Design and analysis of rigid and compliant mechanisms doctor of philosophy major mechanical engineering

國 立 高 雄 科 技 大 學 機械工程系博士班 博士論文 剛性與柔順機構的設計與分析 Design and Analysis of Rigid and Compliant Mechanisms 研究生：黃裕泰 指導教授 ：黃世疇 教授 中華民國 108 年 月 剛性與柔順機構的設計與分析 Design and Analysis of Rigid and Compliant Mechanisms 學生：黃裕泰 Ngoc-Thai Huynh 指導教授：黃世疇 教授 Shyh-Chour Huang 國 立 高 雄 科 技 大 學 機械工程系博士班 博士論文 A dissertation Submitted to Department of Mechanical Engineering National Kaohsiung University of Science and Technology in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mechanical Engineering June 09, 2019 Kaohsiung, Taiwan, Republic of China 中華民國 108 年 月 日 剛性與柔順機構的設計與分析 研究生：黃裕泰 指導教授： 黃世疇 教授 國立高雄科技大學 機械工程系博士班 摘 要 本論文研究第一目標為探討多剛體機構接頭的設計參數，如間隙尺寸，材料 特性，轉動間隙接頭摩擦，運轉速度，軸頸與軸承半徑等對其動態反應之影響； 第二個目標為設計新型撓性鉸鏈接頭，以改善這些傳統接頭的缺點。 首先設計一個具二個滑塊與七個轉動間隙接頭的曲柄滑塊機構，研究中以有 限元素法 ANSYS 分析該機構的動態特性。其次設計撓性鉸鏈的橋式柔性機構與張 力位移放大器，然後以有限元素法 ANSYS 分析其輸出位移與輸出應力。文中應用 田口方法，灰色關聯分析，熵測量技術，回歸方程與人工神經網絡等方法分析各 機構之最佳化組合參數。 研究結果顯示，這些參數對曲柄滑塊機構的動態反應有顯著影響。加速度與 接觸力的最佳結果分別為 186.45（m/s2）與 106.854（N），加速度誤差為 3.92 ％，接觸力誤差為 9.99％。橋式柔性機構撓性鉸鏈的設計參數最佳化及實驗結果 一致，顯示其對輸出位移與輸出應力均有顯著影響。分析得到的最佳位移放大率， 田口方法為 71.2，回歸方程為 71.05，人工神經網絡為 79.21。最佳輸出應力結 果，田口方法為 73.44 MPa，回歸方程為 76.116 MPa，人工神經網絡為 73.362 i MPa。實驗結果與模擬誤差為 4.895％，田口方法誤差為 12.64％，回歸方程誤差 為 3.94％，人工神經網絡誤差為 13.83％。 有限元素與最佳化結果顯示設計參數對採用撓性鉸鏈的張力位移放大器的輸 出位移和輸出應力均有顯著影響。對於田口方法，最佳輸出位移和輸出應力結果 為 0.6938mm 與 52.314MPa；灰色關聯分析為 0.6040mm 與 53.561MPa。其最佳位 移放大率，田口方法為 69.38，灰色關聯分析為 60.4。 關鍵字：轉動間隙接頭，橋式柔順機構，張力位移放大器，田口方法，回歸方程， 灰色關聯分析，人工神經網絡 ii Design and Analysis of Rigid and Compliant Mechanisms Student: Ngoc-Thai Huynh Advisor: Shyh-Chour Huang Department of Mechanical Engineering National Kaohsiung University of Science and Technology Abstract This study concludes two primary objectives The first objective was to investigate the effect of design parameters such as clearance size, material characteristic, friction in revolute clearance joints, driving speed, journal and bearing radius on the dynamic response of joints of rigid multibody mechanism The second objective was to design a new type flexure hinge joint to improve the drawbacks of these traditional joints First of all, a slider-crank mechanism (SCM) with two sliders and seven revolute clearance joints was designed The behavior dynamic of this mechanism was obtained by using finite element method in ANSYS Second, a bridge-type compliant mechanism and tensural displacement amplifier employing flexure hinge was designed And then output displacement and output stress were achieved by FEM in static structural of ANSYS The Taguchi method, Grey relational analysis, entropy measurement technique, regression equation and artificial neural network were applied to optimize three mechanisms and determine optimal combination parameters The simulation and optimization results demonstrated that these design parameters have significantly affected on dynamic response of a slider-crank mechanism The optimal results of acceleration and contact force are 186.45 (m/s2) and 106.854 (N) respectively, with a 3.92% error for acceleration and 9.99% for contact force The simulation, optimization and experiment results are good agreed with design parameters of a bridge-type compliant mechanism flexure hinge have significantly influenced on iii displacement and stress The optimal displacement amplification ratio obtained was 71.2, 71.05, and 79.21 by the Taguchi method, regression equation and artificial neural network, respectively The optimal stress results obtained were 73.44 MPa, 76.116 MPa and 73.362 MPa by the Taguchi method, regression equation and artificial neural network, respectively The deviation error between experiment and simulation, Taguchi method, regression equation, artificial neural network is 4.895%, 12.64%, 3.94%, 13.83%, respectively The FEM and optimization results are line with each other with design parameters have significantly influenced on displacement and stress of a tensural displacement amplifier employing flexure hinge The optimal displacement and stress results were obtained by Taguchi method, grey relational analysis are 0.6938 mm and 52.314 MPa, 0.6040 mm and 53.561 MPa, respectively The optimal displacement amplification ratio was obtained 69.38 for TM and 60.4 for GRA Keywords: Revolute clearance joint, Bridge-type compliant mechanism, Tensural displacement amplifier, Taguchi method, Regression equation, Grey relational analysis, Artificial neural network iv Acknowledgments During my studies and research at the National Kaohsiung University of Science and Technology, I received great support from my teachers, my family, my friends, and my coworkers Through this opportunity, I want to present my deep sincere thanks to them First, I would like to express honest thanks and respect from my heart to my academic supervisor, Professor Shyh-Chour Huang, who pointed me to the direction of research, gave me motivation and support me throughout this study work Without his dedicated help, my research will not be as successful today In addition, I would like to choose this opportunity to indicate my sincere thanks to the members of the Computer Aided Engineering Application and Design LAB has helped me very enthusiastic during my time at National Kaohsiung University of Science and Technology Last but not least, I would like to acknowledge my mother Thi Be Nguyen who helped, raised and inspired me through my graduate study I would like to thank my brothers, sisters for their love to my academic pursuit Ngoc-Thai Huynh Taiwan, June 2019 v Contents 摘 要 i Abstract iii Acknowledgments v Contents vi List of Tables x List of Figures xii Nomenclature xvii Latin symbols xvii Greek symbol xviii Abbreviations xviii Chapter Introduction 1.1 Overview 1.2 Advantages of rigid multibody and compliant mechanisms 1.2.1 Advantages and disadvantages of rigid multibody 1.2.2 Advantages of compliant mechanisms 1.3 Application of rigid multibody and compliant mechanisms 1.3.1 Application of rigid multibody mechanisms 1.3.2 Application of compliant mechanisms 1.4 Motivations, scope and objectives of the dissertation 1.4.1 Motivations 1.4.2 Scopes 1.5 Literature Reviews 10 1.5.1 Computational Methods for rigid and compliant Mechanisms 10 1.5.2 Optimization Methods for rigid and compliant Mechanisms 13 1.6 Organization of the dissertation 14 Chapter Introduction kinematic joints and flexure hinge 15 2.1 Kinematic joints 15 2.2 Revolute clearance joint model 17 2.3 Translation joint 18 vi 2.4 Flexure hinge 18 Chapter Dynamic and static analysis of rigid multibody and compliant mechanism by using finite element method 20 3.1 Dynamic analysis of a slider-crank mechanism with two sliders and revolute clearance joints by using finite element method 20 3.1.1 Introduction 20 3.1.2 Advantages and application of slider-crank mechanism with two sliders and revolute clearance joints 21 3.1.3 Finite element method 21 3.1.4 Effect analysis of clearance size 22 3.1.5 Effect analysis of bearing length 29 3.1.6 Effect analysis of radius of journal 31 3.1.7 Effect analysis of different of quantity of revolute clearance joints 32 3.1.8 Effect analysis of material 36 3.2 Static analysis for a bridge-type compliant mechanism flexure hinge using FEM in ANSYS 37 3.2.1 Introduction 37 3.2.2 Analysis finite element method 38 3.2.3 Advantages and applications of a bridge-type compliant mechanism flexure hinge 39 3.2.4 Effect analysis of input body length 39 3.2.5 Effect analysis of thickness of flexure hinge 40 3.2.6 Effect analysis of incline angle between of two flexure hinges 41 3.2.7 Effect analysis of width of flexure hinge 42 3.3 Effect analysis of design parameters to displacement and stress of a tensural displacement amplifier employing flexure hinges by using finite element method 42 3.3.1 Introduction 42 3.3.2 Finite element method 43 3.3.3 Advantages and applications of a tensural displacement amplifier employing flexure hinges 44 3.3.4 Influence analysis of thickness of the mechanism 44 3.3.5 Influence analysis of thickness of flexure hinge 45 3.3.6 Influence analysis of incline angle between two flexure hinges 45 3.3.7 Influence analysis of width of mechanism 46 vii Figure Compliant mechanisms: (a) Shampoo cap, (b) Bottle cap, (c) Hair pin Besides, compliant mechanism also was applied in biomechanical engineering and medicine such as S Kota et al [7] designed and applied compliant mechanism for Surgical tool as shown in Figure 1.7 Frecker [8] designed compliant scissors-forceps for minimally invasive surgery as depicted in Figure 1.8 Figure Prototype of the compliant gripper in its inactive mode (left) and gripping mode (right) [7] Figure Compliant scissors-forceps design [8] Yong-Mo Moon [9] designed finger mechanism with contacting aided compliant mechanism as shown in Figure 1.9 Amir Jafari et al [10] presented a design a new actuator capable of adjusting the stiffness using flexure structures, as pointed out in Figure 1.10 was applied in actuators Figure Design of finger mechanism with contacting aided compliant mechanism [9] Figure 10 Actuator principle with adjustable stiffness [10] Xing Chen [11] created a micro-cantilever for enhancing the deflection of micro actuator as presented in Figure 1.11 was applied in micro-electro mechanical system Figure 11 Schematics showing the structure of micro-cantilever system, the close-up of flexure hinge array, and actuation principle including states (a) before actuation and (b) after actuation [11] 1.4 Motivations, scope and objectives of the dissertation 1.4.1 Motivations In this study multi-objective optimization methods were applied to optimize design, analysis kinematic, dynamic and static for rigid and compliant mechanism such as SCM with two sliders and RCJ, bridge-type compliant mechanism flexure hinge, tensural displacement amplifier employing flexure hinge Up to date, many methods were proposed by many researchers, for example to analyze dynamic of multibody systems, contact force models were presented such as spring damper, Hertz, Hunt-Crossley, Lankarani-Nikravesh, Hybrid Newton-Euler equation and Lagrange equation were also applied to solve dynamic equation motion To compute and design compliant mechanism, many methods proposed such as the flexible matrix method, finite element method, lumped model Calculated methodologies for design and analysis compliant mechanism have challenges The methods have large deviation error or inadequate Hence, the dissertation would like to donate a basic tool to optimize design and analysis rigid and compliant mechanisms 1.4.2 Scopes The dissertation researches analysis and optimal design mechanical systems: - Analytical effects of design parameters on dynamic response of SCM with two sliders and RCJ by using FEM in ANSYS - Application multi-objective optimization methods optimize effects of design parameters on dynamic response of SCM with two sliders and RCJ - Analytical effects of design parameters on DI and ST of a BTCMFH by using FEM in ANSYS - Analytical effects of design parameters on DI and ST of a tensural displacement amplifier compliant mechanism employing FH by using FEM in ANSYS - Application multi-objective optimization methods optimize effects of design parameters on displacement and stress of a BTCMFH - Application multi-objective optimization methods optimize effects of design parameters on displacement and stress of a tensural displacement amplifier compliant mechanism employing flexure hinge 1.4.3 Objectives The purposes of this dissertation include three major objectives The first objective analyzes and optimizes the acceleration of the 1st slider and the contact force in the first RCJ using the TM with GRA The second objective presents a design and optimizes the effects of design dimensions on the DAR of a BTCMFH by using the FEM in ANSYS, the TM and ANN and is confirmed by an experiment The final objective analyzes and optimizes effects of the design parameters on the displacement amplification of a tensural displacement amplifier employing flexure hinge by using TM and GRA 1.5 Literature Reviews 1.5.1 Computational Methods for rigid and compliant Mechanisms In recent years, some researchers have focused on the slider-crank mechanism but only considered one slider Muvengei [12] investigated the effects of different driving speeds and clearance effects Yao [13] demonstrated the clearance influence on the dynamics of two coordinate systems Yu Chen et al [14] revealed the effects of different clearances and driving speeds on the dynamic behaviour of the mechanisms Influences of the clearance and friction in the clearance joint were shown by Bai and Zhao [15] To maximize the income and reduce the high cost for maintenance of the mechanical systems, the influence of a harmonic and flexible rod dynamic in revolute non-ideal joints was researched by Yuanyuan Li et al [16] Bai and Sun [17] used the Coulomb friction model and the Nonlinear equivalent spring-damp model to research the clearance radius and friction influences Reis [18] investigated influences of contact friction and lubrication in joints with clearance Most of the previous studies have considered only one slider and two or three revolute joints with clearance Filipe Marques et al [19] utilized several friction models to investigate the effect of friction in RCJ of multibody mechanical systems The Newton Euler method was used to analyze the effect of spatial RCJ on the dynamics of mechanical systems with two spatial real joints [20] Tan et al [21] employed Newton Euler combined with several CF models to estimate the influences of the RCJ on the dynamics of planar rigid body mechanisms The Revised Coulomb’s friction model was employed by Rooney [22] was used to estimate the friction force in RCJ of multibody dynamic mechanisms A unified mesh of absolute nodal coordinate formulation was utilized for a flexible multibody system with uncertain joint clearance [23]; the absolute nodal coordinate formulation reference nodes were used to describe how a rigid body and a modified extended delayed feedback control could reduce the chaotic vibration of mechanical systems The dynamic characteristic of a space robot manipulator with 10 revolute imperfect joints [24] was presented and analysed by Zhao and Bai A formulation for both perfect and clearance/bushing joints were stated in [25] Comparisons were made between the contact force models to estimate a suitability model [26] A new nonlinear contact force model was utilized to investigate and verify the clearance size, material characteristics and restitution coefficient that have important effects on the clearance joints [27] The dynamic equations of a 3-RRR parallel mechanism were established in ref [28] However, in any actual mechanical system, there are more than three revolute clearance joints Unlike previous studies, this study proposes a mechanism with two sliders to increase the productivity for a planning machine In addition, it considers the influences of clearance, the different clearance radii and the number of joints with clearance Furthermore, friction effects are considered simultaneously To decrease the undesired vibration from outside or inside the proposed mechanism, an optimization design is prepared to reduce the influences of the clearance radius, driving speed, length of the crank and the friction If the velocity of a slider is as high as possible, the productivity will be high However, if the acceleration of the 1st slider is high, undesirable vibrations appear Obviously, these objectives are conflicting In recent years, many researchers have designed many types of flexure hinge to replace traditional joints For example, Yong and Lu proposed the kinetostatic modeling for 3-RRR compliant mechanisms [29] These joints were used as the rotation joints for a 3-DOF parallel mechanism for smooth and high precision motion in micro/nano manipulation work, designed by Tian et al [30] Bhagat et al [31] proposed a new 3DOF compliant mechanism employing miniature flexure The closed form compliance equations for power function shaped FHs was established by Li et al [32] based the unit-load method Lobontiu and Cullin [33] compared a similar straight-axis flexure design with two-segment circular-axis symmetric notch flexure hinges Qi et al [34] applied the kinematics theories and elastic beam theory (EBT) to determine DAR for a BTCMFH The equivalent formula and FEM were applied to analyze failure for TripleLET and LET FH by Qiu, Yin and Xie [35] Tian et al [36] applied closed-form compliance equation to compute deformation of filleted V-shaped flexure hinges and 11 was verified by FEM Yang et al [37] applied superelastic materials for a FH and their numerical computations were able to accurately forecast the displacement and effectually decrease the computation cost compared with FEA and was confirmed by the experiments Ling et al [38] applied Lagrange’s equation to design semi-analytical FEM for a flexure hinge in complex compliant mechanisms Xu and Li [39] applied the Euler-Bernoulli beam theory to calculate the DAR o and was confirmed their results by FEA and experiment Liu and Yan [40] proposed a new analytical method employing EBT to determine influences of external force on the DAR, and was verified by FEM in ANSYS Ling et al [41] applied the energy conservation law and EBT to enhance a mathematic model for BTCMFH rhombus-type compliant mechanisms, and the achieved results was confirmed by the FEM in ANSYS and experiments Choi et al [42] proposed fully bridge-type compliant mechanism with input concentration and distribution force to calculated the DAR and was verified by experiment and previous research Ma et al [43] stated that the amplification ratio increased as the TOFH was reduced, and this problem was explored using the FEM and a mathematic model Ling et al [22] proposed a modular and assembled statics modeling tool for the analysis and design of a wide variety of FHs used in the precision positioning stage This method was verified by FEM and their previous investigation In 2018, Ling et al [44] established the semi-analytical finite element model of complex compliant mechanisms by employing Lagrange’s equation Mohd Faizul Mohd Sabri et al [45] performed an experiment to measure the displacement of silicon XY-microstages A new pseudorigid-body model of a flexure hinge was proposed by Šalinic et al [46] The principle of virtual work yielded a matrix relation which was applied to determine the quasi-static responses of a compliant mechanism due to external loads Lai et al [47] used two Lshape lever-type mechanisms and one BTCMFH to eliminate bending moment and lateral forces The stiffness matrix method was applied to calculate the DAR and was verified by FEM and experiment To ensure high rigidity, large magnification, high-precision tracking, and high-accuracy positioning, Wang and Zhang [48] proposed a compact planar three-degrees-of-freedom nano-positioning platform in which three two-level lever amplifiers were arranged symmetrically to obtain large magnification The 12 kinematic and dynamic modelling precision was enhanced by the compensation afforded by the three displacement loss model, and was verified by experiment Chen et al [49] stated tensural a tensural displacement amplifier mechanism using FH subject to loaded tension and bending rather loaded compression and bending when deflected The kinetostatic model was applied to determine DAR and amplification ratio value obtained 40 The results of this model also confirmed by FEM and experiment 1.5.2 Optimization Methods for rigid and compliant Mechanisms Yuanyuan Li et al [16] utilized response surface modeling to optimize dynamic response of a planar slider-crank mechanism with rigid and harmonic drive body Varedi et al [50] applied a Particle swarm optimization algorithm to optimize the dynamics of the mechanical systems with an imperfect joint Selỗuk Erkay [51] utilized neural network to forecast oscillation attribute of a planar mechanism with revolute clearance joints Selỗuk Erkaya and Ibrahim Uzmay [52] proposed a neural network and genetic algorithm to optimize design parameters was effected on dynamics of fourbar mechanism by non-ideal joints Zhao Hai-yang et al [3] used genetic algorithms method to minimize effects of design parameters and oversized joint clearance on dynamics response of reciprocating compressor Kailash Chaudhary et al [53] applied distributing the link masses and cubic B-spline curves to optimize design shape and balance dynamic of four-bar mechanism Transmission angle for slider-crank mechanism with clearance joint was optimize by Selỗuk Erkaya and IbrahimUzmay [54] by using Multi-Layered Neural Network (MLNN) structure and the design parameters also were optimize by using a genetic algorithm The equivalent static load was applied to optimize structural of flexible components in a flexible multibody mechanism via Absolute Nodal Coordinate Formulation (ANCF) by Jialiang Sun et al [1] The response surfaces method was used by Z Zhang et al [55] to optimize effects of revolute clearance joints of mechanisms Radial Basis Function Neural Network (RBFNN) technique were applied by Bo Zhao et al [56] to forecast wear at revolute imperfect joints in flexible mechanism Zheng Feng Bai et al [57] a generalized reduced gradient (GRC) algorithm was utilized to reduced vibration for dual-axis driving mechanism with clearance joints 13 Dao and Huang [58-63] designed and applied multi-objective optimization to optimize design parameters of compliant mechanisms Qingsong Xu and Yangmin Li [39] applied particle swarm optimization to optimize effects of design parameters on displacement amplification ratio of a compound bridge-type compliant displacement amplifier 1.6 Organization of the dissertation The remainders of this dissertation are organized in following order Chapter Analytical dynamic and static of rigid multibody and compliant mechanisms by using finite element method Chapter Application of optimization methods to optimize design parameters for rigid and compliant mechanisms Chapter Conclusions and Future Works 14 Chapter Introduction kinematic joints and flexure hinge 2.1 Kinematic joints There are many joints such as fixed, revolute (hinge), cylindrical, translational, slot, universal, spherical, planar, general - Fixed joints support all degrees of freedom - Revolute (hinge) joint constrained degree of freedom: Transform according to x, y, z axis, rotation according to x and y axis as depicted in Figure 2.1 Figure Revolute joint - Cylindrical joint constraint degree of Freedom: UX, UY, rotation according to x and y axis as depicted in Figure 2.2 Figure 2 Cylindrical joint - Translation joint constrained degrees of freedom: Transform according to y and z axis, rotation according to x, y, z axis as illustrated in Figure 2.3 15 Figure Translation joint - Slot joint constrained degrees of freedom: Transform according to x and y axis as depicted in Figure 2.4 Figure Slot joint - Universal joint constrained degrees of freedom: Transform according to x, y, z axis, rotation according to y as illustrated in Figure 2.5 Figure Universal joint - Spherical joint constrained degrees of freedom: Transform according to x, y, z axis as shown in Figure 16 Figure Spherical joint - Planar joint constrained degrees of freedom: Transform according to z, rotation according to x and y axis as presented in Figure 2.7 Figure Planar joint - General joint can set the constrained degrees of freedom and the rotation All the degrees of freedom are fixed default It can set the translation options to fixed or free, and the rotation option to fixed, all free, or free about the x, y, or z axis In this study investigated effects of revolute clearance joint (RCJ) and translation joint in contact condition dry with friction 2.2 Revolute clearance joint model In general, a joint includes two bodies which are journal-bearing In actuality, the gap cannot be avoided due to the manufacturing and assembly The gap or clearance also is the clearance radius in a revolute imperfect joint, as shown in Figure 2.8 It is the difference between the radius of the journal and the bearing and is determined as follows: c  rB  rj (2.1) 17 where rB , rj are the radii of the bearing and the journal, and lB (L) and dB, are the bearing length and bearing diameter, respectively Figure Revolute imperfect joint 2.3 Translation joint In this study translation joint is an ideal joint not to have clearance as illustrated in Figure 2.3 2.4 Flexure hinge Some shapes of flexure hinge were designed and proposed by Y Tian et al [36] as presented in Figure 2.9 and Figure 2.10 [64] The T-shape flexure hinge was designed by Kunhai Cai et al [65] (a) Cicular hinge (b) Flexure hinge (c) Eliptical hinge Figure Three shape flexure hinge [36, 64] 18 Figure 10 Geometric parameters and loads of the FHs [36, 64] Figure 11 T-shape flexure hinge mechanism [65] In this investigation utilized leaf flexure hinge for bridge-type and tensural displacement amplifier compliant mechanism Because of advantage of the flexure hinge is high amplification ratio 19 Chapter Dynamic and static analysis of rigid multibody and compliant mechanism by using finite element method 3.1 Dynamic analysis of a slider-crank mechanism with two sliders and revolute clearance joints by using finite element method 3.1.1 Introduction The slider-crank mechanism (SCM) was used for analysis as presented in Figure 3.1 The rigid mechanism includes the 1st ray; 1st connecting rod; 2nd connecting rod; 2nd ray; 1st slider; crank; motor and 2nd slider In a model with ideal joints, none of the revolute joints have clearance or friction On the other hand, in a model with imperfect joints all revolute joints have clearance and friction A projection of the mechanical system with two sliders is depicted in Figure 3.2 It includes seven imperfect revolute joints as presented in [66] Figure Slider-crank mechanism, 1st connecting rod, 2nd connecting rod, 1st ray, 1st slider, 2nd ray, Crank, Motor, Base, 2nd slider, 10 Rotation of motor control and 11 DC Figure Projection of a mechanism on the oxy planar 20 ... 灰色關聯分析，人工神經網絡 ii Design and Analysis of Rigid and Compliant Mechanisms Student: Ngoc-Thai Huynh Advisor: Shyh-Chour Huang Department of Mechanical Engineering National Kaohsiung University of Science and. .. Advantages of rigid multibody and compliant mechanisms 1.2.1 Advantages and disadvantages of rigid multibody 1.2.2 Advantages of compliant mechanisms 1.3 Application of rigid multibody... tool to optimize design and analysis rigid and compliant mechanisms 1.4.2 Scopes The dissertation researches analysis and optimal design mechanical systems: - Analytical effects of design parameters