Parallel Manipulators New Developments Part 1 docx

Parallel Manipulators New Developments Parallel Manipulators New Developments Edited by Jee-Hwan Ryu I-Tech Published by I-Tec h Education and Publishing I-Tech Education and Publishing Vienna Austria Abstracting and non-profit use of the material is permitted with credit to the source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside. After this work has been published by the I-Tech Education and Publishing, authors have the right to repub- lish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work. © 2008 I-Tech Education and Publishing www.i-techonline.com Additional copies can be obtained from: publication@ars-journal.com First published April 2008 Printed in Croatia A catalogue record for this book is available from the Austrian Library. Parallel Manipulators, Edited by Jee-Hwan Ryu p. cm. ISBN 978-3-902613-20-2 1. Parallel Manipulators. 2. New Developments. I. Jee-Hwan Ryu V Preface Parallel manipulators are characterized as having closed-loop kinematic chains. Compared to serial manipulators, which have open-ended structure, parallel ma- nipulators have many advantages in terms of accuracy, rigidity and ability to ma- nipulate heavy loads. Therefore, they have been getting many attentions in astron- omy to flight simulators and especially in machine-tool industries. The aim of this book is to provide an overview of the state-of-art, to present new ideas, original results and practical experiences in parallel manipulators. This book mainly introduces advanced kinematic and dynamic analysis methods and cutting edge control technologies for parallel manipulators. Even though this book only contains several samples of research activities on parallel manipulators, I believe this book can give an idea to the reader about what has been done in the field re- cently, and what kind of open problems are in this area. Finally, I would like to thanks all the authors of each chapter for their contribution to make this book possible. Jee-Hwan Ryu Korea University of Technology and Education Republic of Korea jhryu@kut.ac.kr VII Contents Preface V 1. On the Robust Dynamics Identification of Parallel Manipulators: Methodo- logy and Experiments 001 Houssem Abdellatif, Bodo Heimann and Jens Kotlarski 2. Application of Neural Networks to Modeling andControl of Parallel Manipu- lators 021 Ahmet Akbas 3. Asymptotic Motions of Three-Parametric Robot Manipulators with Parallel Rotational Axes 041 Ján Baksa 4. Topology and Geometry of Serial and Parallel Manipulators 057 Xiaoyu Wang and Luc Baron 5. Conserving Integrators for Parallel Manipulators 075 Stefan Uhlar and Peter Betsch 6. Wire Robots Part I Kinematics, Analysis & Design 109 Tobias Bruckmann, Lars Mikelsons, Thorsten Brandt, Manfred Hiller and Dieter Schramm 7. Wire Robots Part II Dynamics, Control & Application 133 Tobias Bruckmann, Lars Mikelsons, Thorsten Brandt, Manfred Hiller and Dieter Schramm 8. Parallel Robot Scheduling with Genetic Algorithms 153 Tarık Cakar, Harun Resit Yazgan and Rasit Koker 9. Design and Prototyping of a Spherical Parallel Machine Based on 3-CPU Kinematics 171 Massimo Callegari 10. Quantitative Dexterous Workspace Comparison of Serial and Parallel Pla- nar Mechanisms 199 Geoff T. Pond and Juan A. Carretero VIII 11. Calibration of 3-d.o.f. Translational Parallel Manipulators Using Leg Observations 225 Anatol Pashkevich, Damien Chablat, Philippe Wenger and Roman Gomolitsky 12. Kinematic Parameters Auto-Calibration of Redundant Planar 2-Dof Parallel Manipulator 241 Shuang Cong, Chunshi Feng, Yaoxin Zhang, Zexiang Li and Shilon Jiang 13. Error Modeling and Accuracy of TAU Robot 269 Hongliang Cui, Zhenqi Zhu, Zhongxue Gan and Torgny Brogardh 14. Specific Parameters of the Perturbation Profile Differentially Influence the Vertical and Horizontal Head Accelerations During Human Whiplash Tes- ting 287 Loriann M. Hynes, Natalie S. Sacher and James P. Dickey 15. Neural Network Solutions for Forward Kinematics Problem of HEXA Paral- lel Robot 295 M. Dehghani, M. Eghtesad, A. A. Safavi, A. Khayatian, and M. Ahmadi 16. Acceleration Analysis of 3-RPS Parallel Manipulators by Means of Screw Theory 315 J. Gallardo, H. Orozco, J.M. Rico, C.R. Aguilar and L. Pérez 17. Multiscale Manipulations with Multiple Parallel Mechanism Manipulators 331 Gilgueng Hwang and Hideki Hashimoto 18. Principal Screws and Full-Scale Feasible Instantaneous Motions of Some 3-DOF Parallel Manipulators 349 Z. Huang, J. Wang and S. H. Li 19. Singularity Robust Inverse Dynamics of Parallel Manipulators 373 S. Kemal Ider 20. Control of a Flexible Manipulator with Noncollocated Feedback: Time Domain Passivity Approach 393 Jee-Hwan Ryu, Dong-Soo Kwon and Blake Hannaford 21. Dynamic Modelling and Vibration Control of a Planar Parallel Manipulator with Structurally Flexible Linkages 405 Bongsoo Kang1 and James K. Mills 22. Task Space Approach of Robust Nonlinear Control for a 6 DOF Parallel Manipulator 427 Hag Seong Kim 23. Tactile Displays with Parallel Mechanism 445 Ki-Uk Kyung and Dong-Soo Kwon IX 24. Design, Analysis and Applications of a Class of New 3-DOF Translational Parallel Manipulators 457 Yangmin Li and Qingsong Xu 25. Type Design of Decoupled Parallel Manipulators with Lower Mobility 483 Weimin Li [...]... r2 6 -1 -1 -1 -1 ] ] ] ] ] ] 0. 017 9 [0.8837 0.9552] - 0.2485 [11 .4803 12 .4742] - 0 .18 61 [4.4350 5 .17 93] - 0.3226 [19 .5075 20.7980] - 0 .18 17 [4.7884 5. 515 1] - 1. 5857 r15 [N ] - 5 .15 18 r1 4 [N ] [0.5440 0.6072] 20 .15 28 r13 [N ] 0. 015 8 4.80 71 r1 2 [N ] 16 .19 20 11 .9772 r 11 [N ] 1. 9 012 [16 . 216 1 16 .4002] 0. 919 5 rβ [Nm] [1. 8774 1. 9 017 ] 0.0460 0.5756 rα [Nm ] 0.0 012 16 .30 81 p10 [kg ] 0.2 618 [1. 0620 2 .10 94] -... 1. 0077 0.0045 [0.9988 1. 016 6] 0.9458 pk p3 [ ] [kgm ] [kgm ] p4 [kgm ] p5 [kgm ] 0.5995 0.0036 [0.5922 0.6068] 0.62 01 -1. 2885 0.0056 [ -1. 2998 -1. 2772] 1. 2295 p6 kgm 2 0.3078 0.00 61 [0.3049 0. 310 6] 0.2878 2 0.30 21 0.0 014 [0.2996 0.3045] 0.2878 2 0 .11 76 0.0 012 [0 .11 52 0 .12 01] 0 .12 17 p7 p8 [ ] [kgm ] [kgm ] p9 [kgm ] 1. 8896 r16 [N ] [ [Nsm [Nsm [Nsm [Nsm [Nsm r2 1 Nsm -1 r2 2 -1 r2 3 r2 4 r2 5 r2 6 -1. .. 1 = I zz1 + I yy 2 p 2 = I xx 2 + I xx 3 p 3 = I zz2 + I yy 3 friction [kgm ] +I [kgm ] −I −I [kgm ] p 11 = rα [N ] 2 zz 3 yy 2 zz 3 p12 = rβ [N ] 2 p13 = r 11 [N ] 2 p 4 = s y2 [kgm ] p5 = sy 3 p14 = r12 [N ] [kgm ] [ ] ⎞ [kgm ] ⎟ ⎠ ⎞ [kgm ] ⎟ ⎠ p15 = r13 [N ] 6 2 p6 = I xxE + m3 ∑ j =1 ⎛ rBy + rBz ⎞ kgm 2 ⎜ 2j ⎟ j ⎠ ⎝ p16 = r14 [N ] 2 p7 = I yyE + m3 ∑ j =1 ⎛ rBx + rBz ⎜ 2j j ⎝ 2 p17 = r15 [N ] 2 p18... 1. 9 017 ] 0.0460 0.5756 rα [Nm ] 0.0 012 16 .30 81 p10 [kg ] 0.2 618 [1. 0620 2 .10 94] - 5.0057 0.3 519 [4.3 018 5.7096] - 16 .87 71 0.5268 [15 .8235 17 .9307] - 16 .7406 0.3 712 [15 .99 81 17.4830] - 6.3408 0.5720 [5 .19 68 7.4848] - 23 .16 62 0.3799 [22.4065 23.9259] - 26.4675 0.44 61 [25.5754 27.3596] - 22.8053 0.5539 [ 21. 6974 23. 913 1] - ˆ Table 2 Estimated dynamics parameters of the hexapod parameters p with corresponding... ⎛ rBx + rBz ⎜ 2j j ⎝ 2 p17 = r15 [N ] 2 p18 = r16 [N ] 6 2 p8 = I zz E + m3 ∑ j = 1 ⎛ rB x + rB y ⎜ 2j j ⎝ 6 p9 = szE + m3 ∑ j =1 rBz 6 p10 = mE + 6m3 [kg ] j [kgm ] [ [Nsm [Nsm [Nsm [Nsm [Nsm p19 = r 21 Nsm -1 p 20 = r2 2 p 21 = r2 3 p 22 = r2 4 p 23 = r2 5 p 24 = r26 -1 -1 -1 -1 -1 ] ] ] ] ] ] Table 1 Rigid-body and friction model parameters for the parallel robot PaLiDA 5.2 Experiment design and... al., 2007; Swevers et al., 19 97): [ r2 i Qfi = f r (q i ) = [sign(q i ) q i ] r1 i ] ] , T (14 ) Regrouping friction forces in all n joints yields to [ T Q f = [D 1 (q ) D 2 (q )] r1 Df T r2 T (15 ) pf with [ ] rkT = rk1 , … , rkn , (16 ) D 1 (q ) = diag{sign(q 1 ), … , sign(q n )} , (17 ) D 2 (q ) = diag {q 1 , … , q n } (18 ) On the Robust Dynamics Identification of Parallel Manipulators: Methodology... resulting from ( 21) is ( 1 P = Ψ T Σ ηη Ψ ) 1 (28) ˆ The confidence area of the estimated parameter set pGM with respect to the unknown true parameter vector p can be calculated for a given quantile α ∈ [0 … 1] as a 10 0( 1 − α )% confidence ellipsoid: 11 On the Robust Dynamics Identification of Parallel Manipulators: Methodology and Experiments ˆ ˆ ε α = {p ∈ ℜn , (p - pGM )T P − 1 (p - pGM ) ≤ χα2... rings (index 1) , 6 identical stators (index 2) and 6 identical sliders (index 3) i di ai αi 1 αi − π 2 0 0 π 2 2 βi − π 2 0 0 − π 2 3 Fig 4 MDH-frames and parameters of the struts ϑi 0 li 0 − π 2 12 Parallel Manipulators New Developments The dynamics model in parameterlinear form results by applying the rules discussed in section 2 The rigid-body part contains 10 base parameters (see Table 1) According... for parallel manipulators Almost all identification methods in robotics are based on the parameterlinear form that is given by (1) in combination with (12 ) and (19 ) (Swevers et al., 19 97; Khalil & Dombre, 2002; Abdellatif & Heimann, 2007) Given experimentally collected and noise corrupted N measurement sets, the estimation problem can be formulated according to (1) as ⎡ Q a ⎤ ⎡ A (x 1 , v 1 , a 1 )... all actuator deviations is depicted in Fig 10 with respect to vE Fig 11 Tracking accuracy of actuator 5 for the two studied trajectories at maximal velocity; comparison between the compensation of nominal model (thin line) and identified model (thick line) 18 Parallel Manipulators New Developments As expected, the use of standard linear control (variation 1) exhibits a significant decreasing accuracy . Parallel Manipulators, Edited by Jee-Hwan Ryu p. cm. ISBN 978-3-902 613 -20-2 1. Parallel Manipulators. 2. New Developments. I. Jee-Hwan Ryu V Preface Parallel manipulators. [ ] n1 ,, T kkk rr …=r , (16 ) { } )(sign,),(signdiag)( 11 n qq  …   = qD , (17 ) {} n qq  …   ,,diag)( 12 =qD . (18 ) On the Robust Dynamics Identification of Parallel Manipulators: . Parallel Manipulators New Developments Parallel Manipulators New Developments Edited