn that this new method to solve the face gear error tooth surface is correct and practicable. Further, comparison can be made for errors between the theoretical face gear tooth surface involving errors (as shown in Fig. 7(a)) and the tooth surface obtained in one of the simulations (the result of simulation I is taken). Similarly, Fig. 13(a) shows the result of overlapping two face gear tooth surfaces, where green areas represent the tooth surface processed in simulation I and brown areas represent the theoretical tooth surface. It is found that the maximum error between two tooth surfaces is 0.104 mm (as shown in Fig. 13(b)), which is also within the range of allowable error, indicating that the results between theoretical derivation and simulation process are identical" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002714_detc2017-67203-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002714_detc2017-67203-Figure6-1.png", "caption": "FIGURE 6", "texts": [ " When Point C is at the target position for the given inputs, the effects of clearances or clearance links cancel each other as shown in Figure 5(d), in which the position and direction of each nominal link is identical to that of the instant structure in Figure 4(a). 4. Since the uncertainty associated to a target position is the concern, Figure 5(d) should be interpreted as the instant structure of Figure 4(a) or Figure 4(b) mounted on the three flexible links AiAi', in which each flexible link represents any possible combination of the three clearance links. Therefore Figure 5(d) is equivalent to Figure 6(a), in which Li is the length AiC obtained in Eq. (3) for the instant structure of Figure 4. For point C to reach a target position, Li and the location of Ai, i = 1, 2, 3, represent the deterministic aspect of the position, while the clearance links the uncertainty. 5 Copyright \u00a9 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/16/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 5. When point C is at an extreme position, i.e. at the boundary of the workspace (uncertainty region) of point C, all clearance links in each leg will be stretched along a line. Since the extreme uncertainty is of the concern, all clearance links in each leg can be modeled as a single clearance link with length ai = 3\u03b4R. Therefore, the 13- bar model in Figure 6(a) can be reduced to the 7-bar linkage in Figure 6(b). The workspace of point C in Figure 6(a) is the uncertainty region associated to the target position. 6. The linkage in Figure 6(b) is a two degree-of-freedom 7- bar linkage. Each loop of the linkage is a Class I fivebar chain with two short clearance links. The angle between any two links on a leg may reach 0 and 180 degrees. For any stand-alone leg, say i, the workspace of point C is the ring area enclosed by the concentric circles with radii (Li + ai) and (Li ai) and center at Ai. Therefore, the workspace of point C of the linkage in Figure 6(b) is the intersection of the three ring areas from the workspaces of the three legs (Figure 7). This workspace is the uncertainty region of point C on the platform of the 8-bar parallel manipulator. It is observed that the boundary of the uncertainty region generally consists of six circular segments. The radial distance between opposite segments is 2ai. If the parallel manipulator has three identical legs, the boundary of this uncertainty region is a hexagon, which inscribes a circle of radius ai (Figure 7) An intriguing issue is the comparison of the uncertainty region of a serial RRR robot with its 3RRR parallel robot counterpart", " As shown in Figure 8(c), this circular uncertainty region is inscribed by the hexagonal region with arcs for edges of its 3RRR parallel robot counterpart. Evidently, compared to a compatible serial robot, the parallel robot has a larger uncertainty region. Multiple loops in parallel robots do have the effect of reducing the uncertainty region but they cannot fully offset the uncertainty caused by using more joints. The methodology of finding the uncertainty region of 3PRR or 3RPR parallel robots is almost identical to that of 3RRR parallel robots. Their uncertainty model is also the same as Figure 6(b). A 3PRR manipulator with three legs carrying a triangular platform B1B2B3 is shown in Figure 1(b). The uncertainty region can be found in the procedure as that of 3RRR parallel manipulators except that the location of A1, A2, and A3 are determined by the sliding inputs and the combined clearance link is ai = 2\u03b4R + \u03b4P. For a 3RPR parallel robot, as shown in Figure 1(c), the linear input determines the nominal length li\u2019= MiBi and the clearance link length is ai = 2\u03b4R + \u03b4P. The uncertainty region is the workspace of the linkage in Figure 9 in which Li = MiC = MiBi + BiC" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002069_icra.2012.6224743-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002069_icra.2012.6224743-Figure1-1.png", "caption": "Fig. 1. Nominal and actual transformation matrices", "texts": [ " Finally, a summary of the paper is given in Section VII. The presence of errors and uncertainties in robotic work cells pose a great challenge to the effective implementation of offline programming. Error sources and uncertainties within the robotic manipulator include manufacturing defects, inertial loading, mechanical wear etc. This result in a deviation between the pose of the nominal {KN t } and actual {KA t } tool frames relative to the base frame {Kb}, described by TN bt and TA bt respectively, and illustrated in an exaggerated Fig. 1 and Fig. 2. Another major source of errors comes from alignment and datuming errors, loading, and external axes, if any, within the work cell. This results in a deviation between the pose of the nominal {KN w } and actual {KA w} work object frames relative to the base frame {Kb}, described by TN bw and TA bw respectively. These errors prevents the robot from reproducing the desired tool to part motion. One solution is to model, identify and subsequently compensate for these error sources. This approach has been proposed and developed in both the academia [4], [5], [6], [7], [8], [9], [10] and commercially in the form of CalibwareTMfrom ABB, ROCALTMfrom Nikon Metrology and DynaCalTMfrom Dynalog" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000119_978-1-4020-8600-7_25-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000119_978-1-4020-8600-7_25-Figure2-1.png", "caption": "Fig. 2 Modeling method.", "texts": [ " In order to place the robot we have only to move the base link. The base link is unique for each robot. A serial link is held to another link (called father link) according to the joint between both links. Supported joints are revolute joints, linear joints, spherical joints and universal joints. A mobile link is positioned using absolute coordinates relative to the base link. Constraints are used to restrict motion between two different links. 236 Singularity Free Path Planning for Parallel Robots As shown in Figure 2, a parallel manipulator is made of a base platform, a mobile platform and serial legs. The idea is to replace a non actuated joint in each leg by the corresponding constraints. These joints are called closure constraints. The base platform is modeled using a base link while the mobile platform is modeled by a mobile link. Legs are modeled using serial links. By replacing only non actuated joints by constraints, we keep the actuated joint coordinates in the generated equations. Constraints between mobile links and some serial links give equations on operational variables and joint coordinates" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003929_codit.2019.8820344-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003929_codit.2019.8820344-Figure1-1.png", "caption": "Fig. 1. A connection scheme of a cart with two robots", "texts": [ " As a result we receive a trajectory of movement for our control object that differs from the optimal trajectory not more than on \u03b5. We can rule accuracy of movement by choosing positions of the stabilization points. We can also receive a value of the criterion that differs from the optimal value not more than on \u03b5 for considered initial and terminal conditions. The theorem is proved. Consider a mathematical model of moving a cart in twodimensional space by two robots. The scheme of movement is presented in fig. 1. In fig. 1 (x0, y0) are coordinates of the cart center, (x1, y1) and (x2, y2) are coordinates of centers of first and second robots, l1 and l2 are lengths of rigid leashes. A system of differential equations for dynamics of the robots have the following form [4] x\u0307i = 0.5(ui,1 + ui,2) cos \u03b8i, y\u0307i = 0.5(ui,1 + ui,2) sin \u03b8i, \u03b8\u0307i = 0.5(ui,1 \u2212 ui,2), (22) where ui,1, ui,2 are components of control vectors ui = [ui,1 ui,2]T , i = 1, 2. For this system given initial conditions xi(0) = x0i , yi(0) = y0i , \u03b8i(0) = \u03b80i , i = 1, 2" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001447_icra.2013.6631237-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001447_icra.2013.6631237-Figure3-1.png", "caption": "Fig. 3. A 3R robot (top), and its kinematically equivalent bar-and-joint assembly (bottom).", "texts": [ " Therefore, by equating the right hand side of the above two equations, we conclude that: A2 n,o,p(\u03a8i,j,k,l,m + 36Vi,j,k,l Vi,j,k,m) \u2212A2 i,j,k(\u03a8n,o,p,l,m + 36Vn,o,p,l Vn,o,p,m) = 0 (6) This equation is the closure condition of a double banana. It is satisfied if, and only if, it can be assembled with the assigned bar lengths. Next, it is shown how, by using this closure condition, univariate polynomials for the position analysis of important serial and parallel robots can be straightforwardly obtained without relying on trigonometric substitutions or difficult variable eliminations A. Inverse kinematics of 3R serial robots Fig. 3(top) shows a general 3R serial robot, a manipulator with three rotational joint variables. This robot has been used for positioning tasks in the Cartesian space or as the regional serial kinematic chain in wrist-partitioned 6R robots, the most common serial robots [9], [10]. The inverse kinematics problem of this serial robot consists in finding the values of its joint angles to attain a given location for its end-effector relative to the base. It has been shown that this problem reduces to compute the solutions of a fourth-order polynomial", " In [12], Smith and Lipkin analyzed geometrically this solution using conic sections. Next we present an alternative to the approach based on homogeneous transformations that exploits the closure condition of the double banana derived in the previous section. In a serial manipulator, a link connecting two skew revolute axes can be modelled by taking two points on each of these axes and connecting them all with edges to form a tetrahedron [13]. Then, a 3R serial robot can be modelled as the bar-and-joint framework involving 7 joints and 15 bars shown in Fig. 3(bottom). Observe how such bar-and-joint framework corresponds to the double banana in Fig. 1 after removing the bars linking Pp and Pm, and Pk and Pm, and then merging Pk and Pp. Therefore, according to the notation of Fig. 3 and equation (6), the closure condition of the 3R serial robot is given by A2 6,7,3(\u03a81,2,3,4,5 + 36V1,2,3,4 V1,2,3,5) \u2212A2 1,2,3(\u03a86,7,3,4,5 + 36V6,7,3,4 V6,7,3,5) = 0. (7) This equation is a scalar radical equation in a single variable: s3,5. The different real roots of this equation \u2014values of s3,5\u2014 correspond to the different solutions of the inverse kinematics problem. The above equation can be reduced to a polynomial by simply clearing the radicals associated with V1,2,3,5 and V6,7,3,5. This yields ( A4 6,7,3\u03a8 2 1,2,3,4,5 \u2212 2A2 6,7,3A 2 1,2,3\u03a81,2,3,4,5\u03a86,7,3,4,5 +A4 1,2,3\u03a8 2 6,7,3,4,5 + 1296A4 6,7,3V 2 1,2,3,4V 2 1,2,3,5 \u2212 1296A4 1,2,3V 2 6,7,3,4V 2 6,7,3,5 )2 \u2212 ( 72A4 6,7,3\u03a81,2,3,4,5 V1,2,3,4 \u2212 72A2 1,2,3A 2 6,7,3V1,2,3,4\u03a86,7,3,4,5 )2 V 2 1,2,3,5 = 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001200_rspa.2010.0617-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001200_rspa.2010.0617-Figure1-1.png", "caption": "Figure 1. Geometry of the contact problem. A wavy surface with wavelength l and amplitude A is indented by a rigid sphere of radius R under applied normal load P and tangential load T . Amplitude and wavelength are exaggerated in this diagram for visual clarity; in this model, l R so that contact with multiple peaks is achieved.", "texts": [ " Axisymmetric wavy surface contact under combined normal and tangential loading (a) Contact model In the following analysis, contact between the axisymmetric wavy surface of an elastic half-space and a rigid spherical indenter subjected to both normal and tangential loading in the presence of adhesion is modelled by building on the solutions presented by Waters et al. (2009), Waters & Guduru (2010) and Johnson (1997). The key assumptions are that complete contact is achieved within the contact area between the sphere and the wavy surface during loading; the normal and tangential tractions are uncoupled; and that slip is negligible within the contact area. The geometry of the wavy surface contact problem is shown in figure 1, where the profile of the rigid sphere of radius R is approximated by the paraboloid z = r2 2R , (2.1) and the height of the wavy surface is described as a sinusoidal function of the radial coordinate r , z = A ( 1 \u2212 cos 2pr l ) , (2.2) where A and l are the amplitude and wavelength of waviness, respectively. When A > 0, the surface is convex up at r = 0; when A < 0, the surface is centrally concave. In this model, it is assumed l R so that the initial contact area consists of multiple wavelengths" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000071_cdc.2009.5400065-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000071_cdc.2009.5400065-Figure1-1.png", "caption": "Fig. 1. (a) Initial deployment with intruder undetected; (b) Final deployment with intruder detected.", "texts": [ " For a given corridor C, let B \u2282 C be a line segment connecting W1 and W2, and \u03b80 be the angle of the corridor C with respect to the x-axis. The first self-deployment objective is to have a network of autonomous mobile sensors to cover a line B across a given corridor C. This kind of coverage forms a sensor barrier that can be used to detect penetrating objects (intruders) in a corridor C. At the time of initial deployment, the mobile sensors scatter around C and they may not detect intruders moving along C, see Fig 1(a). To meet the self-deployment objective, the mobile sensors must move autonomously to cover the line segment B so that the sensor network guarantees that any intruder will be detected when it crosses the line segment B, see Fig 1(b). According to the terminology introduced by Gage [5], the first deployment problem studied in this paper is a barrier coverage problem. In this paper, we consider a mobile sensor network consisting of n autonomous sensors labeled 1 through n. Let vi(t) and \u03b8i(t) be the linear velocity and heading of the sensor i, respectively. The kinematic equations of the sensors are given by: x\u0307i(t) = vi(t) cos(\u03b8i(t)), y\u0307i(t) = vi(t) sin(\u03b8i(t)) (1) for i = 1, 2, . . . , n, where (xi(\u00b7), yi(\u00b7)) \u2208 R 2 be the Cartesian coordinates of the sensor i and \u03b8i(\u00b7) \u2208 R be its heading with respect to the x-axis measured from the xaxis in the counter-clockwise direction" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003238_imcec.2018.8469605-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003238_imcec.2018.8469605-Figure2-1.png", "caption": "Fig. 2. Hysteresis performance under sinusoidal excitation.", "texts": [ " The hysteresis model commendably describes the quasi-static transmission process of the geared mechanical system. The describing function method has been demonstrated to be an effective tool used for nonlinear system stability analysis [12~13]. This method considers that the fundamental wave of the output of the nonlinear system that satisfies certain conditions is approximate to the system output with the sinusoidal excitation. It's applicable to most nonlinear systems [12~13]. With sinusoidal signal as the input of the system with gear backlash, the system outputs are shown in (1) and Fig. 2. in out in 1 ( ) 0 2 ( ) 2 ( ) 2sin ( ) m m m k t k t k t (1) where 2\u03b4 is the backlash angle, \u03b8m and \u03c9 are the amplitude and frequency of excitation, respectively, k is the slope of the output characteristics. The describing function N(\u03b8m) of the nonlinear system with hysteresis [14] is described in (2). 1 22 2 2( ) [ sin (1 ) (1 ) 1 (1 ) ] 2 4j ( 1) m m m m m m kN k (2) B. Identification method based on describing function method Based on the describing function method, the output fundamental wave of the nonlinear system with sinusoidal excitation is approximated to represent the system response" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001739_s0081543813040093-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001739_s0081543813040093-Figure8-1.png", "caption": "Fig. 8. Trajectory of the center of the ball during the fast slip period.", "texts": [ "1) The trajectory of the mass center is a parabola. Indeed, assume without loss of generality that x\u03020 C = 0, y\u03020 C = 0 and \u03d5\u03020 s = 0 at the initial time moment. Hence x\u0302C = \u2212\u03bb \u03c42 2 + v\u03020 s \u03c4 + \u03c9\u03020 h sin \u03b30 s \u03c4, y\u0302C = \u2212\u03c9\u03020 h cos \u03b30 s \u03c4, and the angle between the axis Oy and the trajectory of the mass center at the initial instant equals \u03b30 s , the angle between the slip velocity and the initial horizontal angular velocity (the slip velocity is directed along the axis Ox at the initial time moment) (Fig. 8). If the component of the angular velocity of the ball along the slip velocity vanishes, we have \u03b30 s = \u03c0/2 and the parabola degenerates (coincides with a part of a straight line). For \u03c4 > \u03c4\u2217, i.e., when the slip velocity becomes of order \u03b5\u03022, the omitted terms of order \u03b5/v\u0302s involved in F\u0302s become of order \u03b5\u0302 and the error of approximation starts to grow up to O(1) (Fig. 9). Hence from this moment more accurate approximations of friction forces must be used. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS Vol" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002595_1350650117727230-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002595_1350650117727230-Figure3-1.png", "caption": "Figure 3. Eccentric deflections of the stationary and rotating seal elements. (a) Planar kinematics of seal eccentricity and (b) film thickness at a corresponding point on each surface.", "texts": [ " The eccentric kinematic analysis is performed in the system-fixed frame because (a) condition monitoring systems usually measure inertial dynamics and (b) the contact reactions will be easier to intuit in the system-fixed frame. The consequence of choosing a system-fixed versus rotating frame is somewhat arbitrary, since other phenomena (e.g. shaft cracks) are easier to understand in a shaft-fixed rotating frame. Nevertheless, a choice must be made, and the systemfixed frame will be employed herein. The eccentric kinematics for the stationary and rotating seal elements are shown in Figure 3(a). The geometric centers of the stationary and rotating seal elements are denoted Cs and Cr, respectively. The undeflected geometric centers of both elements lie at Os and Or along the shaft rotation axis; in this work, these points are assumed to be co-linear. The eccentric deflection of element j in the ith direction is labeled ji. Using the inertial frame, the planar position vectors locating the center of each element with respect to Or,s are r\u00f0CO\u00des \u00bc s e\u0302 \u00fe s e\u0302 \u00f06\u00de r\u00f0CO\u00der \u00bc r e\u0302 \u00fe r e\u0302 \u00f07\u00de As will be seen, friction forces and fluid shear forces depend on the relative eccentricity between the elements and the relative eccentric velocity. From Figure 3(a), the relative eccentricity vector is \u00bc r\u00f0CO\u00des r\u00f0CO\u00der \u00f08\u00de The dynamic forces are functions of the acceleration of each element\u2019s center of mass. This work assumes that the stationary seal element is eccentrically balanced, that is Cs\u00bcGs; consequently, the acceleration of the stationary element center of mass relative to Cs is found by differentiating equation (6) aGs \u00bc aCs \u00bc ao \u00fe @2 r\u00f0CO\u00des @t2 \u00fe _ l0 r\u00f0CO\u00des \u00fe l0 l0 r\u00f0CO\u00des \u00fe 2 l0 @ r\u00f0CO\u00des @t \u00f09\u00de where l0 is the maneuver rotation of the system, and thus, the system-fixed frame rotation rate", " The locations on the seal elements commensurate with point p in the sealing dam are denoted ps and pr for the stationary and rotating seal elements. The position and velocity of these points must be found to determine the fluid and contact pressures. For consistent comparison, these quantities must be described using the same coordinate system. The maneuver velocities act with parity on both seal elements, and therefore, do not affect the fluid pressure or shear forces. Furthermore, this work assumes that the rotating element is always contained entirely within the bounds of the stationary element (see Figure 3(a)). The geometry of the sealing apparatus lends itself naturally to a polar coordinate description; here, a polar coordinate system \u00f0r, \u00de will be referenced relative to the rotating seal element\u2019s center. The unit vectors defining the and r frames are related by the following rotation transformation e\u0302 e\u0302 e\u0302 8>< >: 9>= >; \u00bc cos sin 0 sin cos 0 0 0 1 2 64 3 75 e\u0302r e\u0302 e\u0302 8>< >: 9>= >; \u00f022\u00de The points pr and ps are located relative to the rotating and stationary seal element geometric centers by the vectors r1 and r2, respectively, as shown in Figure 3(a). In the polar coordinate frame, these vectors are r1 \u00bc re\u0302r \u00f023\u00de r2 \u00bc r1 \u00bc \u00bdr\u00fe \u00f0 r s \u00de cos \u00fe \u00f0 r s \u00de sin e\u0302r \u00fe \u00bd\u00f0 r s \u00de cos \u00f0 r s \u00de sin e\u0302 \u00f024\u00de Every point ps on the stationary element has the same velocity in the frame because the element does not rotate about . The velocity Vps is then always equal to the velocity of point Cs Vps \u00bc _ s e\u0302 \u00fe _ s e\u0302 \u00bc \u00f0 _ s cos \u00fe _ s sin \u00dee\u0302r \u00fe \u00f0 _ s cos _ s sin \u00dee\u0302 \u00f025\u00de The velocity of every point pr on the rotating element accrues an additional contribution from the element\u2019s rotation ", " These forces depend on the complex interactions between fluid pressures, fluid shear, surface roughness, and friction, all of which are influenced strongly by the system dynamics (as described using the kinematic expressions provided in earlier sections). The requisite relationship required for deriving the fluid and contact forces is the clearance between the seal elements (i.e. the fluid film thickness), which is discussed first. The fluid and contact forces are then derived as a function of the clearance. The fluid film clearance, shown in Figure 3(b), is the axial offset between corresponding points on the stationary and rotating seal elements, and contains contributions from axial and angular deflections in addition to the seal face geometry contributions. To ensure consistency, the film thickness h\u00f0r, \u00de is given with respect to the polar coordinate system attached to the rotating seal element center h\u00f0r, \u00de \u00bc Co \u00fe \u00f0usz urz\u00de \u00fe \u00f0 s r2 r r1\u00de e\u0302 \u00fe \u00f0t\u00de\u00f0r ri\u00de \u00f031\u00de where the coning \u00f0t\u00de is left as a general function of time since it depends on transient thermoelastic deformations of the seal faces" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001375_j.piutam.2011.04.011-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001375_j.piutam.2011.04.011-Figure2-1.png", "caption": "Fig. 2: Foot-shank model", "texts": [ " Therefore, the interpretation of an effective mass is possible only under special circumstances. Otherwise, the foot strike intensity is characterized by the pre-impact CMSKE and it depends on the pre-impact velocity and a tensorial quantity, PT c MPc, that may be termed effective mass matrix of the foot touchdown. The detailed, closed-form expression of this for the general case is quite complex. However, it becomes significantly simpler for the L-shaped foot-shank configuration investigated in [1], where \u03b1 = 0 and \u03b2 = 0 (Fig. 2). For this simpler case, the expressions of PT c MPc are shown in Eqs. (A.3) and (A.4) for the very compliant and very stiff cases, respectively. The specific case investigated in [1] is represented in our description by pre-impact velocity v\u2212 = [0, y\u0307\u2212A, 0, 0]T . For this case, assuming the L-shaped foot-shank configuration as in [1], and using Eqs. (5), (A.3) and (A.4) the pre-impact CMSKE reduces to T\u2212c = 1 2 [ m(m + 4M) 4(m \u2212 3ms + 3(m + M)s2) ] ( y\u0307\u2212A )2 (7) for the very compliant ankle, and T\u2212c = 1 2 [ 4L2M(m + M) + l2m(m + 4M) 4(L2M + l2(m \u2212 3ms + 3(m + M)s2)) ] ( y\u0307\u2212A )2 (8) for the case of a very stiff ankle", " We can see that for small values of the strike index the variation of the ankle angle can have an effect, which cannot be represented by simple, one DoF models. However, FFS based running is usually characterized by higher strike index values, where the effects of the changes in the ankle angle are not significant. The characteristic joint angles for different foot strikes are presented in Table 2 based on the experimental kinematic data reported in [1]. If the assumption of the L-shape, zero values for both \u03b1 and \u03b2 Fig. 2, does not hold, but we assume that the velocity of the foot-shank model is composed of only the vertical velocity component of the foot, then the pre-impact CMSKE can still be expressed in closed form based on (5). For the compliant ankle case this can be written as 2T\u2212c = [ 12(4m2 + 5mM + M2) sin(\u03b1)2s2 \u2212 6m sin(\u03b1)((8m + 5M) sin(\u03b1) + 3M sin(\u03b1 + 2\u03b2))s 6(8m + 5M + 3M cos(2(\u03b1 + \u03b2)))s2 \u2212 48ms + 16m \u2212 2m(\u22125(m + M) + 3m cos(2\u03b1) \u2212 3M cos(2\u03b2)) 6(8m + 5M + 3M cos(2(\u03b1 + \u03b2)))s2 \u2212 48ms + 16m ] ( y\u0307\u2212A )2 (9) The term in the square bracket represents the effective mass that can be obtained for this more general case" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001926_codit.2013.6689629-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001926_codit.2013.6689629-Figure3-1.png", "caption": "Fig. 3. Coordinate Frames and Hovering\u2013Mode Operational Principles", "texts": [ " h) A Commercial Off-The Shelf (COTS) USB camera, which combined with Optical Flow for indoor spaces [1, 5] image processing algorithms implemented in the open-source Computer Vision software framework OpenCV [6], provides an estimation of the UAV\u2019s translational motion. i) 3 high-torque Servos, for the control of the rotors\u2019 orientation. j) 2 high-power Scorpion SII-v2-3020 780kV Brushless DC (BLDC) main motors with 3-bladed 13x8-inch propellers for the main rotors, and a 63 mm-diameter Ducted Fan tail rotor. k) 3 high-efficiency fast-acting Electronic Speed Con- trollers (ESCs) driving the BLDC motors. The UPAT-TTR\u2019s translational hovering mode operation principles are presented in Figure 3, along with the BodyFixed coordinates Frame (BFF) B = {Bx, By, Bz} and the North-East-Down (NED) [7] Local Tangential coordinates Plane (LTP) E = {N, E, D}. Let \u0398 = {\u03c6 , \u03b8 , \u03c8} be the LTP-based rotation angles vector, and XW = {x, y, z} the LTP-based position vector. Also, let \u2126 = {p, q, r} be the BFF-based angular rotation rate vector, and U = {u, v, w} be the BFF-based velocity vector. In achieving the system\u2019s rotational (attitude) control, the roll (\u03c6 ) is controlled via the differential thrusting of the main rotors, the pitch (\u03b8 ) via the differential thrusting of the front and tail rotors, and the yaw (\u03c8) via the tilting of the tail rotor. Also, as depicted in Figure 3, the translational motion is controlled as follows: The vertical (Bz direction) translation is controlled via the total thrust produced by the 3 rotors. The lateral (By direction) translation is controlled via the projection of the total thrust vector in that direction, which is achieved by producing a roll (\u03c6 ) angle. The longitudinal (Bx direction) translation is controlled via vectoring/projection of the 2 main rotors\u2019 thrust vector, which is achieved by equally tilting them by an angle \u03b3x with respect to the Bz axis" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002397_b978-0-12-812644-8.00003-5-Figure3.23-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002397_b978-0-12-812644-8.00003-5-Figure3.23-1.png", "caption": "FIGURE 3.23", "texts": [ " Since the robot hangs on the overhead lines, when crossing obstacles, the posture of the robot should be kept stable and the clearance between the robot and other conductors and line tower metal parts should be adequate, and these make the design of the robot difficult. One kind of obstacle-crossing mechanism adopts curved arms mimicking the climbing of apes, and posture controlling here is complicated. Another kind adopts a snake-like obstacle-crossing mechanism, but it is not suitable for crossing large obstacles or big spaces. Fig. 3.23 shows the mechanical structure of an inspection robot of the small vehicle type, and its obstacle-negotiation mechanism also has the problem of small crossing space. Since the simple wheeled locomotion mechanism has no obstacle-crossing ability, the obstacle-negotiation mechanism for it still needs to be designed. The forms of alternative body mechanism are a wheel and arm composite mechanism, the apelike arm climbing mechanism, and a multisection split mechanism, etc. the apelike arm climbing mechanism can be classified into a scalable arm and an assistant probe arm" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002894_mepcon.2017.8301302-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002894_mepcon.2017.8301302-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of the measurement platform", "texts": [ " 1 can be written in discrete form as given by Eq. 2 based on Improved Euler\u2019s formula, which approximates the integration by summation of rectangular areas [14]. )0()]()([)( 1 \u03bb\u03bb +\u22c5\u22c5\u2212= = s n k TkiRkVn (2) where n is the number of sampling points for calculations, k is the number of sampling points before n, and Ts is the sampling period. For direct measurement of static torque characteristics, the phase current is kept at the desired value, and the torque is recorded directly from static torque transducer or using force measurement unit. Fig. 1 shows the schematic diagram of the measurement platform while Fig. 2 illustrates the practical implementation of this platform. The platform consists of SRM, Force sensor, data acquisition board (DAQ NI-6009), a personal computer (PC), digital signal processor (DSP), IGBT asymmetric bridge converter, and other electronic interface boards. Brief descriptions of the components are given below: 1) SRM: four-phase 8/6-pole con guration with 4 kW, 600 V, 9A, and 1500 r/min rated values. 2) Force Sensor: it is KALIBER product with the full-scale force of 1 kN and accuracy of 0", " A maximum current of 18A is adopted for flux measurements with positioning step of one mechanical degree. After measurement of flux-linkage characteristics, the phase self-inductance can be calculated using Eq. 3 [2]. The inductance profile is plotted as a function of rotor position at various current magnitudes as shown in Fig. 5. It can be noted that the saturation levels are changed according to the current value. diiiL /),(),( \u03b8\u03bb\u03b8 = (3) The motor torque is measured directly based on force measurement as given in Fig. 1. The force signal is measured and recorded along with motor current while the rotor is fixed at a certain position. Fig. 6 shows the recorded force waveform. After force measurement, the motor torque (Nm) is calculated as the multiplication of force (N) by force arm (m). Fig. 7 shows the measurement results of the static torque characteristics as a function of rotor position for several excitation currents. The maximum current adopted in the torque measurement is 18 A with a step of 2A. The numerical computation errors and measurement noise/ errors affect measurement accuracy" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003076_0954406218784619-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003076_0954406218784619-Figure7-1.png", "caption": "Figure 7. Steady thermal deformation nephogram of hob assembly.", "texts": [ " A reasonable explanation for this observation is that although a small portion of cutting heat transfers to the bracket and motor cover via bearings, the cutting heat left at the hob surface could not dissipate quickly. The accumulated heat caused the hob centre to have the highest temperature. Because the rack was far away from the heat sources and had the largest contact area with the ambient air, the rack had the lowest temperature among all components. Subsequently, according to the calculated steadystate temperature distribution, further structural deformation analysis was conducted, and the X/Y/ Z-direction deformation of the hob assembly is shown in Figures 7 and 8. Figure 7(a) shows that the largest total thermal deformation (94.5 mm) appeared at the bracket. This is because the bracket was adjacent to two major heat sources, namely, the adjacent bearing and the hob, both of which had a high temperature. So the lower temperature of the bracket inevitably caused a large temperature gradient at this region and consequently a large deformation there. The thermal deformation in the X-axis direction considerably affects the gear hobbing accuracy, hence, it is necessary to locate the position which has the largest deformation in the X-axis direction. According to Figure 7(b), the hob had the largest structural deformation in X-direction (65.1 mm). This is because the gear hobbing machine used a hydraulic cylinder to fix the tool bar during the machining process, thereby limiting the axial deformation of the tool bar, which is connected to the bracket. When the bracket was heated, the tool bar would displace in the X-axis direction along with the bracket. Therefore, the largest deformation of the hob appeared in the X-direction. Transient temperature field and thermal deformation analysis To understand how the temperature distribution of the hob assembly changes with time, a transientstate thermal characteristics analysis was conducted, and temperatures at six selected points were monitored" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001295_j.msea.2011.12.092-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001295_j.msea.2011.12.092-Figure3-1.png", "caption": "Fig. 3. Schematic illustration for measurement of bond width and depth.", "texts": [ " Cross-sectional samples for metallurgical examination were cut from the welded joint at four locations as shown in Fig. 1. The samples were mounted in polymer resin and etched in a solution composed of either 10 ml of acetic acid diluted with 100 ml of distilled water for macroscopic observation or a solution of 5 ml of acetic acid + 5 g of picric acid + 10 ml of distilled water and 70 ml of ethyl alcohol for microscopic observation. The macrostructure and microstructure of the weld joint were examined using an optical microscope and a scanning electron microscope (SEM), respectively. As shown in Fig. 3, bond width and penetration depth were measured at all four locations by using an image analysis software. The length of the grain was measured to determine the grain size. The elemental compositions were analyzed by Energy dispersive x-ray spectroscopy (EDX). The sample was also used for Vickers microhardness testing under a load of 245.2 mN and a dwell period of 15 s. Tensile tests were performed on welded metal with and without nanoparticles. 3. Results and discussion 3.1. Effect of scan speed on weld appearance In autonomous welding, the favorable clearance gap between the two sheets was below 35 m because the gap acted as a barrier that diminished heat transfer from the upper to the lower sheet, thereby producing a small bond width and shallow penetration depth [9]" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000058_epepemc.2008.4635600-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000058_epepemc.2008.4635600-Figure1-1.png", "caption": "Fig. 1 Simplified PMSM drive fed by a matrix converter", "texts": [ " It also provides more choice of voltage vectors than a two-level, three-phase inverter, so that smaller input voltages may be employed when the position estimated is needed. In this way, the motor line ripple can be reduced. Experimental results of position estimation at low and zero speed are given in this paper to validate the proposed principle. The effect of applying smaller input voltages on the motor line currents is also reported. II. POSITION ESTIMATION ALGORITHM FOR A THREE-PHASE MATRIX CONVERTER A. Introduction to the SVPWM of the Matrix Converter The schematic of the matrix converter fed PMSM drive is shown in Fig. 1. Many modulation schemes have been developed with an aim to find the appropriate switching pattern for each of the nine power devices [7]. As one of the most general modulation schemes used in direct matrix converters, the direct SVPWM is chosen in this work. The brief introduction to its principle is given here. While in the indirect SVPWM of the matrix converter, the modulation is split into two successive stages, i.e. the rectification stage and the inversion stage, to simulate the operation of an inverter, the direct SVPWM considers these two stages simultaneously" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001164_s11012-012-9660-0-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001164_s11012-012-9660-0-Figure2-1.png", "caption": "Fig. 2 Internal mechanical seal with oscillating stator: 1\u2014chambers on stator; 2\u2014channels on rotor; 3\u2014the seal rotor; 4\u2014the seal stator; 5\u2014four springs mounted equidistant; 6\u2014the shaft; 7\u2014the sealing enclosure; 8\u2014O rings", "texts": [ " In this section, the hydrostatic effect on the mechanical seals with oscillating stator is probed and static analyses as well as dynamic response of the oscillating stator are theoretical and experimental investigated. Relations to design a mechanical seal with oscillating stator and to verify their operating conditions are accurate presented. The installation for experimental tests, the methodology for experimental investigations and the experimental results are presented, respectively. In Sect. 3, finite element analysis of stator is developed in order to estimate the stress distribution as a function of the forces which are applied on the sealing rings. The paper is ended in Sect. 4 with conclusions. Figure 2 presents an internal mechanical seal with oscillating stator. On the frontal face of the stator (4) there are n chambers (1) and on the frontal face of the rotor (3) there are i channels (2). During operating, the channels from rotor are connected periodically to the chambers from stator. At that moment, when the channels from rotor are overlapping to the chambers belonging to stator, the pressure in chambers increases and moves away the stator. At the very next moment, when the channels are rotating from the chambers, the pressure in chambers decreases and the stator is approached to rotor", " The frequency of the axial impulses of stator depends on the number of chambers and it is influenced by the rotational speed of rotor. The maximum pressure p2 max of fluid in the sealing gap corresponds to that moment when the channels are overlapping to the chambers and its value can be calculated as: p2 max = p1 \u2212 p (1) p = 0.5\u03c1\u03c92(r2 3 \u2212 r2 2 ) (2) where p1 is the pressure of the sealed fluid, p is the pressure given by the centrifugal effect, \u03c1 is the density of fluid, \u03c9 is the rotational speed of rotor, r3 and r2 are the outer and average radius of the sealing gap (Fig. 2). The pressure of fluid film between the sealing faces of an internal mechanical seal with oscillating stator depends on the geometry of the sealing gap. It is influenced by the pressure of sealed medium and depends on the rotational speed of rotor. Periodically, the channels from rotor connect the chambers from stator to the sealed fluid. Assuming parallel sealing faces, the pressure field inside of the sealing gap of a mechanical seal with oscillating stator (Fig. 3) is generated by a hydrostatic effect [9]", " Based on the equilibrium equation of the forces which are applied on stator, the opening force of the sealing gap Fa (Fig. 3) is computed and after, the axial stiffness of fluid film. At the end of this section, the equation needed to estimate the average leakage of fluid is provided, respectively. The equation of the volumes of fluid which enter and leave the sealing gap during a period t = 2\u03c0/\u03c9i (i is the number of channels from rotor) can be written as: Q1(t \u2212 tc) + Q3tc = Q2t (3) where Q1 and Q2 are the volumes of fluid corresponding to the S1 and S2 annular sectors of the sealing gap (Fig. 2) which are described by the angle \u03b1 and the time t (the time needed to cover the distance between two consecutive channels); Q3 is the volume given by the compression of fluid in chambers during a period tc (the period when the channels are overlapping to the chambers and the pressure increases from p2 min to p2 max). Using the well known equation of the laminar flow, the volumes of fluid Q1 and Q2 from the sealing gap can be computed as [9]: Q1 = \u03b1(r2 + 0.5b1)j 3 12\u03b7l1 (p1 \u2212 p2 med) (4) Q2 = \u03b1(r2 \u2212 0.5b1)j 3 12\u03b7l2 (p2 med \u2212 p3) (5) where j is the thickness of the sealing gap; b1, l1 and l2 are the geometrical dimensions of frontal faces of seal rings (Fig. 2); \u03b7 is the dynamic viscosity of fluid; p2 med is the average pressure and p3 is the pressure of fluid on the inner diameter. The volume Q3 given by the compression of fluid in chambers during a period tc can be written as [9]: Q3 = 2 V El \u00b7 p2 max \u2212 p2 med tc (6) where El is the bulk modulus of fluid and V is the volume of chambers from stator. Considering the equations of volumes of fluid described above, Eq. (3) can be rewritten in a dimensionless form as: c10j 3 r (p1r \u2212 p2r ) + c30\u03c9r ( p1r \u2212 p2r \u2212 pir\u03c9 2 r ) = c20j 3 r (p2r \u2212 p3r ) (7) where c10 = \u03b1(r2 + 0", " The effective average pressure of fluid from the sealing gap can be calculated as: p2 med = p2r \u00b7 p0 (18) The derivative of the load carrying capacity with respect to the seal clearance is the seal stiffness k which depends on the thickness of sealing gap and is influenced by the axial forces from stator. The axial force between the sealing faces can be computed using the following equation: Fa = 0.5(p1 + p2 med)S1 + p2 medS0 + 0.5(p2 med + p3)S2 (19) where the areas of annular sectors S1, S2, and S0 of the sealing gap (Fig. 2) can be computed as S1 = \u03c0 [ r2 3 \u2212 (r2 + 0.5b1) 2] S2 = \u03c0 [ (r2 \u2212 0.5b1) 2 \u2212 r2 1 ] S0 = \u03c0 [ (r2 + 0.5b1) 2 \u2212 (r2 \u2212 0.5b1) 2] (20) The dimensionless axial force can be written in a form of: \u03d5a = Fa Fa0 (21) where Fa0 is a reference force corresponding to the begin of the seal operating when the sealing faces are close and the fluid cannot penetrate the sealing gap to the outer diameter. In this situation the pressure from the sealing gap equals with the reference pressure p0 and Fa0 = S \u00b7 p0 (22) where S = 0.5(S1 + 2S0 + S2) (23) Using Eqs. (16), (19) and (22), Eq. (21) can be rewritten as: \u03d5a = p1r ( 0.5 S1 S + 1 + \u03b113 j3 r \u03c9r 1 + C j3 r \u03c9r ) + p3r ( 0.5 S2 S + \u03b123 j3 r \u03c9r 1 + C j3 r \u03c9r ) \u2212 pir \u03c92 r 1 + C j3 r \u03c9r (24) The total force given by pressure of fluid on stator is Fp = Fa \u2212 p1S5 (25) where the surface S5 of stator (Fig. 2) can be computes as S5 = \u03c0 ( r2 3 \u2212 r2 4 ) (26) The dimensionless form of Eq. (25) is: \u03d5 = Fp Sp0 = Fa Sp0 \u2212 p1 p0 S5 S = \u03d5a \u2212 p1r S5 S (27) and using Eq. (24) it became: \u03d5 = 0.5p1r S1 S + p1r + p1r\u03b113 j3 r \u03c9r 1 + C j3 r \u03c9r + p3r\u03b123 j3 r \u03c9r 1 + C j3 r \u03c9r \u2212 pir\u03c9 2 r 1 + C j3 r \u03c9r + 0.5p3r S2 S \u2212 p1r S5 S (28) The dimensionless axial stiffness of an internal mechanical seal with oscillating stator and hydrostatic lubrication can be computed as: ks = \u2202\u03d5 \u2202jr = \u22123 \u03b123 j2 r \u03c9r (1 + C j3 r \u03c9r )2 [ p1r \u2212 p3r \u2212 pir\u03c9 2 r (1 + \u03b112) ] (29) where \u03b112 = c10 c20 (30) The condition of the static equilibrium is: p1r \u2212 p3r > pir\u03c9 2 r (1 + \u03b112) (31) Usually, the pressure of fluid given by the centrifugal forces is less than the pressure of the sealed fluid and the condition (31) of static equilibrium is satisfied" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003255_s12541-018-0173-1-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003255_s12541-018-0173-1-Figure8-1.png", "caption": "Fig. 8 Obstacle avoidance based on safety boundary", "texts": [ " The algorithms set the safe boundary at regular intervals based on the outline of the object identified by OVSLAM for collision avoidance. We propose a method for moving smoothly and quickly according to the safe boundary. This method determines the complexity of the surrounding object region based on the OVSLAM, which is able to search in all directions at the same time. It conducts a flexible control of the constant safety boundary distance from the center of the object to compensate the disadvantages of the velocity-space command method. (3) As shown in Fig. 8, the radius of rotation and angle (rA, \u03b8A) in the avoidance path, which is defined based on the distance and angle (dRO, \u03b81) to the obstacle, is obtained from OVSLAM as defined in Eq. (3), where ro represents the safety boundary radius of the obstacle and L represents the center distance of the robot modeling information. In particular, it adjusts the speed of the robot by adding the acceleration component \u03b1 for the robot to return to the desired path within a similar time as required by moving to the desired path in the absence of an obstacle" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002580_icuas.2017.7991355-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002580_icuas.2017.7991355-Figure1-1.png", "caption": "Fig. 1. Pure pitching motion", "texts": [ " The used dynamical model to control the altitude of the MAV is given by [14]: \u03b8\u0307 = q (1) q\u0307 = Mqq+M\u03b4e \u03b4e (2) h\u0307 = V sin(\u03b8) (3) where V is the magnitude of the airplane speed, \u03b8 denotes the pitch angle. q is the pitch angular rate with respect to the yaxis of the aircraft body, h defines the airplane altitude and \u03b4e represents the elevator deviation [14]. In aerodynamics, Mq and M\u03b4e are linked with the stability derivatives which are implicit in the pitch motion. We can see these variables in the in Figure 1. The aerodynamic stability derivatives are defined by: Mq = \u03c1SV c\u03042 4Iyy Cmq M\u03b4e = \u03c1V 2Sc\u0304 2Iyy Cm\u03b4e where: \u03c1: Air density (1.05 kg/m3). S: Wing area (0.09 m2). c\u0304: Standard mean chord (0.14 m). b: Wingspan, (0.914 m). Iyy: Moment of inertia in pitch (0.17 kg \u00b7m2). Cmq : Dimensionless coefficient for longitudinal movement, obtained experimentally (-50). Cm\u03b4e : Dimensionless coefficient for elevator movement, obtained experimentally (0.25). The lateral dynamics generates the roll motion and, at the same time, induces a yaw motion (and vice versa), then a natural coupling exists between the rotations about the roll and yaw axes [10]" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001678_2.1206303-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001678_2.1206303-Figure1-1.png", "caption": "Fig. 1. The angular displacement of the flexible joint.", "texts": [ " Furthermore, the flexibility and the mass of the joint are considered too. The dynamic stiffening effects are captured in the dynamic modeling. A general-purpose software package of multi-link spatial flexible manipulator arms is developed and several illustrative simulation examples are given to validate the dynamic model and the corresponding software package. In this paper, a spatial chain manipulator composed of N flexible link and N flexible joint is investigated. The flexible joint is simplified as a linear elastic torsion spring. As shown in Fig. 1, q1i is the proximal angular displacement of the joint i, and q2i is the distal angular displacement of the joint i. The flexible link is simplified as an Euler-Bernoulli beam, which ignores the shear deformation. Assuming that the flexible link is straight before deformed, two coordinate systems are established each at the proximal and distal end of link i to express the transformation between different coordinate systems clearly.14 The definition of the coordinate systems (XbYbZb)i, (XdYdZd)i, (HxHyHz) \u2032 i and (HxHyHz)i can be seen in Ref" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003200_speedam.2018.8445272-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003200_speedam.2018.8445272-Figure1-1.png", "caption": "Fig. 1. Basic model", "texts": [ " In this paper, we propose a new consequent pole motor using Nd-Fe-B magnets that can drastically reduce the torque ripple. This motor model has different pole structure between N-pole and S-pole. It can reduce the torque ripple rate from 111 % to 22 % compared to an original consequent pole motor with symmetric rotor structure developed in this study. Furthermore, the torque characteristic shows about the same. Simulation software by FEM is used to analyze and discuss the threedimensional structure of IPMSM. II. BASIC MODEL A structure of the basic motor model to compare with developed models is shown in Fig. 1. The specifications of the basic model and details of the magnet used in this model are shown in TABLE and TABLE , respectively. This model has 6 poles and 36 slots, and uses Nd-Fe-B magnet. Armature coils of the basic model employ distributed windings. The basic model is used as a standard motor for comparison, and development of IPMSM is carried out by changing only rotor pole structure without changing the volume of the magnets used. III. CONSEQUENT POLE MOTOR MODELS The rotor structure of the new model developed in this study is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001375_j.piutam.2011.04.011-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001375_j.piutam.2011.04.011-Figure1-1.png", "caption": "Fig. 1: left: Rear-foot (RFS) and fore foot (FFS) strikes", "texts": [], "surrounding_texts": [ "A main idea we use here is related to the characterization of the impact intensity during foot strike. The ground reaction force and its impulse can generally be used for this. However, there is also an alternative possibility that can give rise to representations where the effects of the system variables and parameters can be clearly illustrated. During foot impact, the motion of the foot, and also the runner, will be constrained in certain ways via the ground contact. The kinetic energy content associated with this constrained motion, and its possible representations can also serve as indicator to represent the intensity of foot impact. It was shown in [2] that the pre-impact value of this so-called constrained motion space kinetic energy (CMSKE) is directly proportional to the impulse of the contact reaction force, hence, can be used to analyze and compare different impacts. The pre-impact instant can be defined as the moment when the foot starts to make contact with the ground. The measurements and analyses reported in [2] also show that usually the CMSKE is also proportional to the peak reaction force. For demonstration we use the foot-shank representation suggested in [1], and also illustrated in Figs. 1 and 2. We employ a full multibody parameterization of this representation. The plantar foot angle is \u03b1 and the ankle angle is \u03b2. The approach can also be readily extended to more complex multibody human models. We consider the two cases given in [1]: (a) The first is the case of a very compliant ankle modelled with a pin joint between the foot and the shank at point B. This leads to \u03b2 playing the role of a variable, or in technical terms, a generalized coordinate. In this case the model has four DoFs. The configuration and velocity for this case can be represented by q = [xA yA \u03b1 \u03b2] T and v = [x\u0307A y\u0307A \u03b1\u0307 \u03b2\u0307] T, respectively, where xA and yA are the coordinates of point A given in the absolute x-y frame. Point A defines an important, representative point of the fore-foot. (b) The second case considers a very stiff ankle that is modelled with a rigid connection between the foot and the shank. The assumption of a rigid connection was also used in [1] to represent a very stiff ankle. For this case, \u03b2 is not a generalized coordinate of the system, and the model has three DoFs. The configuration and velocity can be represented by q = [xA yA \u03b1]T and v = [x\u0307A y\u0307A \u03b1\u0307]T. The strike index s is defined to quantify the different possible foot strike patterns. It takes zero value for a heelstrike when the impact constraints can be represented with the motion of point B. In principle, the strike index could also take negative values for a rear-foot strike (RFS). However, we follow the assumption made in [1] that RFS based running can be well-characterized by strike index values greater than or equal to zero. The value of s is unity for a specific fore-foot strike when the motion of point A is restrained by the foot impact. Typical RFS based gaits are characterized by the strike index range of 0.05\u22120.25, and typical fore-foot strike (FFS) gaits have a strike index in the range of 0.75 \u2212 0.95. If s is 0.5 then we have a complete mid-foot strike (MFS), but a range of s can also be defined for that. The finite-time dynamics of the system can be described by equations Mv\u0307 + c(v,q) = f (1) where M represents the mass matrix of the system, array c contains the centrifugal and Coriolis effects, and f is the array of generalized forces (forces and moments). These quantities are defined according to the description selected for the two cases described above: (a) very compliant ankle - four DoF model; (b) very stiff ankle - three DoF model. The expressions for M for these two cases are detailed in the Appendix, Eqs. (A.1) and (A.2). The impulsive dynamics can be described by M(v+ \u2212 v\u2212) = f\u0304 (2) where v\u2212 and v+ represent the velocities just before and after the impulsive event, respectively, and f\u0304 is the impulse of f. The determination of the CMSKE relies on the mapping that connects physical directions/motion to be constrained by the foot strike to the velocity representation of the system. In our case the physical directions are associated with the two velocity components of the point of the foot that is representative of the particular foot strike pattern, as determined by the strike index. The two velocity components are interpreted for the horizontal, x, and vertical, y, directions of the absolute reference frame. Using the parameterization described above, the mapping can be given for the very compliant case as A = [ 1 0 \u2212(1 \u2212 s)l sin(\u03b1) 0 0 1 (1 \u2212 s)l cos(\u03b1) 0 ] (3) and for the very stiff case as A = [ 1 0 \u2212(1 \u2212 s)l sin(\u03b1) 0 1 (1 \u2212 s)l cos(\u03b1) ] (4) Based on these considerations the pre-impact CMSKE can be defined for our case as T\u2212c = 1 2 v\u2212T PT c MPcv\u2212 (5) where Pc =M\u22121AT ( AM\u22121AT ) A (6) v\u2212 represents the velocity of the system at the instant of foot touchdown, M and A are evaluated for the configuration at that instant. The detailed derivation of the formulas for Tc and Pc can be found in [2]." ] }, { "image_filename": "designv11_29_0003734_978-3-030-20131-9_186-Figure8-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003734_978-3-030-20131-9_186-Figure8-1.png", "caption": "Fig. 8: Discretization of generally routed robot(Four-bar linkage shown in red)", "texts": [ " The solution procedure consists of solving the pose of the base segment and progressively moving till the free end of the robot. The resulting profile of the robot is a curve in 3D space. For the case where single cable is routed through a non-linear path, a 3D profile is obtained without the use of an additional cable. This is because now the four-bar linkage in a discretized segment is not a planar mechanism unlike in a straight routed case. Hence, we assume the adjoining linkage b from the above formulation as a virtual linkage shown in Fig. 8. With reference to equation (1), we assume that the 3-dimensional deformation of robot is characterized by the minimization of coupler angles of those couplers which are mutually perpendicular to each other\u2013as is the case for straightly-routed robots. Taking this reasoning into account, we modify the above equations as follows: argmin xi+1 0 ,xi+1 a [ arccos (( Xi 0 \u2212Xi a \u2016Xi 0 \u2212Xi a\u2016 ) \u00b7 ( xi+1 0 \u2212 xi+1 a \u2016xi+1 0 \u2212 xi+1 a \u2016 ))]2 + (3) [ arccos (( Xi 0 \u2212 X\u0304i b \u2016Xi 0 \u2212 X\u0304i b\u2016 ) \u00b7 ( xi+1 0 \u2212 xi+1 b \u2016xi+1 0 \u2212 xi+1 b \u2016 ))]2 Subject to: \u2016xi+1 0 \u2212Xi 0\u2016 = l0 (4) \u2016xi+1 a \u2212Xi a\u2016 = la \u2016xi+1 0 \u2212 xi+1 a \u2016 = a Given data: Xi 0,X i+1 0 ,Xi a,X i+1 a , l0, la, a where the co-ordinate Xi+1 b is chosen to be that point in the spacer disk which is perpendicular to the coupler link Xi+1 a Xi+1 0 , X\u0304i b = a ( Xi a \u2212Xi 0 )\u00d7 ( Xi+1 0 \u2212Xi 0 ) \u2016 (Xi a \u2212Xi 0 )\u00d7 ( Xi+1 0 \u2212Xi 0 ) \u2016 (5) It may be noted that the same formulation is valid for a robot with linear routing as well" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000626_sisy.2010.5647201-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000626_sisy.2010.5647201-Figure2-1.png", "caption": "Figure 2. The inverted pendulum on cart system", "texts": [ "00 \u00a92010 IEEE achieve real-time control an AVR-board (Automatic Voltage Regulator-board) and a PC (personal computer) are used to stabilize Inverted Pendulum system. Experimental studies evaluate the FSC performance. The rest of this paper is organized as follows. Section II presents a solution to stabilize inverted pendulum system with the associated nonlinear force to the cart and Sugeno controller. Section III presents the results in two part of simulation and implementation of controller for inverted pendulum system and analysis. Section IV concludes and highlights the future works. II. SOLUTION The inverted pendulum on cart system shown in Fig. 2 is composed of a cart and a pendulum. The pendulum is hinged to the cart via a pivot and only the cart is actuated. Table 1 shows the system parameters and experimental values. parameter Definition Experimental values \u03b8 pendulum angle (rad) , 6 6 \u03c0 \u03c0\u239b \u239e\u2212\u239c \u239f \u239d \u23a0 x cart position (m) 1m\u00b1 M mass of the cart (kg) 0.5 kg. m mass of the pendulum (kg) 0.3 kg l distance from the turning center to center of mass of the pendulum (m) 0.6 m b cart's friction coefficient (kg/s) 0.1 / / secN m F force applied to the cart (N) 2N\u00b1 I Inertia of pendulum 20" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000317_j.diamond.2010.01.048-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000317_j.diamond.2010.01.048-Figure1-1.png", "caption": "Fig. 1. (a) Schematic illustration for the fabrication of BDD microband electrodes. (b) A typical SEM image of a nominally 30 \u03bcm-thick BDD microband electrode.", "texts": [ " The well defined (known dimensions) geometry of microfabricated electrodes is a clear advantage in voltammetric analysis, however, such electrodes have some disadvantages on the stability. Moreover, fabrication of microband electrodes by these techniques does not require cleanroom facilities. First, in this work, we describe a simple bench top method for fabricating diamond microband electrodes about 10 to 25 \u03bcm wide and 0.2 to 0.7 cm long by sealing conductive Chemical vapor deposition (CVD) diamondfilms with a layer of resin (Fig. 1a). Whereas BDD electrodes are useful for electrochemical analysis, they are very inactive for the oxidation of glucose and other carbohydrates, while transition metals such as Au, Pt, Ni and Cu are known to be active for such oxidation. In order to detect these species with high sensitivity, metal-modified BDD electrodes modified using chemical precipitation [16], electrochemical deposition [17], and ion implantation [18,19] were designed. As one of the best examples, we have reported Cu-implanted BDD electrodes, with which sensitive and selective detection of glucose in solutions containing interfering species such as ascorbic acid (AA) and uric acid (UA) was achieved [18]", " Electrochemical measurements were conducted using a potentiostat (HZ-100 and HZ-5000, Hokuto Denko) with a standard three electrodes configuration and a single-compartment glass cell. An Ag| AgCl|KCl (saturated in water) electrode was used as the reference electrode and a Pt wire was used as the counter electrode. A Faraday cage (Hokuto Denko, HS-101) was used to reduce external electromagnetic waves that might interfere with the small current response. SEM images of BDD microband electrodes revealed square-shaped features well sealed by the surrounding polymer composite (Fig. 1b). The cross-sectional surfaces of BDD films are relatively rugged with vertical grooves, because grain boundaries are preferentially broken when the BDD films are snapped off. The height of the protrusions in the rough surface is less than the diffusion-layer thickness, so the real and apparent areas are the same i.e. most diffusion-controlled processes are not affected by this roughness [21]. Raman spectra of the BDDmicroband electrodes indicates the high quality of the diamond, as evidenced by the characteristic peak at 1332 cm\u22121 for sp3 carbon bonds, and lack of peaks at 1350 cm\u22121 and 1580 cm\u22121, generally attributed to non-diamond carbon impurities (not shown) [7]", "45 \u03bcm, which is consistent with the electrode size observed by SEM observation (l=ca. 0.5 cm w=ca. 12 \u03bcm). Preparation of metal-modified macrosized BDD electrodes using several methods has been reported [16\u201319]. However, metalmodified microsized BDD electrodes have not yet been reported, because it is quite difficult to disperse and deposit metallic particles on microelectrodes. Here, we describe, for the first time, the preparation and characterization of Cu-modified microsized BDD electrodes. The preparation was almost the same as that for BDD microband electrodes (Fig. 1a) except that Cu sputtered BDD films were used. The bonding of BDD with metal depends in particular on wetting and Cu shows poor wettability on BDD surfaces. In order to improve the contact stability, we developed an intermediate layer using titanium. Because titanium has good electrical and mechanical contact to both BDD and Cu surfaces, many researchers have used Ti to obtain an ohmic contact to the BDD surface [27,28]. Cu and a Ti underlayer were sputtered using an RF-sputtering system onto the smooth surface of the BDD, which was deposited previously on a Si substrate" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003115_lcsys.2018.2857512-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003115_lcsys.2018.2857512-Figure1-1.png", "caption": "Fig. 1. Gantry crane with a flexible cable and an eye-in-hand camera.", "texts": [ " In the second section, the dynamic model of the flexible cable is established through ANCF. In the third section, the perspective projection of the point feature and the estimation error of the point feature\u2019s position are discussed. In the fourth section, the controller and adaptive law are proposed and the stability of the controller is verified based on Lyapunov theory. Simulation is used to demonstrate the capability of the proposed controller in the fifth section. The conclusion is made in the final section. In Fig.1, O-XY is a base frame which is fixed on the base of the crane. Oc-XcYc is the camera frame which is fixed on the camera. One end of the cable is fixed with the trolley and the other end of the cable is fixed with an eye-in-hand camera. The black block, of which the coordinate is brb=( bxb, byb)T in the base frame, is the object which is going to be grasped by the crane and which can be regarded as a point feature. u(t) is the input force to drive the trolley. d(t) is the disturbance on the trolley with the assumption that | ( ) |d t d ", " According to the Hamilton principle and by combining (5), (7), (10), (11), and (12), the dynamic of the crane system is ( )s f G iMq K q q K q Q Q with a constraint 2 0Aq y because there is no movement of the trolley along the vertical direction in the base frame. Thus we redefine the dynamic of crane system by eliminating the second row and the second column of the matrix M, Ks and Kf. At the same time, we delete the second element of q, QG and Qi, after which the dynamic model of the crane is established with seven general coordinates. In Fig.1, the displacement of the camera with respect to the base frame is that of the cable\u2019s end point B. The direction of the camera is parallel to the tangent vector of the cable at the end point B. Therefore we can obtain / norm( ) Oc B c B B r r r r X s s where the function norm is used to calculate the length of a vector. According to (2) and (14), the displacement and the direction of the camera are determined by q. Therefore the homogenous transform matrix of the camera frame with respect to the base frame can be calculated as ( ) ( ) ( ) 0 1 c B c R q r q T t where Rc(q) is the rotation matrix from the camera frame to the base frame", " The variable \u03b2 is defined as 2 1 1 1 1 1 2 2 2 ( ) [log( )]r r r C m M M M C When the input of the crane system is determined by (24), combining (22), (23), (24), and (25), one can find that 1 1 1 1 1 1 1 1 1 1 12 2 2 1 1 1 2 2 [ sgn( ) ] [ ( ) 2 \u02c6( )][log( )] r e s r r T r b f p b m q d q d m k q m q K q q M q C C q K k q x C According to (21), the adaptive law can be designed as 1 1 1 \u02c6 ( ) ( ) ( ) ,0 k T b T b i i p i d r t W t e t k q dt where \u0393 is a positive matrix and \u03b3 is a positive scalar. Definition. The equilibrium of qr, which is expressed as qr0(q1), is defined as the solution to the equation ( ) 0r r s GK q q Q where q1 is considered as a fixed value. According to Fig.1 and (28), when the position of the trolley q1 changes, the equilibrium of other general coordinates qr also changes with respect to q1. When qr is at the equilibrium state, there is no transverse deformation of the cable and the cable is just stretched by gravity. Theorem. With the assumption that the object is within the viewable range of the eye-in-hand camera, for the dynamic of the crane system (22), the control (24) and the adaptive law (27), if the initial states are bounded and satisfy the constraint and the number of captured pictures is not less than two, then the properties mentioned below hold: (\u2170) When considering disturbance d(t), during the motion of the crane system, all states are bounded and the constraint 0C t can be guaranteed" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003816_s00170-019-04082-6-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003816_s00170-019-04082-6-Figure2-1.png", "caption": "Fig. 2 Schematic of the grooved plates and standard specimens", "texts": [ " This experiment is designed in order to provide some data in comparing the fatigue strength of these two sets of specimens with each other. In the following section, the steps of this experimental activity are described. The provided bulk material, in the shape of a rod with 50 mm diameter, is first analyzed to ensure that the chemical composition is in agreement with Inconel 718. The chemical composition for the provided material is shown in Table 1. Then, \u201cthe grooved plates\u201d and \u201cthe standard fatigue test specimens,\u201d schematically shown in Fig. 2, are built by wire cutting. All the surfaces of the parts are then polished to remove surface irregularities caused by wire cutting. The fatigue tests on the specimens with continuous radius between ends, which their dimensions are shown in Fig. 3a, are conducted according to the ASTM E466 standard practice [24]. The groove in the middle of a grooved plate has the role of an artificial damage to the base material which in next steps will be filled thoroughly by the laser-cladding process to restore the geometry" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001948_sav-2010-0577-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001948_sav-2010-0577-Figure3-1.png", "caption": "Fig. 3. Orientation of a rigid rotor in space.", "texts": [ " The bearings are mounted into their rigid housings that are firmly attached to a fixed rigid base (platform). The details of the bearing are depicted in Fig. 2. The position of the disk along shaft axis is at distance Lr (not shown on Fig. 1) from the right bearing and at distance Ll (not shown on Fig. 1) from the left bearing. The rigid shaft inertia is neglected compared to the disk inertia and therefore the system mass center is at the geometric center of the disk. The orientation of the vibrating rigid rotor in space (Fig. 3) is monitored using Euler angles (Fig. 4). In Fig. 3, XsYsZs is an inertial frame (Fig. 1) and its origin (point Os) at the left bearing pedestal center. The triad abc is a body fixed coordinates system that rotates with the rotor differential element and represents its principal directions where ia, ib, and ic are unit vectors along axes a, b, and c, respectively. In Fig. 4, XsYsZs is an inertial frame and abc is a body fixed one (see Fig. 3). x\u0304y\u0304z\u0304 is an auxiliary, moving, frame initially coincides with theXsYsZs. Euler angles are not unique and are adopted as the following: 1. Rotation \u03c8 about Zs axis results in Xs coincides with x\u0304; 2. Rotation \u03b8 about x\u0304 results in the moving frame coincides with cx\u0304y\u0304; 3. Spin \u03c6 about c axis results in the moving frame coincides with abc one. The components of the rotor angular velocity vector \u03c9\u0304 = \u03c9\u0304aia + \u03c9\u0304bib + \u03c9\u0304cic in the abc frame are [41].\u23a1\u23a3 \u03c9\u0304a \u03c9\u0304b \u03c9\u0304c \u23a4\u23a6 = \u23a1\u23a3 \u03c8\u0307 sin \u03b8 sin\u03c6+ \u03b8\u0307 cos\u03c6 \u03c8\u0307 sin \u03b8 cos\u03c6\u2212 \u03b8\u0307 sin\u03c6 \u03c8\u0307 cos \u03b8 + \u03c6\u0307 \u23a4\u23a6 ", "0 Kb 24, N rad\u22121 4390000.0 \u22120.45 4409792.6 4414719.7 0.11 Kb 25, N rad\u22121 \u22121500000.0 \u22120.62 \u22121509343.5 \u22121471843.7 \u22122.55 Kb 33, N mm\u22121 225000.0 \u22120.45 226011.1 226011.1 0.0 Kb 34, N rad\u22121 \u2212863000.0 \u22120.68 \u2212868886.0 \u2212885433.0 1.87 Kb 35, N rad\u22121 1550000.0 \u22120.03 1550500.8 1550500.8 0.0 Kb 44, N mm/rad 139300000.0 \u22120.003 139304365.4 139304365.4 0.0 Kb 45, N mm/rad \u221249400000.0 \u22120.79 \u221249788394.5 \u221249563464.7 \u22120.45 Kb 55, N mm/rad 157000000.0 \u22120.10 157160958.5 157160958.5 0.0 aThis study; bResults listed in Fig. 3.19 of [8]; cDietl\u2019s model including geometric stiffness term. %errab = Muhlner[8]\u2212(DAMRO\u22121) Muhlner[8] \u00d7 100, %errac = Dietl[9]\u2212(DAMRO\u22121) Dietl[9] \u00d7 100. Table 3 The bearing Parameters, [44] The variable elastic compliance induced vibrations occur in a bearing under constant radial load or combined load but not under pure axial load [49]. The bearing example presented in [44] is studied. The bearing whose data are given in Table 3 is given a constant vertical displacement ey = \u22120.061 mm and the bearing forces are computed while the shaft makes one revolution", " He calculated the bearingHertzian contact stiffness coefficient using the approximatemethod of [45\u201347]which requires calculation of the contacting bodies radii of curvature that in turn depend on the ball contact angle. But he assumed ball contact angle to be of zero value. However, this assumption of zero value introduces small error [48]. The bearing forces are calculated using our analyses of Eqs (19) to (32). Analysis of [44] is used to reproduce the plot of the bearing horizontal forceF b x against shaft rotation of Fig. 3.12 in [44]. The plot is shown in Fig. 6 (dashed line) along with our model plot (solid line) and Muhlner\u2019s model plot (dash-dot line). Our model and Muhlner\u2019s model produce typical results. The small difference between our results and Kiskiniva results may be due to approximation stated above. However, there is good qualitative and quantitative agreement. Variation in F b x is periodic of period \u22480.00433 s. i.e. 230.947 Hz which could be due to fo = Nbfc = 230.625 Hz (the outer ring ball passing frequency, also known as elastic variable compliance frequency), fc = 25" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000601_s10483-010-0208-x-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000601_s10483-010-0208-x-Figure3-1.png", "caption": "Fig. 3 Finite element model of the roller and wheels", "texts": [ " The roller is supported by two supporting wheels, which are located on both sides at 30\u25e6 angle from the vertical line. Physical dimensions of the roller are the width B1 = 0.725 m, the inner radius R1 = 2.1 m, and the outer radius R2 = 2.33 m. In addition, the wheel has the width B2 = 0.78 m, the inner radius R2 = 0.2 m, and the outer radius r2 = 0.7 m. The elastic modulus is defined as 2.1\u00d71011 Pa, the friction coefficient is 0.2, and the Poisson ratio is 0.3. The finite element model of the roller and wheels is shown in Fig. 3, where two contact pairs are defined as the roller surface and the wheels. The applied loads include the constraint on the internal surface of the wheel and the pressure on the internal surface of the roller. The wheel shaft is fixed tightly in the wheel, and the nodes on the internal surface of the wheel are all constrained. The loads, associated with the load ratio, are applied to the internal surface of the roller according to Section 3. With the ANSYS, the circumferential stress and the contact stress curves of the roller are plotted" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000632_j.proeps.2009.09.208-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000632_j.proeps.2009.09.208-Figure1-1.png", "caption": "Fig. 1. Imperfect Shaft Steelwork Patterns Fig. 2. Hoisting Process", "texts": [ "208 8 5220 simulation of the vibration signals in different fault situations through the dynamic model of steelwork faults; the processing results of practical signals are shown in the last section. With the aging of mine, the shaft steelwork will become invalid (Jiang Yao-Dong, 1999; J. S. Redpath, 1977; Wang Peng, 2005). There are many typical shaft steelwork faults, such as loose-joints between rails when there is impact or load deflection during hoisting, rail curving due to the extrusion of peripheral rock and earth, etc. In practice, the generalized imperfect shaft steelwork patterns are shown in Fig. 1 under the assumption that the shaft steelwork is aligned properly on one side and has faults on the other side. In Fig. 1(a), it is a straight guide, but outof-plumb; In Fig. 1(b), the guide has a certain degree deflection; In Fig. 1(c), one segment of guide has a certain angular displacement; In Fig. 1(d), one segment of guide has a certain displacement in horizontal direction; In Fig. 1(e), there is a pitting fault or protuberant fault on the guide. It is well known that the conveyance in mine is restrained from moving laterally by steelwork that provides the fixed track the conveyance follows as it ascends or descends in shaft. The conveyance is equipped with four sets of rollers, and each set consists of three rollers running on the steelwork, located orthogonally, and supported in a compression spring. The operation procedure of the conveyance is shown in Fig. 2. Over the past several decades (Liu Chun-feng, 2003), the rollers of vertical shaft cage shoe have developed from rigid rollers to rubber roller even to compound-rubber rollers", "5a x l\u03b8= + &&&& (5) And when the conveyance runs in even speed v, then, 3 3 ( )x x vt= (6) 4 4 ( )x x vt l= \u2212 (7) And when the conveyance runs in run-ups stage or deceleration stage, then, 2 3 3 0 1 ( ) 2 x x v at= + (8) 2 3 3 0 1 ( ) 2 x x v at l= + \u2212 (9) During operation, the stability of conveyance is subject to the steelwork fault patterns, which can excite the conveyance to vibrate. Here, we can express the steelwork faults by mathematical function. Under the assumption that the steelwork has deflection fault in one steel rail, poor joints and joints with protrusions as illustrated in Fig. 1(b), Fig. 1(d), Fig. 1(e), respectively, we simulated the vibration while conveyance is running over the steelwork fault on the run-ups stage and even speed stage. Fig. 4. (a) Curve fault signal response at run-ups stage; (b) curve fault signal response at even speed stage 1 2 3 4 5 6 7 -4 -3 -2 -1 0 1 2 3 4 Fig. 4. (c) Displacement fault signal response at run-ups stage; (d) displacement fault signal response at even stage Fig. 4. (e) Protuberant fault signal response at run-ups stage; (f) protuberant fault signal response at even speed stage A comparison of different faults causing lateral vibration between the run-ups stage and even stage are illustrated in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003298_icelmach.2018.8506767-Figure20-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003298_icelmach.2018.8506767-Figure20-1.png", "caption": "Fig. 20. Contour plot of dxx vs. slip vs. vx, (vy = 0)", "texts": [ " More stability is observed as the slip magnitude increases. This is a fortunate dynamic, since one would expect a significant slip in order to maintain an airgap and provide thrust. Fig. 19 shows this strong linearity when rotational velocity is held such that (vx, vc) = (0,10) m/s. This can be exploited to simplify run-time re-calculations of kyy in a state-space system. Fig. 19. Plot of kyy and Fx vs. vy when (vx, vc) = (0,10) m/s The thrust translational damping, dxx, is defined in (28) as the partial derivative of Fx with respect to vx. Fig. 20 shows the how dxx varies with slip and vx. Stabilizing damping is observed near s = vx. The damping increases nonlinearly as the system moves away from this line until plateauing near zero for large slip and vx values. Fig. 21 shows the behavior of dxx as vx varies and (vy, vc) = (0,10) m/s. When the rotor\u2019s surface velocity matches the x velocity, the damping is minimized to produce more stable dynamics. The non-linear behavior means a more compute-intensive algorithm is required for re-calculating dxx during run-time, rather than a linear interpolation" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001506_1.4005058-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001506_1.4005058-Figure4-1.png", "caption": "Fig. 4 Schematic of bolt head free body diagram and contact pressure distribution", "texts": [ " 3), the displacements of points A and B due to bolt head sliding are given by DxA and DxB, as follows: DxA\u00bc 1 m 1\u00f0 \u00de cos w /\u00f0 \u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ri\u00fe re\u00f0 \u00de2\u00feh2 q re\u00fe ri\u00f0 \u00de \u00bcDxB m (4) where / is the bending angle of the bolt head about y-axis (Fig. 3), h is the height of the bolt head, m is a constant defined as the ratio of the change DxB=DxA, and w is a constant angle from the bolt head geometry. The displacement of point O in x-direction is given by DxO as follows: DxO \u00bc DxA m\u00fe ri ri \u00fe re m 1\u00f0 \u00de (5) Figure 4 shows a free body diagram of the bolt head. The normal forces on the conical bearing surface are simplified by two normal forces F1 and F2 acting at points B and A, respectively. The pressure distribution along the peripheral of the bolt head is assumed to vary sinusoidally with the angular location h on small area at A and B reaching a maximum pressure at the line of action of the transverse excitation. The normal force vector ~F1 acting at B is obtained by integrating the normal pressure q1 on the surface S shown with the shaded area in Fig. 4 as follows: 021210-2 / Vol. 134, APRIL 2012 Transactions of the ASME Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use ~F1 \u00bc riDh cos u \u00f03p 2 p 2 q1 cos hj jn\u0302dh \u00bc q1Dhri p 2 tan ui\u0302\u00fe 2 cos uk\u0302 h i (6) where n\u0302 is the unit normal vector acting perpendicular to the bolt head surface (Fig. 4), and Dh is the vertical height of the small area dS upon which the pressure q is acting. Following the same procedure, the normal force vector ~F2 acting at A is given by ~F2 \u00bc reDh cos u \u00f0p 2 p 2 q2 cos hj jn\u0302dh \u00bc q2Dhre p 2 tan ui\u0302\u00fe 2 cos uk\u0302 h i (7) Since the frictional forces are always opposing the sliding tendency, the direction of the frictional forces ~Fbf 1 and ~Fbf 2 would be opposite to the velocity vectors of points B and A, respectively. Substituting the corresponding radii in Eq. (3) and defining the ratio gb as the translational-to-rotational speed ratio of the bolt head (gb \u00bc vO=xb), the velocity vectors~vbf 1 and~vbf 2 are given as follows: ~vbf 1 \u00bc gb LB LO cos u\u00fe ri sin h i\u0302 ri cos h\u00bd j\u0302 gb LO LB sin u ri ri cos h\u00f0 \u00de k\u0302 (8) ~vbf 2 \u00bc gb LB LO cos u\u00fe re sin h gb LO re ri\u00f0 \u00de tan u i\u0302 re cos h\u00bd j\u0302 gb LO re cos h LB sin u\u00fe ri\u00f0 \u00de k\u0302 (9) The frictional forces ~Fbf 1 and ~Fbf 2 are obtained by integrating the frictional force vectors on their corresponding contact surface (Fig. 4) as follows: ~Fbf 1 \u00bc lb \u00f03p=2 p=2 qh1 ~vbf 1 ~vbf 1 dS \u00bc lbq1 \u00f03p=2 p=2 Fbf 1xi\u0302\u00fe Fbf 1y j\u0302\u00fe Fbf 1zk\u0302 dh (10a) ~Fbf 2 \u00bc lb \u00f0p=2 p=2 qh2 ~vbf 2 ~vbf 2 dS \u00bc lbq2 \u00f0p=2 p=2 Fbf 2xi\u0302\u00fe Fbf 2y j\u0302\u00fe Fbf 2zk\u0302 dh (10b) where Fbf 1x, Fbf 1y, and Fbf 1z are, respectively, the x, y, and z components of the force ~Fbf 1 divided by q1lb. Similarly Fbf 2x, Fbf 2y, and Fbf 2z are, respectively, the x, y, and z components of the force ~Fbf 2 divided by q2lb. From the free body diagram of the fastener in Fig. 4, the frictional shear force Fbs under the bolt head can be obtained from the equilibrium condition as follows: Fbs \u00bc q1 Dhri p 2 tan u \u00fe lb \u00f03p=2 p=2 Fbf 1xdh \" # \u00fe q2 Dhre p 2 tan u \u00fe lb \u00f0p=2 p=2 Fbf 2xdh \" # (11) The bearing friction torque Tb is obtained by integrating the cross product of the forces ~Fbf 1, ~F1, ~Fbf 2, and ~F2 with their respective moment arm vector as follows: Tb \u00bc ~ae q2 lb \u00f0p=2 p=2 ~Fbf 2dh\u00fe \u00f0p=2 p=2 ~Fdh2 !\" # k\u0302 \u00fe ~ai q1 lb \u00f03p=2 p=2 ~Fbf 1dh\u00fe \u00f03p=2 p=2 ~F1dh !\" # k\u0302 (12) where ~ae and ~ai are the radial vectors from the reference point O to the point of action of the forces ~F2 and ~F1, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000045_cca.2008.4629597-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000045_cca.2008.4629597-Figure4-1.png", "caption": "Fig. 4. 3 DOF levitation setup with ball joint", "texts": [ " The derivation of the transform matrix and the analysis of the coil configuration for this simplified planar rigid-body motion case is presented here to illustrate the methods used and the relationship between the arrangement of the coils, the position of the magnet, and the performance and stability of magnetic levitation in general. A single row of 3 actuation coils with centers spaced 35 mm apart is used to control the 3 DOF of the magnet motion. A thin disk of clear plastic with 4 infrared LED position markers is attached to the top of the magnet for motion tracking position feedback, as shown in Fig. 4. Given the horizontal and vertical magnet position and the coil positions, and using the single coil and magnet force and torque data of Fig. 3, it is straightforward to combine the force and torque contributions from each coil on the magnet to generate a 3x3 element transformation matrix which can be used to calculate a vector of forces and torques from a vector of coil currents. In this planar motion magnetic levitation case, the force/torque and current vectors from equation (1) are F = fx fz \u03c4y , I = i1 i2 i3 , (2) and the transformation matrix A is A = u(mx \u2212 c1,mz) u(mx \u2212 c2,mz) u(mx \u2212 c3,mz) v(mx \u2212 c1,mz) v(mx \u2212 c2,mz) v(mx \u2212 c3,mz) w(mx \u2212 c1,mz) w(mx \u2212 c2,mz) w(mx \u2212 c3,mz) , (3) where the horizontal and vertical position of the magnet is given as mx and mz , and the positions of the coil centers are c1, c2, and c3" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003008_j.isatra.2018.04.003-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003008_j.isatra.2018.04.003-Figure3-1.png", "caption": "Fig. 3. Quanser 3-DOF Hover.", "texts": [ " (47) At each instant, the method treats the state-dependent coefficients matrices as being constant, and computes a control action by solving a linear quadratic optimal control problem. This paper makes use of the Quanser 3-DOF Hover parameters in order to emulate a real platform. The values were obtained from the user\u2019s manual and they can be seen in Table 1. This equipment is similar to a quadrotor, but is mounted on a three degree of freedom pivot joint that enables only the rotational motion (see Fig. 3). The communication between the plant and the personal computer running Simulink was made via QUARC, a tool developed by Quanser that accelerates the control design and implementation process for hardware-in-the-loop. It generates a real-time code directly from Simulink-designed controllers and allows parameter tuning of the model by simply changing block configurations in the Simulink diagram. However, this educational platform presents an additional spring-damping behavior differently from a conventional MAV" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001782_pime_proc_1964_179_008_02-Figure17-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001782_pime_proc_1964_179_008_02-Figure17-1.png", "caption": "Fig. 17. Second modified design of the casing in Fig. 19", "texts": [ " The use of electro-slag welding for producing this pad is considered later, but at the moment it is proposed to consider the alternative designs shown in Figs 16-18. For comparison, Fig. 19 shows a typical cast casing of the present design. VoI179 Pt I No 2 at Purdue University Libraries on June 4, 2016pme.sagepub.comDownloaded from 48 J. A. ROGERS AND R. C. BREWER Fig. 16 shows a typical casing of present design but with the casing split at A. This split could be made with or without the vertical flange at A and the design lends itself readily to semi-automatic welding. In contrast to Fig. 16, with its valve chest cast with the casing, Fig. 17 shows welding with a flange although the flange may not be necessary in some instances. This is a robust construction and again lends itself to semi-automatic welding. Fig. 18 shows a design similar to that in Fig. 17, but in this instance the valve chest and main cylinder are cast with three stub pipes and then welded at A, B and C . The proposal will now be considered from a casting point of view. Turbine casings used to be cast with the horizontal flange at the bottom of the mould but as these flanges were made thicker because of more severe operating conditions, shrinkage and tearing defects became common. To overcome this the casings were cast with the horizontal flange on top. By this method it is necessary to have large, almost continuous heads to avoid shrinkage and tearing between the flange and body, and extensive padding is necessary to give good directional solidification", " 21 shows a method of doing this which offers several advantages : (1) the feeding system is simpler than in the previous examples; (2) the moulding is much easier since both sections can be lifted straight out of the mould; (3) the casing is easier to fettle, clean and inspect; (4) the hot-spot areas can be fed more effectively; (5) the pattern and feeding tackle is simpler and cheaper. The welding of the stub pipes is a simple process. At the time of writing, this design has not been completely evaluated but there seems no great objection to it and it is certainly economic. If a more robust design is desirable the authors suggest a casing based on Fig. 17. As casings get larger, welded steel castings should be employed, not only to reduce casting faults, but to make mouldings simpler and create a more economical use of heat treatment furnaces. Examples of more detailed considerations of design will now be given, using the research results of Briggs, Gezelius and Donaldson (12) and the Commission Technique de la Mitallurgie des Aciers (13). For this purpose, the casing shown in Fig. 22 will be considered. This figure shows a drawing based on proposed design No", " As the weld-metal level rises the carriage lifts up the column and this can be controlled either automatically or manually. The authors have shown in Figs 16, 17 and 18 various methods of applying the electro-slag process to the welding of a casing. The method suggested in Fig. 16 is possible and Fig. 29 shows a circumferential seam being welded. The vessel is 5 ft in diameter and the wall thickness is 23 in. The weld was completed in a single pass at a speed of approximately 3 ft/h. The method suggested in Fig. 17 is feasible-Fig, 30 shows a machine welding a block 17 in thick using three wires. The method indicated in Fig. 18 I would not recommend-other welding processes would be preferred on such a configuration. A recent development called consumable-nozzle electroslag welding has enabled thicknesses greater than 18 Proc h s t n Mech Engrs 1964-65 Fig. 29. Electro-slag sub-arc welding inches to be welded and simpler machines to be designed. In this method the machine is positioned on, or straddles, the workpiece" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003467_ica-acca.2018.8609836-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003467_ica-acca.2018.8609836-Figure5-1.png", "caption": "Fig. 5. Estructura 3D de la transicio\u0301n con un a\u0301ngulo de apertura de 90\u25e6 y 107\u25e6.", "texts": [ " Para el ana\u0301lisis tambie\u0301n se supone cuanto sigue: (a) que todo el momento de torsio\u0301n recae sobre la estructura; (b) que todo el momento de torsio\u0301n recae sobre el servomotor de transicio\u0301n. Para la suposicio\u0301n (a) se opto\u0301 por utilizar 4N-m (valor cercano al mayor momento de torsio\u0301n) y 20MPa como l\u0131\u0301mite ela\u0301stico del material (menor al l\u0131\u0301mite ela\u0301stico en [6]). Utilizando el toolbox Solidworks Simulation disponible en la herramienta de disen\u0303o Solidworks se obtuvieron los resultados de los esfuerzos que se muestran en la Fig. 5. En la simulacio\u0301n se consideraron el tipo de material, los torques y se ubicaron las sujeciones. Para la simulaciones primeramente se considero\u0301 a la estructura con un a\u0301ngulo de apertura de 90\u25e6 y luego con un a\u0301ngulo de apertura de 107\u25e6. Analizando los esfuerzos en ambos escenarios se eligio\u0301 el caso de la estructura con un a\u0301ngulo de apertura de 107\u25e6, ya que los esfuerzos esta\u0301n mejor distribuidos. Para la suposicio\u0301n (b) como el servomotor opera a 5V y teniendo en cuenta la Tabla I, interpolando se obtiene que el torque del servomotor es 4,78 kg-m (0,46875787N-m)" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003860_1350650119866026-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003860_1350650119866026-Figure1-1.png", "caption": "Figure 1. Schematic representation of a smooth porous journal bearing.", "texts": [ " Very few studies have been found in open literature related with thermal analysis of textured porous journal bearings. Therefore, in the present work, the generalized Reynolds equation with power law model and adiabatic energy equation has been considered for the computation of performance parameters for textured porous journal bearings. The combined effects of microsurface texturing and nonNewtonian fluid rheology may play an important role in forthcoming designs of porous bearings. A schematic diagram of a porous journal bearing with lubricating fluid is shown in Figure 1. The circumferential length of the bearing has been taken in the X direction, film thickness in the Y direction, and length in the Z direction and these are denoted by R ,H, and L, respectively. The typical arrangement for texture adopted in this study of porous journal bearing in unwrapped form with number and location of texture is depicted in Figure 2. Kango et al.30 have already highlighted that partial texture gave the best performance of the journal bearing among all considered locations. The locations of the textures therefore have been adopted based on the findings of Kango et al" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001894_s12239-012-0026-3-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001894_s12239-012-0026-3-Figure3-1.png", "caption": "Figure 3. Boundary conditions for analyzing the press fitting process.", "texts": [ " (7) (8) The warm shrink fitting process consists of a heating u 1 \u03c5\u2013 E ---------- r1 2 pi r2 2 po\u2013 r2 2 r1 2 \u2013 ---------------------r 1 \u03c5+ E ---------- r1 2 r2 2 pi po\u2013( ) r2 2 r1 2 \u2013 ------------------------- 1 r --+= u por Ea ------ 1 \u03c5a\u2013( )\u2013= u r2 2 pir Eb r3 2 r2 2 \u2013( ) ---------------------- 1 \u03c5b\u2013( ) 1 \u03c5b+( )r3 2 r 2 ---+= \u03b4Fitting pOr Ea ------- 1 \u03c5a\u2013( ) r2 2 pir Eb r3 2 r2 2 \u2013( ) ---------------------- 1 \u03c5b\u2013( ) 1 \u03c5b+( ) r3 2 r 2 ---++= \u03b4Expansion \u03b1 T\u2206 L\u22c5 \u22c5= \u03b4Fitting \u03b4Interference \u03b4Expansion\u2013= k r3 r2 ---= \u03b4Fitting 2r2k 2 E k 2 1\u2013( ) -------------------PInterference= \u03b4Fitting r3 1 v\u2013( ) k 2 1\u2013( ) 2+[ ] E k 2 1\u2013( ) -----------------------------------------------PInterference= process, a press fitting process, and a cooling process, as shown in Figure 2. The commercial code, ANSYS Workbench, is used for the FEA of the warm shrink fitting process. The element type used in ANSYS is a tetrahedral mesh, and the mesh size and the total number of elements for FEA are about 1.0 mm and 80,000, respectively. 3.1. Boundary Conditions The boundary conditions are applied to fix the lower surface of the shaft and restrict the axial movement of the gear in the direction of the outer diameter of the shaft, as shown in Figure 3. During the heating process, the temperature of the gear increases from 20 oC to 140 oC. After the press fitting has been performed, the temperature decreases from 140 oC to 20 oC during the cooling process. The material for the gear and the shaft is a Cr-Mo alloy steel, SCR 420H, and is elastic in the FEA. The mechanical and thermal properties are listed in Tables 1 and 2, respectively. The numerical model for the analysis of the warm shrink fitting process is shown in Figure 4. To find the coefficient of friction, we obtained the fitting load from the shrink fitting machine indicator, and we substituted this load into Equation (9)" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001401_iecon.2011.6119325-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001401_iecon.2011.6119325-Figure4-1.png", "caption": "Fig. 4. Schematic diagram of the Stewart structure", "texts": [ " The matrix structural analysis (MSA) is widely used to calculate the stiffness of the frame-based structure [6] [7]. By applying the MSA on the frame elements of bearing house and U-joint, the corresponding stiffness matrices have been calculated. Based on these results, the stiffness matrix of the base joint of Stewart in the i\u2019th limb, denoted by iftK _ , can be deduced by employing principle of virtual work [8]. The up-joint in the end-effector is considered to be perfectly rigid and the stiffness of the i\u2019th hydraulic limb is represented by ihyk _ . For the purpose of analysis, as demonstrated in the Fig. 4, let the coordinate frame ggg ZYX 444 be attached to the Stewart base in the geometric centre, the coordinate frame ggg ZYX 555 be attached to the moving platform, and its origin be located at the mass centre. Hence, the stiffness matrix of the parallel mechanism in the frame ggg ZYX 444 is generated by taking account of the deformations in the six base joints and hydraulic limbs: [ ] 11 )*][*( \u2212\u2212= T stwlistwstw JKdiagJK (1) where stwJ is the Jacobian matrix of the Stewart with [ ]iftihyli KkdiagK __= , 1,2" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000033_roman.2008.4600696-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000033_roman.2008.4600696-Figure5-1.png", "caption": "Fig. 5. Task oriented example 1: demonstrated grasps (left column) and incremental FWS projected onto the force space (right column).", "texts": [ " The teacher demonstrates a sequence of peculiar grasps given a target object and the demonstrated functional wrench space is built as the convex union of the demonstrated wrenches. Grasp evaluation is performed after the construction of the FWS using the task oriented measure defined in equation 7. As the evaluation process is highly dependent on the shape of the FWS it is assumed that the demonstration phase does not include non force closed or erroneous grasps, i.e. grasps which are not task-oriented from a user perspective. Experiments reported hereafter have been performed with the 3D model of the Barrett hand, which has three fingers and four degrees of freedom. Figure 5 shows three example grasps for a hammer, as well as the incremental FWS projected onto the force space. In particular, in figure 5 the intention of the demonstrator is to teach that the hammer should be grasped on its handle by applying a power grasp. Figure 6 shows the results of the evaluation of two grasps for the object. In the first example it can be seen that trying to grasp the hammer on its vertical handle, even in a different configuration from the demonstrated grasps, leads to a good quality grasp (Q = 0.53). In the second case, when the Barrett hand grasps the hammer from the top, the grasp is evaluated as force closed but with a lower quality (Q = 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000405_j.ijsolstr.2010.01.005-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000405_j.ijsolstr.2010.01.005-Figure4-1.png", "caption": "Fig. 4. Displacements.", "texts": [ " 8>< >: 9>= >;; \u00f010\u00de where v j s 8>< >: 9>= >; \u00bc j sinv j cosv s v0 8>< >: 9>= >; \u00bc j sin ls j cosls s l 8>< >: 9>= >;; \u00f011\u00de in which, v is the pre-twist angle to bring the intrinsic triad into the principal axes and v0 \u00bc l is the pre-twist rate. Therefore, in general, \u00f0 v; j; s\u00de are functions of \u00f0x; y; s\u00de. 4. Displacements To obtain the strain components, we need to study the displacements. Refer to the coordinate system attached to the positive face across the centerline along the principal axes for a straight prismatic beam shown in Fig. 4 and follow Timoshenko\u2019s assumption of plane-remain-plane cross-section during deformation. The displacements u1\u00f0x1; x2; x3\u00de; u2\u00f0x1; x2; x3\u00de; u3\u00f0x1; x2; x3\u00de are to be defined by the displacements at the centerline v1\u00f0x3\u00de; v2\u00f0x3\u00de; v3\u00f0x3\u00de along the local axes in the \u00f0P ! ;Q ! ; T ! \u00de directions and the rotations of the cross-section h1\u00f0x3\u00de; h2\u00f0x3\u00de; h3\u00f0x3\u00de about the three local axes. We shall assume that the rod is so thin that 1 x1j and 1 x2s. The two assumptions imply that the Jacobian is one. Therefore, u \u00bc u1\u00f0x1; x2; x3\u00de u2\u00f0x1; x2; x3\u00de u3\u00f0x1; x2; x3\u00de 8>< >: 9>= >; \u00bc v1\u00f0x3\u00de v2\u00f0x3\u00de v3\u00f0x3\u00de 8>< >: 9>= >;\u00fe 0 0 x2 0 0 x1 x2 x1 0 2 64 3 75 h1\u00f0x3\u00de h2\u00f0x3\u00de h3\u00f0x3\u00de 8>< >: 9>= >; \u00bc 1 0 0 0 0 x2 0 1 0 0 0 x1 0 0 1 x2 x1 0 2 64 3 75r \u00bc Nr; \u00f013\u00de where rT \u00bc v1 v2 v3 h1 h2 h3\u00bd is the vector of the main unknown displacement functions" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000359_s1068799809020111-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000359_s1068799809020111-Figure2-1.png", "caption": "Fig. 2. To a problem of determining the phase shift between the vibrator vectors of force and displacement.", "texts": [ " 2 2009 204 the external force vector P, it would be possible to find the n 1 values of the vector modulus A. Nonetheless, the n 1 values of the phase shift angles \u03b2 between the vectors of the force P, and the displacement A remain unknown. For this reason, it is necessary to add more n 1 equations to this system; then it can be solved with respect to all unknowns to be sought. In order to find the phase shift angle \u03b2, we will make use of the following considerations. Let the system be in the position shown in Fig. 2. We will assume that the vector A turned through some elementary angle d\u03b1. The point O 1 was displaced in this case to the position O 2 along the path of the locus ( )A \u03b1 by the value ds. In order to produce a turn of the vector A, the force P must perform at the ds distance the following work: ( )cos ,du = \u2227 Pds P ds . (14) In accordance with the law of energy conservation, this work will be equal to that dissipated in the damper when the vector A turns through the elementary angle d\u03b1: ( ).du d W= \u0394 Let us construct the perpendicular from the point O 1 to the vector A (Fig. 2). The sides of the triangle O 1 BO 2 obtained will be equal: 1O B Ad= \u03b1 ; 2 dA O B d d = \u03b1 \u03b1 ; 1 2O O ds= . On using the Pythagorean theorem, we will find: 2 1 dA 1 ds A d d A \u239b \u239e = + \u03b1\u239c \u239f\u03b1\u239d \u23a0 . (15) If we denote the angle O 2 O 1 B through \u03bc, we can express the angle between the vectors P and ds in the form: ( ), 2 \u03c0 = \u2212\u03b2 \u2212\u03bc \u2227 P ds . (16) On substituting Eqs. (15) and (16) into (14) and making some transformations, it is possible to obtain the final expression determining the phase shift angle: THEORY OF AN ANNULAR CORRUGATED DAMPER RUSSIAN AERONAUTICS Vol", " It seems to be convenient to determine the energy that is dissipated by the damper for a loading cycle as a finite sum: ( ) ( )1 1 1 1 1 2 n k k k k k d W d W W d d + = + \u239b \u239e\u0394 \u0394 \u0394 \u2248 + \u03b1 \u2212\u03b1\u239c \u239f \u239c \u239f\u03b1 \u03b1\u239d \u23a0 \u2211 , and the stiffness C in the direction k\u03c7 in the form: ( ) ( )cosk k kC P A\u03c7 = \u03b2 . In order to find the coefficient of dissipation \u03c8 we can use, for example, the well-known technique that makes it possible to determine the ratio of the energy \u0394W being dissipated in a cycle to the amplitude of the conditional potential energy of the elastic deformation \u03a0( \u03c7k). According to Fig. 2, we have ( ) 1 cos 2k k k kP A\u03a0 \u03c7 = \u03b2 . (19) Since the value of \u0394W is the constant for this damper and conditions of its loading, the coefficient of dissipation \u03c8, in accordance with Eq. (19), will be variable and dependent of the direction of the vector force action P: \u03c8k = \u0394W/\u03a0(\u03c7k). In order to evaluate the damper stiffness characteristics, it may be useful to introduce the notion of mean integral stiffness per a cycle; it can be determined as: BELOUSOV et al. RUSSIAN AERONAUTICS Vol. 52 No. 2 2009 206 ( ) 1 11 1 n av k k C C n = = \u03c7\u2211 " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002714_detc2017-67203-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002714_detc2017-67203-Figure2-1.png", "caption": "FIGURE 2 Model of the joint clearance for revolute pair", "texts": [ " Figure 1(a), (b), and (c) show the planar parallel robots of interest with three revolute-revolute-revolute (3RRR), prismatic-revolute-revolute (3PRR), and revolute- prismaticrevolute (3RPR) legs, in which the underline letter denotes the active joint. Revolute and prismatic joints are often used in serial and parallel manipulators. Clearance is required in any joint to permit relative motion between the connected links. However, clearance also brings unwanted motion freedom and therefore, position uncertainty to the machine. With the worst deviation of position uncertainty, the clearance of a revolute joint can be modeled as a massless rigid short link [26, 27], called clearance link (Figure 2). The length \u03b4R of the clearance link is equal to the difference of the radii of the pin and hole of the joint [25]. Each clearance link introduces an extra degree of freedom to the linkage. According to Ting's rotatability laws [26, 27], because a clearance link is a short link, it may rotate freely with respect to any adjacent nominal link as well as any link in the loop. 2 Copyright \u00a9 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/16/2017 Terms of Use: http://www", " If a clearance link is added to each leg, the structure in Figure 4(b) will have two degrees-of-freedom. This mobility allows point C to drift away from the target position and causes position uncertainty. In the discussion throughout this paper, the worst case scenario and hence the boundary of the uncertainty region is the concern. Assume that all joints have the same clearance. Each joint clearance is represented by a clearance link with the common length \u03b4R, which is the difference of the radii of the pin and hole of a revolute joint (Figure 2) [25]. By replacing each joint clearance with a clearance link of length \u03b4R, the eight-bar linkage in Figure 1(a) is remodeled as a 17-bar linkage (Figure 5(a)). Ting\u2019s rotatability laws lead to the following observation in the 17-bar linkage. 1. All clearance links in a leg may be connected in series following the principle of invariant link rotatability [28] as demonstrated by applying parallelograms to change the order of connection between nominal link and clearance links, as shown in Figure 5(b), in which all clearance links in a leg are grouped at Ai" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001522_cdc.2011.6160665-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001522_cdc.2011.6160665-Figure5-1.png", "caption": "Fig. 5. An example of quasi\u2013saturation.", "texts": [ "1 { y = N0(1 + \u2206)u+N0r u = \u03930u (11) The input to the k-th agent at time t is given by uk + \u2206k(uk(t)) and we assume that \u2206k(u) = 0 if |u| \u2264 uth, where uth is a certain threshold value, and that in general it satisfies the slope restriction \u2212\u03b1min \u2264 \u2206k(x1)\u2212\u2206k(x2) x1 \u2212 x2 \u2264 0. (12) By making use of such an operator we can model quasi\u2013 saturation of the input, in which the interconnection input uk(t) is used if it is small enough in absolute value, while if it is too large it is underestimated. If \u03b1min = 0 then the effect of \u2206k disappears, and we keep \u03b1min < 1 in order to avoid the pure saturation of the input, which in general could prevent our notion of synchronization. An example of what can be expressed using this \u2206 is shown in Fig. 5. A first, simple multiplier is the sector\u2013condition multiplier \u03c0\u2206, C = [ 2 \u03b1min \u03b1min 0 ] which, however, offers too conservative results. We will combine it with the Zames\u2013Falb multiplier, see e.g. [12], \u03c0\u2206, ZF (j\u03c9) = [ 2Re( \u2212j\u03c9 1\u2212j\u03c9/\u03c4 ) \u03b1min \u2212j\u03c9 1\u2212j\u03c9/\u03c4 \u03b1min j\u03c9 1+j\u03c9/\u03c4 0 ] . for which \u2206k \u2208 IQC(\u03c0\u2206, ZF ) thanks to the slope condition. If we choose \u03c4 large enough, this bounded multiplier approximates, at sufficiently low frequency, as \u03c0\u2206, ZF (j\u03c9) \u2248 \u03b1min\u03c0\u2206,P (j\u03c9), where the Popov multiplier is \u03c0\u2206, P (j\u03c9) = [ 0 \u2212j\u03c9 j\u03c9 0 ] " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000308_15397734.2010.483574-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000308_15397734.2010.483574-Figure1-1.png", "caption": "Figure 1", "texts": [ " In the case of considered axisymmetric problem we assume KW = KW r = r V = V r (20) Consequently we will have p\u2217 = p\u2217 r r \u2264 R (21) where R is the given radius of contact region. Using Galin decomposition (Galin, 1980; Goryacheva, 1998) we obtain the following representation for the optimal punch shape: uz = uz r = k \u222b f p\u2217 \u221a r2 + 2 \u2212 2 r cos d f (22) where k = 1\u2212 2 E d f = d d (23) E is Young modulus, is Poisson ratio. D ow nl oa de d by [ C ol um bi a U ni ve rs ity ] at 1 6: 15 0 8 D ec em be r 20 14 Consider at first the case when the punch is in translationary motion and KW , and V are constant over the contact region and consequently p\u2217 = const (Fig. 1). In this case, as it is well known (see e.g., Timoshenko, 1934), the integral in (22) can be represented as uz = uz r = 4kp\u2217R ( r R ) 0 \u2264 r \u2264 R r\u0303 = r/R (24) where r\u0303 is the complete elliptic integral of the second kind defined as (Janke et al., 1960) r\u0303 = /2 r\u0303 = \u222b /2 0 \u221a 1\u2212 r\u03032 sin2 d (25) From contact condition it follows uz r \u2212 uz 0 + f\u2217 r = 0 (25a) because uz 0 is approach of the rigid body. In this way the shape in the origin equals to zero and at the radius R equals to f\u2217 R = 2 1\u2212 2 p\u2217R E \u2212 4 1\u2212 2 p\u2217R E (26) The shape function (24) is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002437_978-3-319-55128-9_5-Figure5.70-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002437_978-3-319-55128-9_5-Figure5.70-1.png", "caption": "Fig. 5.70 Staircase effect for cellular structures. a Staircase effect with different orientation angles [170]. b struts at 20\u00b0 angle [171]. c struts at 70\u00b0 angle [171]", "texts": [ " Limited literatures are available for the investigation of manufacturing issues with cellular structures, although it has been identified that factors such as energy density, energy beam power, scanning speed, part location, part orientation and scanning strategies all have potentially significant effect on the mechanical properties of the cellular structures [140, 166\u2013169]. Staircase effect tends to be more significant for cellular structures due to the small dimensions of the geometries. It has been suggested that at smaller orientation angles (i.e. more aligned to horizontal plane) the staircase effect of struts could become significant enough to affect the structural integrity as shown in Fig. 5.70a [170]. As shown in Fig. 5.70b\u2013c, at 20\u00b0 the cross section geometry of the strut exhibits more significant fluctuation compared to the 70\u00b0 struts [171]. Beside staircase effect, another intrinsic effect that introduces geometrical error is the surface powder sintering for the powder bed fusion AM processes, which is caused by the heat dissipated away from the processed areas. As shown in Fig. 5.71, these surface defects causes dimensional variations on the cellular struts. For the calculation of mechanical properties, it was suggested that the minimum strut dimension (d in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000763_ptc.2009.5282005-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000763_ptc.2009.5282005-Figure5-1.png", "caption": "Figure 5 shows the inductance in respect to the rotor position; it shows where the excitation and generation stages are. Figure 3&4 shows the Hall Effect components placement on the rotor and stator, the output of the Hall Effect will was fed to the D flip flop and the output of the flip flop was fed to the switching bipolar BC107 transistor.", "texts": [], "surrounding_texts": [ "I. KEY WORDS\nRenewable energy, Switched Reluctance Generator, new generation technology, green house effect\nII. INTRODUCTION\nSwitched reluctance generator is a new machine that will convert mechanical power into electrical power; this machine has many advantages when it comes to wind power generation than the permanent magnet and induction generator [1]. The cycle of this machine consist of two stages, excitation and generation stage, the determination of these two stages will determine the efficiency of the machine. The boom in the power electronics market gave the advantages of developing the controller and the switching phenomena for this machine. IGBT or MOSFET transistors will be used as switching device in this controller, for rotor detection can be use a sensor like the Hall Effect for example or a sensor less circuit that rely on reading the inductance value in the winding to determine the rotor position. This paper will discuss the using of the Hall Effect sensor to determine the rotor position and the switching angle, two proposed method one is for high speed and one for low speed will be discussed in this paper and that will depend on the excitation voltage. In this paper the following has been used during the experiment:\n1 hp switched reluctance machine 8/6 rated current at 5 amps\nBUZ71 MOSFET power transistors IGBT 55100 Mini Flange Mount Hall Effect Sensor Permanent magnet Bipolar BC107 74HC/HCT74 Dual D-type flip-flop AD8564 Quad 7 ns single supply comparator\nM. Nassereddine, Research student at University of Western Sydney, Australia (e-mail: m.nassereddine@uws.edu.au) J. Risk, senior lecture at the University of Western Sydney, Australia (email: j.rizk@uws.edu.au M. Nagrial, A/Prof at the University of Western Sydney, Australia\nDC power supply for the excitation AC 50 hz power supply for the inductance test of the winding\nIII. COIL INDUCTANCE\nEquation (1) shows the non-linear inductance model for SRG after taken into consideration the symmetrical of the inductance about the y-axis in the section between rr PP /,/ . This Fourier series of inductance is a function of the excitation current and the rotor angle ),( iL . The value of the inductance is constant and periodic with period equal to 2 /Pr where, Pr is the number of rotor poles:\n1 0 )Prcos()()(),( n n niLiLiL (1)\nThe result of the first 4 harmonics is shown in equation (2) will be acceptable as a final result of the inductance calculation; therefore:\n-0.4 -0.2 0 0.2 0.4 0.6 0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\nRotor Position in Rad\nIn du\nct an\nce L\nii n\nH\nInductance against rotor position in different input current value\nL at I=1 A L at I=2 A L at i=3 A L at I=4 A\nFigure (1) inductance vs rotor positions\nFlux Vs current in defferent rotor position\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0 1 2 3 4Current (A)\nFl ux\n(w b)\n0 deg 2 deg 7 deg 10 deg 12 deg 15 deg 17 deg 20 deg 30 deg\nFigure (2) Flux vs current in different at different current and rotor position\n978-1-4244-2235-7/09/$25.00 \u00a92009 IEEE", ")Pr3cos()()Pr2cos()()cos(Pr)()(),( 3210 iLiLiLiLiL (2)\nFigure (1) and (2) shows the experimental result of the inductance of the machine as well as the flux, the results shows the inductance in respect of the rotor angle and the excitation current.\nIV. SWITCHING PHENOMENA\nThe determination of the switching will determine the excitation and the generation mode of the machine, in this section some discussion in regard to several proposed idea of the switching will be shown.\nFirst proposal is under the following conditions: The excitation voltage is 30 volts with limited\nUnder these conditions the coil will be fully excited under the 4 amps excitation current, the coil is fully excited in\n5 and is the time constant and equal to phaser L .\nFigure (5) the on and off using the Hall Effect circuit\n(a)\n(b) Figure (6) the experimental output of the Hall Effect and the switching on and off of the transistor\nFigure 6 shows the experimental switching in respect of the hall effect output, when the first permanent magnet cross the Hall Effect the output of the Flip Flop will be active high and the switching transistor is on, when the second magnet cross the hall effect the output of the Flip flop turn low and the transistor switched off, the position of the magnet and the Hall Effect determine the On and Off stage. Measuring the current that run through the winding of the stator under this condition is 4 amps. This circuit only will be efficient under low speed; high speed doesn\u2019t allow the magnetic field to be built to meet the generation mode, there fore other arrangements is needed.\nSecond proposal is under the following condition:\nSpeed higher than 200 rpm Excitation current higher than 5 amps,", "The total resistance of the winding is 1.5 ohms\nAt higher speed than 150 rpm, the first proposal won\u2019t be efficient as the excitation in the winding wont reach the required level, to over come this problem a higher excitation current is required, a new circuit to overcome any possible damage to the winding is needed, two proposed method one is the hard current chopping and the second is soft current chopping\nThe proposed tested circuit is shown in figure 7, is shows the Hall Effect sensor output and the output of the current sensor circuit. The output of the flip flop will be the activating signal of the switching transistors. Figure (8) shows the proposed output waveform, the switch on will depend on the Hall Effect output and the switching off will depend on the current sensing circuit output.\nThe back emf exist in the shaded area in figure (9), the excitation current increases at higher ration in this area due to the existence of back emf, that will have some small impact on the speed of the rotor but will be neglected at high speed.\nThe switching on for the tw proposed method can be adjusted by placing the permanent magnet at different location. The off position can be changed for the first one by relocating the permanent magnet on the rotor location at different place and for the second one by variant the reference current. The first one show that have better output under the hight speed and can achieve the highest excitation stage by choosing the right place for the magnet; The second one will have a better performance under high speed,\nFigure (7) proposed tested circuit\nThe output of the second proposed switching shows a higher efficiency. The reason is the higher speed and it is ability to use the maximum excitation current which leads to higher magnetic field. This will give the machine to operate\nat higher efficiency. During the experiment it is found that the excitation energy is higher than the generating energy, that will lead to lower efficiency, this excitation energy will depend on the winding characteristics and the cross section area of the stator and rotor. Refer to the formula\nl ANL 2 where L is the inductance in the coil, N is\nnumber of turns, A is the cross section area, l is the length of the cupper and is the permeability of the cupper. By increasing the number of turn in the coil the inductance will increase. A modification on the winding of the switched reluctance motor machine done, figure 9 shows the new flux density curve for the modified machine. Figure 10 shows the energy level between the old machine and the modified one, it is clear that at lower current the modified machine have the ability to produce higher power output at the same speed.\nFigure (8) the output voltage of the circuit in figure (7)\nFigure (9): flux density at different stator winding N\nFrom figure 9 and 10 it is possible to calculate the ratio between the generation energy and the excitation energy using the following:" ] }, { "image_filename": "designv11_29_0001891_icccn.2013.6614201-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001891_icccn.2013.6614201-Figure6-1.png", "caption": "Fig. 6. This figure illustrates how the \u201cactual target-temporal coverage\u201d of a target is calculated. We assume the weight of t1 and t2 are 4 and 6, respectively. In the figure, t1 is effectively-covered by s1 and s2, and t2 is effectively-covered by both s2 and s3. If we use the schedule (1), the period that t1 is effectively-covered by some nodes is 4 = 2 + 2 and that of t2 is 2 + 2 \u2212 1. Therefore, the actual target-temporal coverage of t1 becomes 4 \u00b7 4 = 16 and that of t2 is 6 \u00b7 3 = 18. If we adopt the schedule (2), the actual target-temporal coverage of t1 is 4 \u00b7 (2 + 2 \u2212 1) = 12 and that of t2 is 6 \u00b7 (2 + 2) = 24.", "texts": [ "begin\u2190 bnew and si.end\u2190 bnew + li. 24: Return si. 25: end function TEC-NC-Greedy. Let us first introduce TEC-NC-Greedy, a new greedy heuristic for TEC-NC. This algorithm is based on a new metric called the actual target-temporal coverage defined on a target tk, which is equivalent to the weight wk of the target tk multiplied by the difference between the total sum of time spent by each sensor node to effectively-covers tk and the total time period that tk is effectively-covered by some node. (see Fig. 6). We define this new metric to evaluate, given a set of camera sensor nodes effectively-covering the same target, how much the sensor nodes are efficiently used to effectively-cover the target. Algorithm 2 is the formal definition of TEC-NC-Greedy. In Line 1, the algorithm uses Identifiability Test and calculates Si = {tk|tk \u2208 T and tk is effectively-covered by si using its fixed sensing direction}. In Line 2, Sch is set to be empty, which will eventually contain the activation period (\u201con\u201d and \u201coff\u201d timing) of each camera sensor node within each cycle, Z is set to be the set of sensor nodes, which will represents the set of sensor nodes whose schedule (activation period) have not been determined yet, and TC is set to be zero, which Algorithm 4 TEC-AC-Anchor (S, T,W,L, l, B, \u03b8, \u03c6) 1: Calculate S(i,j) for each 1 \u2264 i \u2264 n and 1 \u2264 j \u2264 q", " Note that since TEC-NC-Adjuster needs an initial schedule of the camera sensor nodes to be adjusted and optimized, we use TEC-NC-Greedy to generate such a schedule. A. Simulation Results for TEC-NC In this section, we discuss about the average behavioral characteristics of TEC-NC-2-MaxEct (2NC), TEC-NC-Greedy (NCG), TEC-NC-Adjuster (NCA), and MNC as well as compare their performance with the upper bound (UB) for TECNC. We first observe the impact of the initial battery lifetime, bl, of each sensor on the target-temporal effective-sensing coverage (TEC). By comparing each pair of Fig. 6(a) and 6(d), Fig. 6(b) and 6(e), and Fig. 6(c) and 6(f), we can observe that if the beamwidth \u03b8 of each sensor\u2019s sector is fixed, as the initial battery lifetime of each node grows, TEC increases independent from the actual algorithm applied to achieve the TEC, and thus the performance of the algorithms (2NC, NCG, NCA) becomes closer to UB. One contributor of this phenomenon is the way we compute UB; the longer the battery lifetime is, the maximum achievable TEC by any algorithm will be greater. Meanwhile, we define the upper bound as the multiplication of the total sum of the weights of the targets and the mission lifetime. Next, we study how the overall TEC is affected by the beamwidth \u03b8 of each sensor\u2019s sector. By comparing each subset of figures, Fig. 6(a)-(c) and Fig. 6(d)-(f), we can learn that TEC increases as \u03b8 grows. This is because, for a target with a fixed face direction, the number of sensor nodes which can effectively cover the target will increase as \u03b8 is getting larger. From Fig. 6, we also can observe that the initial battery lifetime of each sensor has more influence on the performance of our solutions than the beamwidth \u03b8 of each sensor node. Despite a proper beamwidth of a camera sensor can contribute to enlarge the coverage of a camera sensor, the particularity of effective sensing model makes such a contribution be less dramatic, i.e. each node and target pair should pass Identifiability Test. Regarding the performance of the proposed algorithms, Fig. 6 clearly shows that our three algorithms, 2NC, NCG, and NCA, outperform the only existing alternative, MNC. This is because, as we explained ealier, MNC is originally designed to compute a schedule of wireless sensor networks (not camera sensor networks), and thus it does not consider the effectivesensing model. From Fig. 6, we also can observe that NCG and NCA almost always work better than 2NC. In addition, NCA always outperforms NCG. This trend becomes more apparent as n increases beyond 210. This result clearly supports that our refinement strategy applied to NCA improves the quality of the schedule generated by NCG. B. Simulation Results for TEC-AC In this section, we discuss the average behavioral characteristics of the proposed algorithms for TEC-AC and compare their performance with UB. To determine the direction of each camera sensor node, we first apply TEC-AC-Anchor, and then use each of TEC-NC-2-MaxEct (2AC), TEC-NC-Greedy (ACG), and TEC-NC-Adjuster (ACA) to solve TEC-AC" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001249_j.compind.2013.08.001-Figure19-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001249_j.compind.2013.08.001-Figure19-1.png", "caption": "Fig. 19. The second layout of the virtual facility for fabrication of the hand skeleton.", "texts": [], "surrounding_texts": [ "The biomedical field has also benefited hugely from LM technology, with which doctors can study prototypes of human organs or injured bones to prepare for complex surgical operations. Similarly, medical students can better understand the intricacy of body organs and structures. In recent years, functional biomedical products have been fabricated directly with LM systems, including highly-customized artificial limbs and porous tissue scaffolds which are difficult to fabricate with traditional manufacturing techniques [6]. VPRA can facilitate fabrication planning of biomedical products. Fig. 17 shows a multi-material hand skeleton model to be made of five materials with dimensions enlarged to 318 mm 223 mm 109 mm. To fabricate this skeleton, a support table and two SCARA robotic arms are loaded from the library to synthesize a virtual MMLM facility. These two actuators can be positioned in two different layouts as shown in Figs. 18 and 19. Moreover, based on the distribution of the five materials of the skeleton, two material strategies may bring about higher efficiency for each layout. In the first strategy, the first robotic arm will Table 1 Build times of the hand skeleton. Concurrent toolpath 1 Concurrent toolpath 2 Concurrent toolpath 3 Concurrent toolpath 4 Sequential toolpath Estimated build time (min) 245.02 253.94 240.86 244.40 293.34 Comparison with sequential toolpath 16.47% 13.43% 17.89% 16.68% \u2013 deposit the blue, green and red materials, while it will only deposit the blue and green materials in the second strategy. Therefore, there are a total of four strategies of actuator layout and material assignment to fabricate the hand skeleton. As stated before, a toolpath planning module based on deposition groups and division of work regions has been incorporated into VPRA. With this module, toolpaths for concurrent deposition by multiple actuators are generated accordingly for these four strategies in which the hand skeleton is sliced into 200 layers with a hatch width of 1 mm. Table 1 shows a comparison of the resulting build times of digital fabrication of the hand skeleton. It can be seen that all the concurrent toolpaths save build time when compared to sequential deposition. Moreover, the third strategy, where the two robotic arms are on the opposite sides of the support table and the first arm deposits the blue, green and red materials, is most efficient. Fig. 20 shows a few screen shots of the hand skeleton being digitally fabricated with the third strategy in the virtual MMLM facility. To reduce the computational burden, the cuboid dexel resolution can be dynamically adjusted during digital fabrication. Fig. 21 shows the digital hand skeleton when the simplification factor s is 1, 3 and 5, respectively. It appears that s = 3 gives a good balance between the computational burden and the dexel resolution of the digital hand skeleton. This case study demonstrates that VPRA can facilitate determination of suitable MMLM facility layouts for specific fabrication tasks by trying out various toolpath planning strategies. Moreover, the dynamic simplification algorithm can properly balance computational burden and simulation perceptual reality." ] }, { "image_filename": "designv11_29_0000017_tmag.2007.916241-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000017_tmag.2007.916241-Figure5-1.png", "caption": "Fig. 5. Different conducting position when WidB >WidC.", "texts": [], "surrounding_texts": [ "In Fig. 3, an instance of the commutation model named is introduced to define the commutation characteristics. For simplicity, but without losing generality, a linear model is used to model the brush voltage drop as a linear function of the contact current. As shown in Fig. 4, the contact conductance between a brush and a commutator segment is proportional to the contact area, and is a periodic function of rotor position. The current rotor position is obtained from the transient FEA solver. In Fig. 4, the initial lagging angle parameter is obtained from the commutator bar component, and its value is different for each individual component. All other parameters ( , , , and ) are specified in the commutation model and their descriptions are given in Table II. Positions a, b, c, and d in Fig. 4 correspond to four positions when one extremity of a commutator segment aligns with one extremity of a brush, as shown in Figs. 5(a)\u2013(d) and 6(a)\u2013(d), respectively. In Table II, and , in mechanical degrees, are derived from (1) (2) where is the brush width measured in length unit, is the commutator diameter, is the thickness of insulation between two commutator segments, and is the segment pitch of the commutator which is derived from the number of segments as follows: (3) For linear commutation model, is derived from (4) TABLE IV PARAMETERS OF THE LINEAR COMMUTATION MODEL where is one-pair brush voltage drop measured at armature current , and is determined by (5) Since the lagging angle parameter and the model instance name are defined in the commutator bar component and the commutation characteristics are defined in the model instance, commutation models [2]\u2013[4] of different complexities and accuracies can be implemented as different model options. If we want to model another commutation pattern, we just need to change the model instance. It is not necessary to modify any part of the circuit for model change." ] }, { "image_filename": "designv11_29_0000757_s10015-010-0806-7-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000757_s10015-010-0806-7-Figure2-1.png", "caption": "Fig. 2. n-link underwater robot model", "texts": [ "8 In this control method, the infl uence of the hydrodynamic force with respect to the vehicle is treated as a disturbance. In this article, we propose a disturbance compensation control method for both vehicle and manipulator. To verify the effectiveness of the digital RAC method with a disturbance observer, experiments were performed using an underwater robot with a vertical planar 2-link manipulator, shown in Fig. 1. From the experimental results, we show that the proposed control method has good control performance. 2 Modeling7 The UVMS model used here is shown in Fig. 2. It has a robot base (vehicle) and an n-DOF manipulator. The symbols used are defi ned below. n: number of joints \u03a3I: inertial coordinate frame \u03a3i: link i coordinate frame (i = 0, 1, . . . , n; link 0 means the vehicle) IRi: coordinate transformation matrix from \u03a3i to \u03a3I pe: position vector of the end-effector pi: position vector of the origin of \u03a3i ri: position vector of the center of gravity of link i \u03c6i: relative angle of joint i \u03c80: roll\u2013pitch\u2013yaw attitude vector of \u03a30 \u03c8e: roll\u2013pitch\u2013yaw attitude vector of the end-effector \u03c90: angular velocity vector of \u03a30 \u03c9e: angular velocity vector of the end-effector \u03c6: relative joint angle vector (= [\u03c61, ", " Our proposed method, described above, can reduce the infl u- x0: position and attitude vector of \u03a30 (= [r0 T, \u03c8 0 T]T) xe: position and attitude vector of the end-effector (= [pe T, \u03c8 e T]T) v0: linear and angular vector of \u03a30 (= [r\u03070 T, \u03c90 T]T) ve: linear and angular vector of the end-effector (= [ p\u0307e T, \u03c9 e T]T) Ej: j \u00d7 j unit matrix {\u00b7}\u02dc : Tilde operator standing for a cross product such that r\u0303a = r \u00d7 a Note that all position and velocity vectors are defi ned with respect to \u03a3I. First, for the model shown in Fig. 2 the following kinematic and momentum equations can be obtained: d I k r r M k r p2 0i T i j Tj i j i j i j = + \u2212( ) \u2212( ){ } = \u2211 M E M I I IT i a T i ai i i i m= + = +3 , and \u03b7 and \u03bc are the linear and angular momentum of the robot. Next, to obtain the dynamic equation of UVMS, the hydrodynamic drag and lift forces are necessary. The drag force and moment of joint i can generally be represented as follows9: f R w wd D i I i i i i l i i i C D dx= \u222b\u03c1 2 0 (3) t R x w wd D i I i i i i i l i i i C D dx= \u00d7\u222b\u03c1 2 0 \u02c6 (4) where w E R r x xi i I i i i i i Tx= \u23a1 \u23a3\u23a2 \u23a4 \u23a6\u23a5 +( ) = [ ] 0 0 0 2 0 0 w \u02c6 , \u02c6 \u03c1 is the fl uid density, CDi is the drag coeffi cient of link i, Di is the width of link i, and li is the length of link i" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000373_ssp.147-149.831-Figure5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000373_ssp.147-149.831-Figure5-1.png", "caption": "Fig. 5. Internal forces", "texts": [ " The non-zero component of strain is: \u2212 in the upper aluminium layer: 2 2 1 0 x w 2 \u2202 \u2202 \u2212 \u2202 \u2202+ = z x hh xx \u03b8\u03b5 , (6) \u2212 in the lower aluminium layer: 2 2 2 0 x w 2 \u2202 \u2202 \u2212 \u2202 \u2202+ \u2212= z x hh xx \u03b8\u03b5 , (7) \u2212 in the MR fluid layer: .) ,(1 x w 0 0 0 2 2 0 \u2212 \u2202 \u2202 += \u2202 \u2202+ \u2212 \u2202 \u2202 \u22c5= tx x w h h xh hh h h z xz xx \u03b8\u03b3 \u03b8\u03b5 (8) It appears that shear deformation occurs only in the MR fluid layer. It is important for further analysis that this deformation is due to the z-component and the x-component of the displacement rate. The deformed segment of the MR fluid layer is provided in Fig. 5. Fig. 6 illustrates the inner forces. The outer layer is bent and stretched. Bending is a result of overall beam deformation and stretching is a result of interaction of the MR fluid layer. The tensile stress xx\u03c3 corresponding to strain component xx\u03b5 in outer layers is given by xxxx E\u03b5\u03c3 = , where E is Young modulus. In the MR fluid layer only the shearing force will appear. The shear stress is associated with shear deformation by Eq. 1. Taking into account the properties of MR fluid we assumed that the non-zero extension strain xx\u03b5 does not develop tensile stress. Thus, there is no bending moment or tensile force in the MR layer. The arrangement of internal forces in the three-layered beam becomes the starting point of the analysis of beam motion for various hypotheses about the forces between MR layer and outer layers. We consider an element of a beam of the length dx (Fig. 5). Applying Newton second law to the motion in z direction, and taking into account the relation between internal forces and displacements, the equation of motion can be written as: ( ) 0122 2 2 0 04 4 2 2 0 = \u2202 \u2202 \u2212 \u2202 \u2202 +\u2212 \u2202 \u2202 + \u2202 \u2202 + xx w h h GA x w EJ t w \u03b8\u00b5\u00b5 (9) where \u00b5 is linear mass density of the aluminium layers, \u00b50 is linear density of the MR fluid layer, EJ is flexural stiffness of the aluminium layer, A0 is the area of the MR fluid layer cross section. The MR-layer element of length dx interacts with appropriate outer layer element by the force " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002714_detc2017-67203-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002714_detc2017-67203-Figure3-1.png", "caption": "FIGURE 3 Clearance model of a prismatic pair", "texts": [ "org/ on 12/16/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use It is well known that a PR dyad with a fixed prismatic joint is equivalent to an RR dyad with the center point at infinity in the direction normal to the sliding path. Likewise an RP dyad is equivalent to an RR dyad with the circle point at infinity. Therefore, the concept of clearance link for R-joint is also applicable to P-joint. The length of the clearance link of a Pjoint can be defined as \u03b4P = (c - b)/2, as shown in Figure 3(a). \u03b4P is the maximum deviation that the slider may have in the guiding slot. The merit of the clearance link concept for a prismatic joint is further explained and justified below. Consider a system of a relative planar motion between a slider and a guiding block. Since only the geometric effect is to be considered, one may assume that there is no position error along the sliding path, i.e. no clearance or uncertainty along the sliding path. Because of clearance, the sliding block is allowed a two degrees-of-freedom motion with respect to the guiding block (Figure 3(a) and 3(b)), i.e. a translation in the direction normal to the sliding path and a rotation, Therefore, the effect of clearance constraint can be modeled as a slider crank mechanism (Figure 3(c)). The crank represents the clearance link, the coupler link motion simulates the motion of the actual slider, and the sliding path direction depicts the no input error assumption. The above clearance link model for prismatic joints is novel and thorough. It offers a unified model for both revolute and prismatic joints and also a method to understand the geometric effect of a seemingly chaotic system. The simplicity of the method is made possible with Ting's rotatability laws [26-29]. In this paper, a joint clearance is depicted as a clearance link" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002998_2018-01-1483-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002998_2018-01-1483-Figure3-1.png", "caption": "FIGURE 3 Test rig: (a) in the laboratory, main dimensions: 470\u00a0mm\u00a0\u00d7\u00a0100\u00a0mm\u00a0\u00d7\u00a0250\u00a0mm, total mass: 17.8\u00a0kg (b) as finite", "texts": [ " The advantage of this routine is, that the Jacobian matrix is calculated numerically and does not have to be\u00a0provided by the user. The size of system (4) depends on the number of harmonics h taken into account and is 2h times the size of\u00a0system (1). For a large system (1) and a large number of harmonics computational effort grows drastically. In order to circumvent computational problems due to system size, the use of reduction methods to system (1) has to be\u00a0considered. For the purpose of validation, the procedure described in section 2 is applied to the test rig shown in Figure 3(a). It has been especially designed to measure the kind of vibration described earlier, i.e. forced vibrations with dry friction damping. Herein, it serves as a reference for the applied mathematical models and the solution procedure. In this section, the test rig and the finite element model describing it are explained. Measurements and results are discussed in section 4. The test rig used in this work is shown in Figure 3. It consists of a beam that is clamped to a stiff frame at one end and has a rounded tip on the other end. It can be\u00a0brought into \u00a9 2018 SAE International. All Rights Reserved. contact with a plate, the normal contact force between the two of them is adjustable. Plate and beam tip can be\u00a0equipped with various materials in order to investigate different contact pairs. Harmonic excitation is applied to the beam by a shaker, leading to forced vibration of the system. For the relative movement between the contact partners, three different behaviors can be\u00a0observed", " and 2. the test rig behaves as a nearly linear system with either the tip attached to the plate or the free tip additionally damped, respectively. The first two cases are unlikely to produce squeak noise as it is described in the references given in section 1. On the other hand, case 3. is strongly nonlinear and depicts a typical vibration that leads to squeak noise. Four accelerometers are attached to the system as illustrated in Figure 4 in order to measure the beam\u2019s response to excitation. Figure 3 b) shows the finite element model for the system. Standard finite element calculations, e.g. modal analysis, are performed applying the software ABAQUS\u00ae. Without exception, quadratic hexahedral elements [16] are used. The models\u2019 parts are connected with tie contacts and multi-point constraints, see [16] for reference. These connections are specified, so that eigenfrequencies in simulation (no contact between beam tip and plate) match resonances in corresponding experimental modal analysis. Four accelerometers are included in the model, they are attached to the beam in experiments and have an influence on the dynamic behavior", " (16) Otherwise, the friction force is not strong enough to hold the contact partners together and sliding occurs: F sign s s FR l l Rl = - -( )-1 \u02c6 , (17) sl is reset to: s F k l Rl= . (18) The procedure steps through time until tl\u00a0=\u00a02T, with T being the period time. The second of the two periods is used to calculate integrals (10)-(12) in order to avoid mistakes resulting from the assumption that at t\u00a0=\u00a00 the contact partners are sticking. The procedure described in section 3 is applied to the finite element model shown in Figure 3 b). Hardware tests conducted at the test rig serve as a reference. Parameters that can be\u00a0set for an experiment are: material pair, normal force, frequency and amplitude of harmonic excitation. Table 2 shows the values for two experiments that will be\u00a0 dealt with in this section: In order to predict noise, it is necessary to know the velocity at the systems surface (see section 5.1). Accordingly, in the following considerations the velocity is used as the quantity to compare simulation and experiment", " the Boundary Element Method [22]. The Equivalent Radiated Power (ERP) estimates the sound, radiated by a vibrating system. It is given by P c OERP f f d= ( ) ( )\u00f21 2 2 r v x x (19) and provides the radiated sound power under the assumption that the radiation efficiency equals 1. In (19), \u03c1f is the density of the surrounding fluid (e.g. air) and cf is the speed of sound in this fluid. Vector v(x) is the velocity at the surface in normal direction. Given a discretized surface as for the finite element model shown in Figure 3, integral (19) can be\u00a0replaced by a sum. Assuming a constant normal velocity vl over each (small) surface element, leads to P c A v l N l l e ERP f f\u00bb = \u00e51 2 1 2r , (20) where Ne and Al are the number of surface elements and their area, respectively. With the results for velocities at finite element nodes from Harmonic Balance Method calculations, the average normal velocity of each surface element can be\u00a0 determined and equation (20) evaluated. In this section, three different possibilities for evaluation of Equivalent Radiated Power results are demonstrated", " Contour Plots In some systems, it is not possible to avoid critical loading or to change contact conditions in order to prevent them from causing noise. For these cases, it is necessary to know where the structure radiates most of the noise. The surfaces at those locations can then be\u00a0treated with measures, e.g. applying acoustic insulation that reduces the radiation efficiency and effectively reduces noise. Figure 9 shows the ERP density, i.e. the ERP per surface area as a contour plot on the test rig\u2019s beam (see Figure 3). It can be\u00a0seen that most of the noise is radiated near the connection to the beam tip. With increasing harmonics, the area of the highest sound radiation is extending and moving towards the beam\u2019s middle. Although the ERP density of harmonics 11 and 21 is low compared to that of the first harmonic, the location of their radiation is of crucial interest, as their frequencies are higher and thus more likely to produce audible noise. The plots in Figure 9 suggest that a treatment of surfaces should not only be\u00a0applied near the beam tip, but rather cover a larger area, i" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002209_6.2011-6455-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002209_6.2011-6455-Figure1-1.png", "caption": "Figure 1: Initial fixed wing perching aircraft configuration.", "texts": [ " [6, 7] In that case, a flat plate glider was launched from a distance of 3.5 m away from a wire with an initial nominal speed of approximately 7 m/s. The MAV immediately pitched up, slowing the aircraft enough to successfully latch a wire. The success rate for that experiment was about 1 out of 5 attempts. This research aims to build on the success of the previous researchers by developing an experiment in which a biomimetic MAV will glide much longer distances before perching. The vehicle used for this simulation is shown in Figure 1. It is notionally based on the geometry of a bird with a wing span of 0.5 m and reference area of 0.064 m2. The aerodynamics and control derivatives were evaluated using the Air Force DATCOM software. [8] \u2217Research is sponsored by ARO and AFOSR. \u2020Doctoral Student, Dept. of Aerospace Engineering, AIAA Student Member; choe19@illinois.edu. \u2021Professor, Dept. of Mechanical Science and Engineering, Associate Fellow AIAA; nhovakim@illinois.edu. 1 of 15 American Institute of Aeronautics and Astronautics AIAA Guidance, Navigation, and Control Conference 08 - 11 August 2011, Portland, Oregon AIAA 2011-6455 Copyright \u00a9 2011 by Ronald Choe" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003298_icelmach.2018.8506767-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003298_icelmach.2018.8506767-Figure2-1.png", "caption": "Fig. 2. Mechanical model of prototype EDW maglev vehicle", "texts": [ " [12] and Uranker [13, 14] pioneered the use of using exact analytic eddy current equations to determine the eddy current stiffness and damping terms for a coil translationally moving over a conductive plate. More recently, Paul et al. used a second order vector potential (SOVP) formulation to analytically derive the stiffness and damping matrices for an EDW above a conductive plate [15-17]. The EDW has both rotational and translational velocity vectors. A laboratory scale EDW vehicle is shown in Fig. 1 and the vehicles coordinate axes are defined in Fig. 2. The EDW vehicle is physically prevented from moving in the translational, and yaw, \u03b8y, axis such that (z,\u03b8y) = (0,0). In this paper, the SOVP-calculated stiffness and damping terms are used in a semi-linear 4 degree of freedom (DOF) maglev system, with a focus on stability and linearity. Recognizing which terms are approximately linear within an EDW vehicle\u2019s operating region is important, because highly non-linear terms will cause the state-space model to become inaccurate if the vehicle drifts from its desired operating point", " Therefore, a slip speed, s, can be defined as c xs v v= - (1) where c o mv r w= (2) and \u03c9m = rotor mechanical angular speed. Analytic Damping and Stiffness Analysis for a 4-DOF Electrodynamic Wheel Maglev Vehicle J. Wright, J. Z. Bird A 978-1-5386-2477-7/18/$31.00 \u00a92018 IEEE 555 If the EDW vehicle is to remain levitated at a desired attitude and location on a conductive track, then it is necessary to control the vertical position, y, translational position (forward and backward), x, roll, \u03b8x, and pitch, \u03b8z angle. These variables are defined in Fig. 2. The EDW\u2019s are hardmounted to the vehicle (i.e. not allowed to pivot relative to the vehicle body). III. 3-D FORCE AND TORQUE EQUATION If an EDW is rotating with rotational speed, \u03c9m and is moving with a velocity described by v x y zv x v y v z= + + (3) then the forces created by the induced eddy currents is [17] F B /2 /2 * /2 /2 1 ( , , ) ( , , ) l w s r y g g o l w B x y z x y z dxdz m - = \u00f2 \u00f2 (4) Solving for the source field, , and the reflected eddycurrent field, Br the force equation yields F \u02c6 \u02c6 \u02c6Re s m n mn mn mn mnm n j jk wl B R x y z x k k \u00a5 \u00a5 =-\u00a5 =-\u00a5 \u00ec \u00fc\u00ef \u00ef\u00e9 \u00f9\u00ef \u00ef\u00ea \u00fa= - +\u00ed \u00fd\u00ea \u00fa\u00ef \u00ef\u00ef \u00ef\u00eb \u00fb\u00ef \u00ef\u00ee \u00fe \u00e5 \u00e5 (5) where is the source field term and Rmn is the reflected eddy current field term for the mth and nth spatial harmonic", " By a similar derivation, the eddy-current torque is [18] Im s mn mn em mnm n B R T wlP k \u00a5 \u00a5 =-\u00a5 =-\u00a5 \u00ec \u00fc\u00ef \u00ef\u00ef \u00ef\u00ef \u00ef= \u00ed \u00fd\u00ef \u00ef\u00ef \u00ef\u00ef \u00ef\u00ee \u00fe \u00e5 \u00e5 (21) In [5], the force and torque term given by (5) and (21) were used to derive 6-DOF stiffness and damping terms. As this laboratory vehicle is suspended above a 1.2m guideway wheel that approximates a flat guideway track it is not desirable to have the vehicle yaw, \u03b8y, about the y-axis since this could lead to the rotors approaching the edge of the finite width conductive plate guideway. It is also assumed in this analysis that the motion along the axial z-axis, as defined in Fig. 2, is constrained and it is therefore not necessary to model transverse z movement. These constraints result in the eddy current model reducing to a 4-DOF model. The damping and stiffness matrix then reduces to k[ ] xy xy x x xx y yyy F F k x y F k Fkk x y \u00e9 \u00f9\u00b6 \u00b6\u00ea \u00fa\u00e9 \u00f9 \u00ea \u00fa\u00b6 \u00b6\u00ea \u00fa \u00ea \u00fa= = -\u00ea \u00fa \u00ea \u00fa\u00b6 \u00b6\u00ea \u00fa\u00eb \u00fb \u00ea \u00fa \u00ea \u00fa\u00b6 \u00b6\u00eb \u00fb (22) where the diagonal terms are given by 2 Re sm xx mn mn mnm n k wl B R x k \u00a5 \u00a5 =-\u00a5 =-\u00a5 \u00ec \u00fc\u00ef \u00ef\u00ef \u00ef= \u00ed \u00fd\u00ef \u00ef\u00ef \u00ef\u00ef \u00ef\u00ee \u00fe \u00e5 \u00e5 (23) Re s yy mn mn mn m n k wl B Rk \u00a5 \u00a5 =-\u00a5 =-\u00a5 \u00ec \u00fc\u00ef \u00ef\u00ef \u00ef= - \u00ed \u00fd\u00ef \u00ef\u00ef \u00ef\u00ef \u00ef\u00ee \u00fe \u00e5 \u00e5 (24) From the energy equation used to form (4), it can be shown that the diagonal stiffness terms in (22) are equal, so that [17] yx FF y x \u00b6\u00b6 = \u00b6 \u00b6 (25) Therefore, the cross diagonal terms in (22) are both equal to Re s xy m mn mn m n k wl j B Rx \u00a5 \u00a5 =-\u00a5 =-\u00a5 \u00ec \u00fc\u00ef \u00ef\u00ef \u00ef= \u00ed \u00fd\u00ef \u00ef\u00ef \u00ef\u00ef \u00ef\u00ee \u00fe \u00e5 \u00e5 (26) Note that the stiffness terms involving rotor angle, \u03b8m, are cyclic with the electrical frequency of the rotor, P\u03c9m, and average to zero for the comparatively larger time constants of the vehicle and the torque stiffness and damping terms with respect to x and y, are very small and are therefore neglected" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001195_b978-1-4557-2550-2.00004-3-Figure4.47-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001195_b978-1-4557-2550-2.00004-3-Figure4.47-1.png", "caption": "FIGURE 4.47", "texts": [ " The explanation is straightforward: using the PQRS saturation model\u2014Eq. (4.58)\u2014 we find Vsat 5 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2\u03b3SL0d \u03b50\u03b5D r 5 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2d\u03b3LG\u00f0cos \u03b8sat 2 cos \u03b80\u00de \u03b50\u03b5D s : (4.92) The right term of Eq. (4.92) is a direct consequence of the PQRS saturation model, in which the following relation yields \u03b3SL0 5 \u03b3LG \u00f0cos \u03b8sat cos \u03b80\u00de: We obtain the plot of Figure 4.47: the whole range of contact angles can be reached, unto the saturation limit. Note that we have not considered here the fringe effect described by Papathanasiou and Boudouvis [15] which results in a lower limit for the breakdown voltage (see Section 4.4.2.4). The different characteristics of substrates found in the literature are given in Table 4.4. At the present time, the usual EWOD microsystems use low voltages The minimum substrate thickness depends on the amplitude of the contact angle variation \u0394cos \u03b8 (limited by \u0394cos \u03b8sat) and on the DBV of the substrate" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002436_s11665-017-2716-5-Figure6-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002436_s11665-017-2716-5-Figure6-1.png", "caption": "Fig. 6 Comparison view of CAD model and CT scanning entity model: (a) predefined views; (b) left view", "texts": [ " Comparison of defects of the samples before and after heat treatment indicated that the areas of the parts containing defects decreased significantly, and density distribution was more homogenous following heat treatment. The three-dimensional point cloud model, and the models built by the three-dimensional software were loaded into Geomagic Quality 2013 so as to conduct error comparisons. The parts were aligned along the bottom edge to ensure that stress distribution, deformation and x-ray radiographic inspection results could be properly compared for different treatments. Figure 6 shows deformation of the SLM-manufactured part without thermal treatment by comparing with the drawing of three-dimensional modeling. In Fig. 6(a), the image of the laser forming component orientation is gray and the thickness is approximately 0.1 mm showing that the manufactured components are about 0.1 mm thinner than the three-dimensional modeling components in the direction parallel to the laser scanning. After removal of the modeling precision error of 0.1 mm, the remaining image discrepancy is deformation of the manufactured part. In the figure, the surface of the location of the gap is dark blue. The blue color becomes less dark, the closer you are to either end of the components", " However, since the parts are aligned along the bottom edge and due to the modeling precision error, both ends of the deformed components are close to the standard model. It could be inferred that deformation at both ends is larger and the stress distribution concentrates mainly at the gap. Stretching the formed parts from the middle of the gap toward both ends could cause the density of the nearby areas to decrease, which would be consistent with the results of the x-ray radiographic inspection. Figure 6(b) shows the reverse side of the gap of the modeled part, which is perpendicular to the orientation of processing. The middle of the part is light green and light blue close to both ends, demonstrating that the deformation in the middle of the component is smaller and larger at each end. This agrees with the analysis shown in Fig. 5(a), i.e., the stress distribution concentrates mainly in the middle. Stretching from the middle of the gap toward both ends could cause the density of the nearby area to decrease, which is consistent with the results of x-ray radiographic analysis" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000936_s0001925900005394-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000936_s0001925900005394-Figure2-1.png", "caption": "Figure 2.", "texts": [ " (15) Equation (14) is identical to that solved numerically by Squire for the unyawed case, except that in the present problem there is no axis of symmetry (i.e. w (0) \u0302 0) where the computation may be started. As Squire showed, before performing the numerical integration it is necessary to specify the initial form of the solution. This he performed by expanding w (\u00a3) about the origin as a power series in \u00a3. More generally, this expansion may be taken about any point on the line w (s)\u2014s. Since the yawed solution must cross this line at least once (at \u00a30 say), as shown in Fig. 2, we expand w(s) as the power series W(J)-&=2*(J-W- (16> i The coefficients at have been obtained for the biconvex section which is given by = A ( 1 - ? / # ? ) . so that dz \\b J \\bx or dy_ dz 2C n \u2022z, where C=h/b\u20ac112 is the thickness parameter introduced in the previous works\" and which equals zero for the flat wing. Since C/fl is the parameter occurring in equations (11) and (14) in this case, we take this as the relevant thickness parameter for the biconvex section. Substitution of (16) into (11) leads eventually, after much complicated algebra, to the determination of the coefficients a," ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002675_j.ifacol.2017.08.1207-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002675_j.ifacol.2017.08.1207-Figure2-1.png", "caption": "Fig. 2. Gravity and buoyancy forces acting in the underwater robot.", "texts": [ " By design the underwater robot has symmetry in two of its planes and is stable mechanically in roll angle, i.e., \u03c6 \u2248 0, and this implies that the lateral displacement is so small. As consequence, it has only four degree of freedom (x,z,\u03b8 ,\u03c8) and four control inputs, where fi is the force of the propeller i = 1 : 4, see Fig. 1. The body frame coordinates are referenced as xB,yB,zB, considering the origin of that the body frame is set in the center of gravity and is collinear with the main axes of the reference frame, besides the center of buoyancy is collinear along the zB axis, see Fig. 2. Solving (1) for the translational movement, it follows that X = (m\u2212Xu\u0307)u\u0307+Xv\u0307v\u0307\u2212 (myg \u2212Xr\u0307)r\u0307\u2212 (Zw\u0307w+mw)q (2) +(Yv\u0307v+mw)r\u2212 (Xu)u+ fB sin\u03b8 Z = (m\u2212Zw\u0307)w\u0307+(myg \u2212Zp\u0307)p\u0307\u2212 (mxg \u2212Zq\u0307)q\u0307\u2212 (Yv\u0307v+mv)p +(Xu\u0307u\u2212 (mu))q\u2212 (Zw)w\u2212 fB cos\u03b8 cos\u03c6 (3) where m denotes the mass of the vehicle, Xi,Yi,Zi,Ki,Mi,Ni are the linear damping coefficients; i : u,v,w, p,q,r and Xk\u0307, Yk\u0307, Zk\u0307, Kk\u0307, Mk\u0307, Nk\u0307 represent the hydrodynamic added mass coefficients; k\u0307 : u\u0307, v\u0307, w\u0307, p\u0307, q\u0307, r\u0307. In addition, xg,yg,zg are elements of the rg which defines the distance from the origin OB of the body frame to the vehicle\u2019s center of gravity (CG), fW introduces the gravity and fB the buoyancy forces, see Fossen (1994)", " The others parameters are too small and for our study, these parameters are considered as nonlinear uncertainties in the model. Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Table 1. UV parameters Estimated prototype parameters m 33.99 kg Ixx 0.99 N*m Iyy -0.02 N*m Izz -0.02 N*m Xu\u0307 0.963 kg Yv\u0307 0.367 kg Zw\u0307 0.367 kg Kp\u0307 0.002 N*m Mq\u0307 0.002 N*m Nr\u0307 0.002 N*m In addition, by design the roll angle is stable mechanically and as a consequence too small, i.e., \u03c6 \u2248 0. This will implies that the lateral displacement is also small and could be neglected, hence, v, v\u0307, p, p\u0307 \u2248 0. Note from Fig. 2 that the origin of the body frame OB coincides with the center of gravity (CG), then xg,yg,zg \u2248 0. From the earlier assumptions and taking into account the characteristics of the underwater robot, the yaw dynamics can be written as \u2212Xr\u0307u\u0307+ Izzr\u0307\u2212Nr\u0307r\u0307\u2212Nrr = u\u03c8 where N is rewrite as u\u03c8 . Note that Izz and Nr\u0307 can be estimated with SolidWorks considering the geometry of the vehicle (more details see Cruz-Villar et al. (2008)), and therefore they could be considered as constants and written as I\u0304r = Izz \u2212Nr\u0307", " \u03b4\u03b1 = cte. This will implies that e\u0307\u03b4\u03b1 =\u2212 \u02d9\u0302 \u03b4\u03b1 . Proposing the following candidate Lyapunov function VL =V2 + 1 2k\u03b4 e2 \u03b4\u03b1 Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 7063 A. Manzanilla et al. / IFAC PapersOnLine 50-1 (2017) 6857\u20136862 6859 In addition, by design the roll angle is stable mechanically and as a consequence too small, i.e., \u03c6 \u2248 0. This will implies that the lateral displacement is also small and could be neglected, hence, v, v\u0307, p, p\u0307 \u2248 0. Note from Fig. 2 that the origin of the body frame OB coincides with the center of gravity (CG), then xg,yg,zg \u2248 0. From the earlier assumptions and taking into account the characteristics of the underwater robot, the yaw dynamics can be written as \u2212Xr\u0307u\u0307+ Izzr\u0307\u2212Nr\u0307r\u0307\u2212Nrr = u\u03c8 where N is rewrite as u\u03c8 . Note that Izz and Nr\u0307 can be estimated with SolidWorks considering the geometry of the vehicle (more details see Cruz-Villar et al. (2008)), and therefore they could be considered as constants and written as I\u0304r = Izz \u2212Nr\u0307" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002355_jifs-161284-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002355_jifs-161284-Figure1-1.png", "caption": "Fig. 1. Interval type-2 Gaussian membership function with uncertain mean (m) and known standard deviation (\u03c3).", "texts": [ " While a type-2 fuzzy system has a similar structure, but one of the main differences arises from the rule base part, where a type-2 rule base has antecedents and consequents using type-2 fuzzy sets. Due to the complexity of the type reduction, the general type-2 FLS becomes computationally intensive. In order to make things simpler and easier to compute, secondary MFs of an interval type-2 FLS (hereafter referred to as IT2FLS) are all equal to the unity, which finally leads to a type reduction. The interval type-2 Gaussian MF with uncertain mean m \u2208 [m1, m2] and a known standard deviation \u03c3 are shown in Fig. 1. By using singleton fuzzification, the singleton inputs are fed into the inference engine. Combining the fuzzy \u201cIF-THEN\u201d rules, the inference engine maps the singleton input x = [x1, x2, \u00b7 \u00b7 \u00b7 , xn] into a type-2 fuzzy system set as the output. A typical form of an \u201cIF-THEN\u201d rule is as follows Ri: IF x1 is F\u0303 i 1 and x2 is F\u0303 i 2 and \u00b7 \u00b7 \u00b7 and xn is F\u0303 i n THEN Z\u0303i where F\u0303 i ks are the antecedents (k = 1, 2, \u00b7 \u00b7 \u00b7 , n), and Z\u0303i is the consequent of the ith rule. First, the firing set for the ith rule is evaluated as follows Fi(x) = [f i(x), f\u0304 i(x)] (10) where f i(x) = \u03bc F\u0303i 1 (x1) \u2217 \u03bc F\u0303i 2 (x2) \u2217 \u00b7 \u00b7 \u00b7 \u2217 \u03bc F\u0303i n (xn) = n\u220f k=1 \u03bc F\u0303i k (xk) f\u0304 i(x) = \u03bc\u0304F\u0303 i 1 (x1) \u2217 \u03bc\u0304F\u0303 i 2 (x2) \u2217 \u00b7 \u00b7 \u00b7 \u2217 \u03bc\u0304F\u0303 i n (xn) = n\u220f k=1 \u03bc\u0304F\u0303 i k (xk) (11) being the term \u03bc F\u0303i k and \u03bc\u0304F\u0303 i k the lower and upper membership functions, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003199_s00170-018-2616-3-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003199_s00170-018-2616-3-Figure1-1.png", "caption": "Fig. 1 Images of a the alloy drop on the ceramic and b the schematic illustration of the measurement of h and d", "texts": [ " The alloy-ceramic couples were drawn from the furnace chamber and cooled down to the room temperature after the melt alloy was kept at 1500 \u00b0C for 20 min. The wetting angle (\u03b8) was then calculated by using the geometric parameters h and d of the solidified alloy droplets, where hmeans the drop height and d is the base diameter of the alloy drop. The relationship expression between h, d, and the wetting angle is \u03b8 = 2arctan(2 h/d), which is deduced from Eq. 1 to Eq. 3. The cooled alloy dropped on the ceramic, and the schematic drawing of the measurement of h and d is shown in Fig. 1a, b, respectively. In Fig. 1a, the expression of \u03b8 is deduced from the following equations: tan\u03b2 \u00bc h r \u00f01\u00de \u03b2 \u00bc arctan h r \u00bc arctan 2h d \u00f02\u00de \u03b8 \u00bc 2arctan 2h d \u00f03\u00de The alloy bottom was photographed to show the residues, and the alloy drops were then cut perpendicular to the interface. The cut samples were embedded for microstructure observation using a scanning electron microscope (JMS-7800F Prime, Japan) equipped with energy-dispersive spectroscopy (EDS) analysis. The photos of the blades and ceramic shells were photographed by a digital camera" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000942_978-4-431-53856-1_4-Figure4.5-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000942_978-4-431-53856-1_4-Figure4.5-1.png", "caption": "Fig. 4.5 Coordinate system", "texts": [ " In this state, the QTW-UAV rotates in the rolling direction by a moment caused by the difference between the lift forces of flaperons F1, F4 and those of flaperons F2, F3; further, the QTW-UAV rotates in the pitching direction by the moment caused by the difference between the lift forces of the flaperons F1, F2 and those of the flaperons F3, F4. Moreover, the QTW-UAV can rotate in the yawing direction by a yawing moment caused by the difference between the rotor thrusts R1, R4 and R2, R3. In this section, a mathematical model of the 3-axis attitude, roll, pitch, and yaw of the QTW-UAV in the helicopter mode is derived. The definitions of the coordinate systems used in this paper are shown in Fig. 4.5. The coordinate system Fi is a ground-fixed frame. The origin of this frame is fixed at an arbitrary point on the ground;Xi axis indicates north; Yi axis, the east; andZi axis, the direction of gravity. The coordinate system Fb is a body-fixed frame. The origin of this frame is fixed on the center of gravity of QTW-UAV.Xb axis indicates the forward direction of the body; Yb axis, the rightward direction of the body; and Zb axis, the downward direction of the body. In this chapter, we use Euler\u2019s angle for attitude expression" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002777_jae-170045-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002777_jae-170045-Figure1-1.png", "caption": "Fig. 1. Cross-section of single-winding BSRGWR.", "texts": [ " All rights reserved of single-winding BSRGWR are explained; Secondly, the levitation force model is derived based on Maxwell stress tensor method; Thirdly, a suspension control scheme is proposed to eliminate the coupling between levitation forces in X and Y directions; Then this article explains the reasons why generation currents should by controlled symmetrically. To clearly illustrate the control of 12/8 single-winding BSRGWR, the calculation of control variables, including suspension and generation currents, are summarized in a flow chart. Finally, the electromechanical energy conversion is discussed in the open-loop control. It\u2019s also verified that the load voltage can be controlled stably in the closed-loop control. Figure 1 is the cross section of the single-winding BSRGWR with only phase-A and phase-B winding shown. Different from the BSRM in [5\u201312], the rotor pole arc of BSRGWR is 30\u25e6 rather than 15\u25e6. In the following context, 0\u25e6 is defined as the position where the axles of stator and rotor teeth are aligned. So the working period of one phase is (\u221222.5\u25e6, 22.5\u25e6). In the single-winding BSRGWR, there is only one set of winding on each stator tooth and all of the currents in each winding are controlled independently" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000681_sled.2010.5542798-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000681_sled.2010.5542798-Figure1-1.png", "caption": "Fig. 1. Inverter switching states and resulting voltage vectors", "texts": [], "surrounding_texts": [ "The stator voltage equation (4) is: us s = Rsi s s + \u03c8\u0307 s s (4) The flux linkage \u03c8s s of an RSM is only caused by the stator currents. \u03c8s s = L s si s s (5) The rotor saliency is modeled by the inductance tensor Ls s which ist constant in rotor fixed frame. L r s = [ Ld 0 0 Lq ] (6) L s s = TL r sT \u22121 (7) = [ Ld cos 2 \u03b8 + Lq sin 2 \u03b8 (Ld \u2212 Lq) sin \u03b8 cos \u03b8 (Ld \u2212 Lq) sin \u03b8 cos \u03b8 Ld sin 2 \u03b8 + Lq cos 2 \u03b8 ] (8) Since Ls s is time variant in the stator fixed frame it has to be considered when deriving the stator flux (5). \u03c8\u0307 s s = L\u0307 s si s s + L s si\u0307 s s = L s s \u2032\u03c9iss + L s si\u0307 s s (9) Using (9) the voltage equation (4) can be transposed to calculate the derivative of the stator current iss. i\u0307ss = L s s \u22121 ( us s \u2212Rsi s s \u2212 L s s \u2032\u03c9iss ) (10) The Torque M of a RSM ist caused by its saliency. M = is T s J \u03c8s s = (Ld \u2212 Lq) id iq (11)" ] }, { "image_filename": "designv11_29_0001631_icma.2012.6282737-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001631_icma.2012.6282737-Figure1-1.png", "caption": "Fig. 1. Biped Balance Control Strategies", "texts": [ " The COM dynamics directly depends upon the gravitational force and other external forces acting on the COM. So all the balance techniques developed so far regulate the position and velocity of COM with respect to COP Three main approaches for balance control so far developed are: a) Ankle Strategy b) Hip Strategy c) Foot Placement / Stepping Strategy The application of these strategies in case of external perturbation depends upon the strength of perturbation and these strategies can be applied subsequently from top to bottom (Fig. 1). We first briefly go through these three strategies in following section and then discuss the foot placement approach in detail. The structure of this paper is as follows. After reviewing the related work in the next section, we describe the 3D Linear Inverted Pendulum Model (LIPM) [7] [8] (on which our robot is modeled for walking pattern generation) in section III. Section IV describes push detection and the model and approach used for push recovery through foot placement is explained in section V" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0003228_icra.2018.8462923-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0003228_icra.2018.8462923-Figure3-1.png", "caption": "Fig. 3: 1/14th scaled excavator robot has four links Turret, Boom, Arm and Bucket. Turret is actuated by an electric motor (not visible). Other links are hydraulic actuated by piston-cylinder mechanism. End-effector pose se is given by the (x, y, z) position of the end-effector joint w.r.t the base reference frame together with the bucket angle.", "texts": [ " Switch between the intermediate action primitives was decided on the basis of error between the mean states of the initiating and terminating sets. This is plausible for robots with oneto-one correspondence between the degree-of-freedom and the actuators. Otherwise, the time duration for intermediate action primitives can be modeled using semi-Markov model. Experiments were performed on a 1/14th scaled 345D Wedico excavator model, a 4 d.o.f hydraulic robotic arm manipulator, controlled by a radio transmitter (see Figure 3 for the robot\u2019s description). Figure 4a shows the human operator performing truck loading task with the excavator robot. The robot communicates instruction to a operator using the visual interface in Figure 4b. The Wedico excavator lacked joint-angle encoders and internal proprioception, hence the experiments were performed within a motion capture facility to provide real-time measurements to the algorithm. Endeffector position w.r.t the base frame together with the bucket angle gives 4-D end-effector pose vector se" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0002593_j.automatica.2017.07.054-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0002593_j.automatica.2017.07.054-Figure2-1.png", "caption": "Fig. 2. Positional reachable sets overlap.", "texts": [ " (18) Actually, although not explicitly specified, the positional reachable set of each entity at a specified time t1 can be placed in the physical space. This results from the solution of the kinematics along X , expressed by the relation in (1), which indicates that time and location along the horizontal reference line are interchangeable. Remark 2.1. For every pursuer Pi, its and the evader\u2019s positional reachable sets at tfi from any instant t are located at the same point along the horizontal reference line (by definition of tfi ). It is therefore at this instant only that an overlap may exist between the two sets, as demonstrated in Fig. 2. Consequently, tfi is the only instant at which the positional coincidence of Pi and E is possible. Let us define the set of all admissible initial conditions \u03c7o = { {to, xoP1 , . . . , x o Pn , x o E} \u23d0\u23d0\u23d0to < tf1 , xoj \u2208 R njz+2 \u2200j \u2208 G } . Definition 2.2 (Independent Capture Zone). A pursuer\u2019s independent capture zone is the set of all initial conditions from which it is capable of guaranteeing point capture, for any admissible evader control sequence, independently{ \u03c7o \u2208 \u03c7o \u23d0\u23d0\u23d0\u23d0\u2200uE(t) \u2208 UE([to, tfi ]) \u2203uPi (t) \u2208 UPi ([to, tfi ]) : yPi (tfi ) = yE(tfi ) } " ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001191_2013-01-1215-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001191_2013-01-1215-Figure4-1.png", "caption": "Figure 4. Connecting Rod Assembly", "texts": [ " In our system the swing speed of the connecting rod is controlled to be 300 rpm because the actuator needs 100 \u03bcs to increase to its maximum load and also needs 100 \u03bcs to return from the maximum load to the original position. The PZT loading cycle is shown in Figure 2. The connecting rod was connected to the arm driven by a cam follower as shown in Figure 3. The cam follower was fixed to a rail that slid linearly to produce the swinging motion of the connecting rod. The rail was driven by another arm connected to the rotation wheel that transferred the rotation from an AC motor to a linear motion. Figure 4 shows the piston and the connecting rod assembly. The piston was flipped over, so the load could be apply directly to the connecting rod small end. It also increases the stiffness of the entire assembly. To ensure that the loading cycle and the connecting rod swing cycle are synchronized, a proximity switch shown in Figure 5 and an electronic circuit consisting of a flip-flop and AND gates were applied to produce a signal with a frequency which is half of the connecting rod swing frequency. The proximity switch can detect magnetic metal objects when they are in very close proximity to the switch and that will trigger a high voltage output to the electronic circuit" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0000426_s11044-009-9159-1-Figure7-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000426_s11044-009-9159-1-Figure7-1.png", "caption": "Fig. 7 On the left, angles yi of the Andrews\u2019 system. On the right, lengths ai and fixed nodes of the Andrews\u2019 system. The circles represent the revolute joints", "texts": [], "surrounding_texts": [ "The ideal S\u03047 contains variables c2, s2, c5, s5, c8, s8 and parameter l5. Now, the necessary condition for the singularity is that one of the equations in (11) is satisfied. Let us investigate the ideal S\u03047 in the ring Q(l5)[c2, s2, c5, s5, c8, s8], where the coefficient field Q(l5) is now field extension of Q, and the field extension has been defined by minimal polynomial r1 [15]. Also lexicographic ordering is used for variables c2, s2, c5, s5, c8, and s8. The radical of S\u03047 is in this field already a prime ideal and when we compute it, we find that \u221a S\u03047 = \u3008t1, . . . , t6\u3009, where t1 = 6344s8 + (\u2212225l3 5 \u2212 1350l2 5 + 1243l5 + 6086 ) , t2 = 4758c8 + ( 50l3 5 + 300l2 5 \u2212 893l5 \u2212 2568 ) , t3 = 5s5 \u2212 4, t4 = 5c5 \u2212 3, t5 = 5s2 \u2212 4, t6 = 5c2 \u2212 3. Now, when we substitute the only positive root of r1, l5 \u2248 1.3402, into ideal \u221a S\u03047, the variables c8 and s8 can also be solved from t1 = 0 and t2 = 0. After these variables have been solved, all other variables can also be solved and we get (c1, s1) = (4/5,3/5), (c2, s2) = (4/5,3/5), (c3, s3) = (\u22124/5,\u22123/5), (c4, s4) = (3/5,4/5), (c5, s5) = (3/5,4/5), (c6, s6) \u2248 (\u22120.9928,0.1196), (c7, s7) \u2248 (0.6565,\u22120.7543), (c8, s8) \u2248 (0.6565,\u22120.7543) (c9, s9) \u2248 (0.3928,\u22120.9196). When we compute the angles \u03b8i from equations (ci, si) = (cos(\u03b8i), sin(\u03b8i)), we get \u03b81 \u2248 0.9273, \u03b82 \u2248 0.9273, \u03b83 \u2248 \u22122.2143, \u03b84 \u2248 0.9273, \u03b85 \u2248 0.9273, \u03b86 \u2248 \u22123.2615, \u03b87 \u2248 \u22120.8546, \u03b88 \u2248 \u22120.8546, \u03b89 \u2248 \u22121.1671. From Fig. 6 one can see that in one case of V(S\u03047) the mechanism is in position where joints 2,4 and joints 3,5 coincide. 3.7 Andrews\u2019 squeezing mechanism In this section we will briefly analyze the Andrews\u2019 squeezing mechanism. Andrews\u2019 mechanism is a seven-body mechanism which consists of three closed kinematical loops, and has been used as a benchmark problem [20] to compare different multibody solvers. In [4] we analyzed the system using the same tools, but different approach. We first analyzed some subsystems of original constraint equations and then we showed that singularities of these subsystems give singularities of the original system. The loop closure equations of the mechanism are given as in [4]. g(y) = \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 a1 cos(y1) \u2212 a2 cos(y1 + y2) \u2212 a3 sin(y3) \u2212 b1 = 0, a1 sin(y1) \u2212 a2 sin(y1 + y2) + a3 cos(y3) \u2212 b2 = 0, a1 cos(y1) \u2212 a2 cos(y1 + y2) \u2212 a4 sin(y4 + y5) = 0 \u2212 a5 cos(y5) \u2212 w1 = 0, a1 sin(y1) \u2212 a2 sin(y1 + y2) + a4 cos(y4 + y5) \u2212 a5 sin(y5) \u2212 w2 = 0, a1 cos(y1) \u2212 a2 cos(y1 + y2) \u2212 a6 cos(y6 + y7) \u2212 a7 sin(y7) \u2212 w1 = 0, a1 sin(y1) \u2212 a2 sin(y1 + y2) \u2212 a6 sin(y6 + y7) + a7 cos(y7) \u2212 w2 = 0. (12) Formulating these again as polynomial equations, we get p(c, s) = \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 p1 = a1c1 \u2212 a2(c1c2 \u2212 s1s2) \u2212 a3s3 \u2212 b1 = 0, p2 = a1s1 \u2212 a2(s1c2 + c1s2) + a3c3 \u2212 b2 = 0, p3 = a1c1 \u2212 a2(c1c2 \u2212 s1s2) \u2212 a4(s4c5 + c4s5) \u2212 a5c5 \u2212 w1 = 0, p4 = a1s1 \u2212 a2(s1c2 + c1s2) + a4(c4c5 \u2212 s4s5) \u2212 a5s5 \u2212 w2 = 0, p5 = a1c1 \u2212 a2(c1c2 \u2212 s1s2) \u2212 a6(c6c7 \u2212 s6s7) \u2212 a7s7 \u2212 w1 = 0, p6 = a1s1 \u2212 a2(s1c2 + c1s2) \u2212 a6(s6c7 + c6s7) + a7c7 \u2212 w2 = 0, pi+6 = c2 i + s2 i \u2212 1 = 0, i = 1, . . . ,7. (13) Let us now apply the same strategy as before. We again denote I = \u3008p1, . . . , p13\u3009 and compute the prime decomposition of the radical of the ideal which is spanned by the maximal minors of dp. Doing this, we find that\u221a I13(dp) = I1 \u2229 \u00b7 \u00b7 \u00b7 \u2229 I85. However, only 21 of these are physically relevant, and it turns out that only 6 of these ideals give singular varieties for the parameters. The relevant prime ideals are I53, I63, I69, I69, I70, and I83. It turns out that the ideal U2 = I63 + I gives the same singular variety which we got from subsystem 367 in [4], and the ideal U3 = I + I69 gives the same singular variety which we got from subsystem 4567 in [4]. But now we found that there are four more possible singular varieties. The notation 367 means here that the subsystem was derived from original constraint equations and contained only variables c3, s3, c6, s6, c7, s7. Similarly notation 4567 means that the subsystem was derived from original constraint equations and only contained variables c4, s4, . . . , c7, s7. Just for example let us investigate one of the \u201cnew\u201d singular varieties. If we set U1 = I + I53 = I + \u3008s2, c1c3 + s1s3\u3009, and compute the Gr\u00f6bner basis GU1 of this ideal in the ring Q [ (c1, s1, . . . , c7, s7), (a1, a2, a3, a4, a5, a6, b1, b2,w1,w2) ] , we find that E = I \u2229 Q[a1, a2, a3, a4, a5, a6, b1, b2,w1,w2] = \u2329 GU1(1) \u232a = \u3008k1k2k3k4\u3009. Here the polynomials ki are k1 = (a1 + a2 \u2212 a3) 2 \u2212 ( b2 1 + b2 2 ) , k2 = (\u2212a1 + a2 \u2212 a3) 2 \u2212 ( b2 1 + b2 2 ) , k3 = (\u2212a1 + a2 + a3) \u2212 ( b2 1 + b2 2 ) , k4 = (a1 + a2 + a3) \u2212 ( b2 1 + b2 2 ) . The necessary condition for singularity of type V(U1) for Andrews\u2019 squeezing mechanism is that one of the equations ki = 0 is fulfilled. Similar conditions also follow from others previously uninvestigated singular varieties." ] }, { "image_filename": "designv11_29_0000448_j.mechmachtheory.2010.03.006-Figure2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0000448_j.mechmachtheory.2010.03.006-Figure2-1.png", "caption": "Fig. 2. The geometry of the parallel mechanism under study. Three angles (\u03c61, \u03c62, \u03c63) are the input variables and (x, y, \u03b8) are assumed to be the output variables.", "texts": [ " The amounts of rotation registered by the three driving motors constitute the three inputs, and the displacement of the mobile platform in the horizontal plane (x, y) and the orientation of the platform (\u03b8) at any instant are assumed to be three outputs of the mechanism. Using the parallel mechanism, different planar motion and orientation can be generated by moving the three sliders independently along a common guide ring. As shown in Fig. 1, the sliders carry three rotating linear guides. The parallel mechanism has a mobile platform that is supported by a symmetrical Y shape object with three shafts passing through three rotating guides. The parallel mechanism has a singularity-free circular workspace in which any orientation can be achieved [13]. Fig. 2 shows the geometry of the parallel mechanism under study. The intersection of the three axes of the linear bearings forms point C (Fig. 2). This point (C) is assumed to be the center of the mobile coordinate. The position of the new coordinate is denoted by x and y. The angle between the reference frame (O, X, Y) and mobile frame (C, X\u2032, Y\u2032) is given by \u03b8, which is the new orientation of the mobile platform. By using x, y and \u03b8, the location of the mobile platform can be defined. The location of the rotating linear bearings on the guide ring is defined by three angles (\u03c61, \u03c62, \u03c63), which are the angles between the base x axis and the vectors OO \u2192 i (Fig. 2). For the kinematic analysis of this parallel mechanism, the three angles \u03c6i and (x, y, \u03b8) are assumed to be the input and output variables respectively. The accuracy of a mechanism is dependent on the condition number of the Jacobian matrix. Gosselin [14] defined the local dexterity, which is the inverse of the condition number of the Jacobianmatrix, as a criterion formeasuring the kinematics accuracy of a parallel mechanism. The local dexterity can be changed between zero and one. A higher local dexterity value indicates a more accurate motion being generated at a given instance", " The inverse kinematics is the process of determining the input parameters in order to achieve a desired position of a mobile platform. For the above mentioned parallel mechanism, the inverse kinematic problem consists of finding the position of Oi which is the intersection points of lines COiwith the circular path of three sliders on the guide ring. For each desired position of themobile platform (x, y, \u03b8), the inverse kinematic problem can be solved geometrically. Bonev et al. [3] reported that there was only one practically feasible solution for the equations of inverse kinematics. where where In Fig. 2, mi denotes the unit vector along each linear bearing (directed outwards), which can be defined as follows: mi = cos\u03b8i sin\u03b8i \u00f01\u00de \u03b8i = \u03b8\u2212\u03c0 6 + 2\u03c0 3 i\u22121\u00f0 \u00de; i = 1;2;3: \u00f02\u00de The vector which denotes the position of the center of platform according to the positions of linear bearings (Oi) can be expressed by using Eq. (3). COi \u2192 = OOi \u2192 \u2212OC \u2192 \u00f03\u00de Assuming that the radius of the guide ring is equal to 1, the following algebraic equations (Eqs. (4) and (5)) can be obtained. \u03c1icos\u03b8i = cos\u03c6i\u2212x \u00f04\u00de \u03c1isin\u03b8i = sin\u03c6i\u2212y \u00f05\u00de \u03c1i is the length of OO \u2192 i which is positive; the positive or negative sign will be determined by the projection (cos \u03b8i or sin \u03b8i)" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001851_s00170-012-4519-z-Figure3-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001851_s00170-012-4519-z-Figure3-1.png", "caption": "Fig. 3 Ultrasonic inspection procedure. a Five longitudinal trajectories of the probe. b Photograph of the probe and the part during the inspection. c The whole \u201cC-Scan\u201d image of a part formed by joining the five partial images obtained during the inspection", "texts": [ " The ultrasonic inspection was made using an Olympus \u201cOmniScan MX\u201d with an acquisition module based on the \u201cphased array\u201d technique and a 10-MHz immersion probe 10L64-I1 with 64 elements. The focal law orientation of the phased array was of 90\u25e6. The movement of the probe was automated, using a milling machine governed by a FAGOR 8025M computer numerical control and the die-cast part was submerged in water during the ultrasonic inspection process, requiring the inspection of five longitudinal trajectories of the probe (Fig. 3a, b) to cover the whole part. The whole \u201cC-Scan\u201d image of each part (Fig. 3c) is formed by joining the five partial C-Scan images obtained as indicated above. The C-Scan image of each part has a color depth of 256 levels of gray, the value 0 representing black and 255 white. An automated inspection equipment can obtain a measurement in less than 15 min. To determine the porosity level in the casting parts, a porosity index, PI , is defined. This index establishes the porosity level of the part from the levels of gray in the image obtained with the radiographic or ultrasonic inspection and the number of pixels occupied by these levels of gray" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001881_s10015-012-0031-7-Figure4-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001881_s10015-012-0031-7-Figure4-1.png", "caption": "Fig. 4 Supporting polygon", "texts": [ " (12) and (2) gives _xg \u00bc FG _x \u00f013\u00de Hence differentiating Eq. (13) with respect to time, we obtain \u20acxg \u00bc _FG \u00fe F _G _x\u00fe FG \u20acx \u00f014\u00de Finally, replacing Eq. (14) into Eq. (10) and rearranging the equation yields f z \u00bc K0\u20acx\u00fe K00\u20acx\u00fe D \u00f015\u00de where K0 \u00bc B\u00f0 _FG \u00fe F _G \u00de K00 \u00bc AE M \u00fe BFG \u00fe C: The tip-over prediction is performed based on the measurement of moments at the candidate of the tip-over axes. This principle can be illustrated using the general form of an imaginary support polygon with n-contact points as shown in Fig. 4. Each point represents the contact point of each wheel with the plane ground. The shape of this support polygon will keep changing according to the current position and the orientation of both dual-wheel casters. The supporting force, fzi can be computed through the dynamics equations as derived in the previous section or measured using force sensors in the actual drive system. The tipping instability may occur in the case when one or more wheels start to lift off the ground, where the value of the supporting forces is approaching zero" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001876_3.2023-Figure1-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001876_3.2023-Figure1-1.png", "caption": "Fig. 1 The coordinate system.", "texts": [ " The distances between these two heat sources and the axis of the cylinder are considered constant and very large compared with the cylinder diameter and cylinder length. The length of the cylinder is large compared with the cylinder diameter so that no heat flow takes place in the axial direction, and therefore all calculations are made per unit length of the cylinder. Differential Equation and Solution The governing differential equation for the temperature as defined in a frame of reference fixed relative to the heat sources (Fig. 1) is _ ^\u00b0 Jf4 d02 fes ks cos+0 + ks - cos+0 = bT where Define ,, _ (cos0 - (ir/2) < 0 < Or/2) COS * ~ \\ 0 Or/2) < 6 < (3ir/2 T(6,t) = (2) where f(d,t) <3C 1, and T9(B) is the steady state temperature distribution due to solar radiation. Hence, the initial condition follows: 7X0,0) = 0 (3) In Ref. 1, the steady state temperature distribution due to solar radiation is expressed as Ts(y) \u2014 TQ[L -\\- j t s(0)j and the solution is obtained in closed form for Ts(0) with the average temperature determined as (4) ' 1, /TT / 7\u0302 \" / \\ 1 I A", "4\"8'10 If one is to use the patched-conic method with confidence, it is imperative that one be able to place bounds on the errors incurred. This means that one must examine each simplifying assumption and its effect. One such assumption is that of the shape of the sphere of influence, and for this reason an exact determination of its shape is desirable. In studying the patched conic method, one need consider only three bodies at a time, since the sphere of influence always is determined by the two major attracting bodies. Figure 1 shows a three-body system (Mi, M^ V) that is restricted only in the sense that the mass of the vehicle V is assumed negligible. It is assumed that the mass MI is greater than Mz. The radius vector convention uses capital letters to denote vectors from MI and lower case letters to denote those from M%. The angle 6 is defined by the dot product z \u2014 \u2014rR% cos# 0 < 6 < TT (D Received April 15, 1963. * Physicist, Flight Dynamics, Apollo Support Department. Member AIAA. D ow nl oa de d by W A SH IN G T O N S T A T E U N IV E R SI T Y o n Ja nu ar y 26 , 2 01 5 | h ttp :// ar c" ], "surrounding_texts": [] }, { "image_filename": "designv11_29_0001032_9781118316887.ch6-Figure6.2-1.png", "original_path": "designv11-29/openalex_figure/designv11_29_0001032_9781118316887.ch6-Figure6.2-1.png", "caption": "Figure 6.2-3: Four-pole, two-phase, 1/10-Hp, 115-V induction motor with reduction gear.", "texts": [ " Therefore, we will focus our attention on the two-phase machine, since this enables us to become familiar with the theory and perfor- 213 Electromechanical Motion Devices, Second Edition by Paul Krause, Oleg Wasynczuk and Steven Pekarek Copyright \u00a9 2012 Institute of Electrical and Electronics Engineers, Inc. mance of induction machines without becoming inundated with trigonometric manipulations. Once the theory has been established, induction-motor performance during balanced operation is illustrated by computer traces. The three-phase induction machine is treated in the last section of this chapter; single-phase and unbalanced operations of the two-phase symmetrical induction machine are covered in a later chapter. A two-pole, two-phase induction machine is shown in Fig. 6.2-1. It is assumed that the stator windings may be portrayed by orthogonal, sinusoidally distributed windings as described in Chapter 4. It is convenient to assume that the rotor of the two-pole, two-phase induction machine may also be portrayed electrically by two sinusoidally distributed windings displaced 90\u00b0. We will talk about forged and squirrel cage rotors of induction motors later. Hence, for our present purposes, we will consider that the ar and br windings are sinusoidally distributed, each with the same total winding resistance", " In some special applications, such as wind turbines, both the rotor and stator windings are connected to sources, whereupon the induction machine is said to be double-fed. In this case, the rotor windings are connected to a stationary multiphase source by a brush and slip-ring arrangement. The slip ring is a solid copper ring and is not segmented as a commutator in a dc machine. As established in Chapter 4, the angular displacement about the stator is denoted 0S, and it is referenced to the as axis. We see from Fig. 6.2-1 that the angular displacement about the rotor is denoted (f)r and it is referenced to the ar axis. The angular velocity of the rotor is ur and 9r is its angular displacement. In particular, 9r is the angular displacement between the ar and as axes. Thus, a given point on the rotor surface at the angular position (j)r may be related to an adjacent point on the inside stator surface with the angular position (j)s as s = r + 0 r (6.2-1) The electromechanical torque Te and the load torque TL are also indicated in Fig. 6.2-1. We are aware from Chapter 2 that Te is assumed to be positive in the direction of increasing #r, whereas the load torque is positive in the opposite direction (opposing rotation). The air-gap mmfs due to the as and bs windings are given by (4.3-4) and (4.3-5). From our work in Chapter 4, we are able to write the air-gap mmfs for the ar and br windings by inspection. In particular, mmfar = \u2014- iar cos (j)r (6.2-2) Nr mmffo. = \u2014- ifr sin (j)r (6.2-3) where A^ is the equivalent number of turns of the rotor windings", " We will find that this device with short-circuited rotor windings operates as a motor when ur < u;e, and as a generator when the rotor is driven above coe by a torque input to the shaft. One may, at first, choose to call this device a four-pole rather than a twopole device since two poles are established by the stator currents and two poles are established by the rotor currents. We must realize, however, that even though we have considered the stator and rotor air-gap mmf separately, they combine to form one resultant two-pole magnetic system. A cutaway of a four-pole, three-phase, 7.5-hp, 460-V, squirrel-cage induction motor is shown in Fig. 6.2-2. It is an enclosed, fan-cooled, severe-duty motor for use in the chemical, paper, cement, and mining industries. A disassembled four-pole, two-phase, ^-hp, 115-V, induction motor, which is used in low-power control applications, is shown in Fig. 6.2-3. Also shown in Fig. 6.2-3 is the case that houses the speed-reduction gears. SP6.2-1 Assume sinusoidally distributed windings on the stator and rotor of the machine shown in Fig. 6.2-1. Express (a) mmfas in terms of 9r and 4>r and (b) mmfflr in terms of 9r and 8. [(a) mmfas =(Ns/2)ias cos(0r + 0r); (b) mmfar = (Nr/2)iarcos((f)s - 6r)] SP6.2-2 The frequency of the balanced stator currents of an induction machine is 60 Hz and mmfs rotates counterclockwise. The device is operating as a motor, and the rotor of the two-pole machine is rotating counterclockwise at 0.9cue. (a) Determine the frequency of the balanced rotor currents. Determine the angular velocity of mmfs and mmfr relative to an observer sitting (b) on the rotor and (c) on the stator, [(a) 6 Hz; (6) 37.7 rad/s, ccw; (c) 377 rad/s, ccw] 6.2. TWO-PHASE INDUCTION MACHINE 219 220 SYMMETRICAL INDUCTION MACHINES SP6.2-3 Repeat SP6.2-2 for a six-pole induction machine operating as a generator being driven at u>r = l.lu;e. [(a) 6 Hz; (b) 37.7/3 rad/s, cw; (c) 377/3 rad/s, ccw] SP6.2-4 Give the phase relationship of the rotor currents for (a) SP6.2-2 and (b) SP6.2-3. [(a) \u00efar = j\u00ef^; (b) \u00efar = -j\u00ef*] WINDING INDUCTANCES The voltage equations for the induction machine depicted in Fig. 6.2-1 may be expressed as dXnx (6.3-1) (6.3-2) (6.3-3) where rs is the resistance of each of the stator windings and rr is the resistance of each of the rotor windings. It is convenient, for future derivations, to write (6.3-1) through (6.3-4) in matrix form as Va&s = rsia6s + p\\abs (6.3-5) Va6r = I>ia&r + P^abr (6.3-6) where (fabs)T = [fas fbs] (6.3-7) (fafcrf = [far fbr] (6.3-8) In (6.3-7) and (6.3-8), / can represent voltage, current, or flux linkages, and T denotes the transpose of a vector or matrix", "3-22) Lmr = Nf-^- (6.3-23) where /io is the permeability of free space, r is the mean radius of the air gap, / is the axial length of the air gap (rotor), and g is the radial length of the air gap. One must perform a rather involved and lengthy derivation to obtain (6.3-22) and (6.3-23). We will not do this derivation; instead, the use of an equivalent magnetizing reluctance 9ftm without evaluation will be sufficient for our purposes. Since the stator (rotor) windings are orthogonal as depicted in Fig. 6.2-1, it would seem that coupling does not exist between the as and bs windings 6.3. VOLTAGE EQUATIONS AND WINDING INDUCTANCES 223 (Lasts or Lisas) or between the ar and br windings (Larbr or Lbrar). However, recall that the equivalent, sinusoidally distributed windings are depicted by one coil placed at the maximum turns density; the windings are actually distributed similar to that shown in Fig. 4.2-2. If we considered, for example, the coupling between the as and bs windings, one would be led to believe that coupling exists since current flowing in the as\\ \u2014 as[ coil in Fig", "\"7r, the windings are again orthogonal and Jasar 0 for 9r = \\K (6.3-29) Prom (6.3-26) through (6.3-29), we see that mutual inductances might be approximated as a cosine function of 9r. In particular, if we define Lsr as N N Lsr = \u0302 P (6.3-30) we can approximate Lasar or Laras as Lasar = Lsr cos 9r (6.3-31) If we were to carry out the derivation as in [1], we would find that (6.3-31) is, indeed, a valid expression for the mutual inductance between the as and ar windings. It follows by inspection of Fig. 6.2-1 that Lasbr = ~~Lsr sin 9r (6.3-32) Lbsar \u2014 Lsr sin 9r (6.3-33) Lbsbr = Lsr cos 9r (6.3-34) Hence, cos 9r \u2014 sin 9r sin 9r cos 9r (6.3-35) One should now be able to write the mutual inductances by inspection. For practice, express the stator and rotor mutual inductances if the positive direction of ibs is reversed. In this case, (6.3-31) and (6.3-32) remain unchanged; however, the sign of (6.3-33) and (6.3-34) would be changed. Once the expressions for the mutual inductances are known, we begin to understand the complexities involved in the analysis of electric machines", "3-44) 226 SYMMETRICAL INDUCTION MACHINES Lrr \u2014 Llr + Nr Note that T\u00bbX ^ s r 7v 7 -^sr Nr \u25a0L'mr -l^lr ' ^ms cos 0r \u2014 sin 0r sin 6r cos 6r (6.3-45) (6.3-46) Comparing Lms, (6.3-20), and Ls r, (6.3-30), we see that ^L -L TVT ^sr ^ms Hence, (6.3-46) may be expressed in terms of Lms and, for compactness, we will define LL as (6.3-47) L' - ^ L -L cos 0r \u2014 sin 0r sin 0r cos 0r Thus, (6.3-43) becomes *abs xabr LS 14 (i4)T K labs abr (6.3-48) (6.3-49) SP6.3-1 Assume that 0r is positive in the clockwise direction in Fig. 6.2- 1 rather than in the counterclockwise direction. Express all inductances. [Lasbr \u2014 Lsr sin 0r] \u00a3&sar = \u2014 L s rsin# r; all others unchanged] SP6.3-2 The as and bs windings in Fig. 6.2-1 are rotated \\n clockwise from the position shown. Express Lasar and Lasbr. [Lasar = Lsrcos(0r + \\K)] Lasbr \u2014 \u2014Lsr sin(#r + JTT)] SP6.3-3 Consider the device shown in Fig. 6.2-1. All windings are opencircuited except the as winding. Ias = sin t, Lms = 0.1 H, Lrr ~ Xjl ujr \u2014 0, and 0r \u2014 |7r. Determine Var. [Var = 0.025cost] k TV* From Table 2.5-1 for a P-pole machine, ^) = f^p (6.4-1) Recall that in Chapter 2 we use i as a short-hand notation for i \u2014 (z1? i2, i\u00df, . . i j ) . Here, i = (ias^bs^ar^br)- Do not confuse this with iabs and w , which are 6.4. TORQUE 227 vectors. In a linear magnetic system, the energy in the coupling field Wf and the coenergy Wc are equal. The field energy can be expressed as w>(i, or) = \\Laseas + \\Lssqs + \\urrc + \\u\u201e%", " For a P-pole machine, since urm \u2014 (2/PH, T e = J l ~^T + Brn^Ur + TL ( 6 .4 -5 ) r at F where J is the inertia of the rotor and, in some cases, the connected load. The first term on the right-hand side is the inertial torque. The units of J are kilogram \u2022 meter2 (kg \u2022 m2) or joules \u2022 second2 (J \u2022 s2). Often, the inertia is given as a quantity called WJR2 , expressed in units of pound-mass-feet2 (lbm -ft2). The load torque TL is positive for a torque load on the shaft of the induction machine (motor action), as shown in Fig. 6.2-1. Since Te is positive in the direction opposite to the positive direction for T^, Te is also positive for motor action. Generation occurs when both are negative. The constant Bm is a damping coefficient associated with the rotational system of the machine and mechanical load. It has the units of N \u2022 m \u2022 s/rad of mechanical rotation and it is generally small and often neglected. SP6.4-1 Why is the sixth term on the right-hand side of (6.4-2) negative? [(6.3-32)] ARBITRARY REFERENCE FRAME In Chapter 5, we introduced the concept of reference frame theory wherein we set forth a change of variables that related the variables associated with symmetrical stationary circuits to variables associated with substitute circuits rotating at an arbitrary angular velocity", " The majority of the performance characteristics given in this and the following section are for the single-fed, two-pole, two-phase, 5-hp, 110-V (rms), 60-Hz, induction machine with the following parameters: rs = 0.295 Q, Lls = 0.944 mH, Lms = 35.15 mH; r'r = 0.201 ft, and L'lr = 0.944 mH. The inertia of the rotor and connected mechanical load is J \u2014 0.026 kg \u2022 m2. The four-pole, two-phase, ^-hp, 115-V(rms), 60-Hz, induction motor has the following parameters: rs = 24.5 fi, Li8 = 27.06 mH, Lms \u2014 273.7 mH, r'r = 23 Q, and L'lr = 27.06 mH. The inertia of the rotor and connected mechanical load is J = 1 x 10~3 kg \u2022 m2. This device is shown in Fig. 6.2-3. Free Acceleration from Stall The free-acceleration characteristics are depicted in Figs. 6.9-1 and 6.9-2 for the 5-hp machine and in Figs. 6.9-3 and 6.9-4 for the ^-hp motor. At t = 0, rated voltages are applied of the form vas = \\/2Kcos377\u00a3 and Vts = v/2Vr ssin377i, where Vs = 110 V for the 5-hp machine and Vs = 115 V for the ^-hp motor. The machines accelerate from stall with zero load torque and, since friction and windage losses are not taken into account, the simulated machine accelerates to synchronous speed", " Park, \"Two-Reaction Theory of Synchronous Machines - Generalized Method of Analysis - Part I,\" AIEE Trans., Vol. 48, July 1929, pp. 716-727. [3] P. C. Krause, 0 . Wasynczuk, and S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems, 2nd Edition, IEEE Press, 2002. [4] A. M. Trzynadlowski, The Field Orientation Principle in Control of Induction Motors, Kluwer Academic Publishers, 1994. [5] F. Blaschke, Das Verfahren der Feldorientierung zur Regelung der Drehfeldmaschine, Ph. D. thesis, TU Braunschweig, 1974. 1. Consider the two-pole, two-phase induction machine shown in Fig. 6.2-1. The device is operating as a motor at ujr \u2014 957T rad/s with I'ar \u2014 cos57r\u00a3 and 1^ \u2014 \u2014 sin birt. Determine the angular velocity and direction of mmfr relative to (a) an observer on the rotor and (b) an observer on the stator. Also determine (c) angular velocity of the stator currents and (d) the direction of rotation of the rotor. 2. The windings shown in Fig, 6.15-1 are sinusoidally distributed and the device is symmetrical. The amplitude of the stator-to-rotor mutual inductance is Lsr. Express all mutual inductances as functions of Lsr and 9r. 2/7/ ? ^