ADVANCES IN ROBOT KINEMATICS pdf

ADVANCES IN ROBOT KINEMATICS Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com Advances in Robot Kinematics Edited by I Jo ef Stefan Institute Ljubljana, Slovenia and B. ROTH Stanford University California, U.S.A. Mechanisms and Motion ý ý ž JADRAN LENAR Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-10 1-4020-4940-4 (HB) ISBN-13 978-1-4020-4940-8 (HB) ISBN-10 1-4020-4941-2 (e-book) ISBN-13 978-1-4020-4941-5 (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com Printed on acid-free paper All Rights Reserved © 2006 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands. Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com Preface This is the tenth book in the series of Advances in Robot Kinematics. Two were produced as workshop proceedings, Springer published one book in 1991 and since 1994 Kluwer published a book every two years without interruptions. These books deal with the theory and practice of robot kinematics and treat the motion of robots, in particular robot manipulators, without regard to how this motion is produced or con- trolled. Each book of Advances in Robot Kinematics reports the most recent research projects and presents many new discoveries. The issues addressed in this book are fundamentally kinematic in nature, including synthesis, calibration, redundancy, force control, dex- terity, inverse and forward kinematics, kinematic singularities, as well as over-constrained systems. Methods used include line geometry, quater- nion algebra, screw algebra, and linear algebra. These methods are ap- plied to both parallel and serial multi-degree-of-freedom systems. The en application. All the contributions had been rigorously reviewed by independent reviewers and fifty three articles had been recommended for publica- tion. They were introduced in seven chapters. The authors discussed their results at the tenth international symposium on Advances in Robot Kinematics which was held in June 2006 in Ljubljana, Slovenia. The symposium was organized by Jozef Stefan Institute, Ljubljana, under the patronage of IFToMM - International Federation for the Promotion of Mechanism and Machine Science. We are grateful to the authors for their contributions and for their efficiency in preparing the manuscripts, and to the reviewers for their timely reviews and recommendations. We are also indebted to the per- sonnel at Springer for their excellent technical and editorial support. Jadran Lenarˇciˇc and Bernard Roth, editors results should interest researchers, teachers and students, in fields of gineering and mathematics related to robot theory, design, control and Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com Contents Methods in Kinematics J. Andrade-Cetto, F. Thomas Wire-based tracking using mutual information 3 G. Nawratil The control number as index for Stewart Gough platforms 15 C. Innocenti, D. Paganelli Determining the 3×3 rotation matrices that satisfy three linear equations in the direction cosines 23 P.M. Larochelle A polar decomposition based displacement metric for a finite region of SE(n)33 J P. Merlet, P. Donelan On the regularity of the inverse Jacobian of parallel robots 41 P. Fanghella, C. Galletti, E. Giannotti Parallel robots that change their group of motion 49 A.P. Murray, B.M. Korte, J.P. Schmiedeler Approximating planar, morphing curves with rigid-body linkages 57 M. Zoppi, D. Zlatanov, R. Molfino On the velocity analysis of non-parallel closed chain mechanisms 65 Properties of Mechanisms H. Bamberger, M. Shoham, A. Wolf Kinematics of micro planar parallel robot comprising large joint clearances 75 H.K. Jung, C.D. Crane III, R.G. Roberts Stiffness mapping of planar compliant parallel mechanisms in a serial arrangement 85 Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com Y. Wang, G.S. Chirikjian Large kinematic error propagation in revolute manipulators 95 A. Pott, M. Hiller A framework for the analysis, synthesis and optimization of par allel kinematic machines 103 Z. Luo, J.S. Dai Searching for undiscovered planar straight-line linkages 113 X. Kong, C.M. Gosselin Type synthesis of three-DOF up-equivalent parallel manipula tors using a virtual-chain approach 123 A. De Santis, P. Pierro, B. Siciliano The multiple virtual end-effectors approach for human-robot in teraction 133 Humanoids and Biomedicine J. Babiˇc, D. Omrˇcen, J. Lenarˇciˇc Balance and control of human inspired jumping robot 147 J. Park, F.C. Park A convex optimization algorithm for stabilizing whole-body mo tions of humanoid robots 157 R. Di Gregorio, V. Parenti-Castelli Parallel mechanisms for knee orthoses with selective recovery action 167 S. Ambike, J.P. Schmiedeler Modeling time invariance in human arm motion coordination 177 M. Veber, T. Bajd, M. Munih Assessment of finger joint angles and calibration of instrumental glove 185 R. Konietschke, G. Hirzinger, Y. Yan All singularities of the 9-DOF DLR medical robot setup for min imally invasive applications 193 G. Liu, R.J. Milgram, A. Dhanik, J.C. Latombe On the inverse kinematics of a fragment of protein backbone 201 V. De Sapio, J. Warren, O. Khatib Predicting reaching postures using a kinematically constrained shoulder model 209 viii Contents Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com Analysis of Mechanisms D. Chablat, P. Wenger, I.A. Bonev Self motions of special 3-RPR planar parallel robot 221 A. Degani, A. Wolf Graphical singularity analysis of 3-DOF planar parallel manip ulators 229 C. Bier, A. Campos, J. Hesselbach Direct singularity closeness indexes for the hexa parallel robot 239 A. Karger Stewart-Gough platforms with simple singularity surface 247 A. Kecskem´ethy, M. T¨andl A robust model for 3D tracking in object-oriented multibody systems based on singularity-free Frenet framing 255 P. Ben-Horin, M. Shoham Singularity of a class of Gough-Stewart platforms with three con current joints 265 T.K. Tanev Singularity analysis of a 4-DOF parallel manipulator using geo metric algebra 275 R. Daniel, R. Dunlop A geometrical interpretation of 3-3 mechanism singularities 285 Workspace and Performance J.A. Carretero, G.T. Pond Quantitative dexterous workspace comparisons 297 E. Ottaviano, M. Husty, M. Ceccarelli Level-set method for workspace analysis of serial manipulators 307 M. Gouttefarde, J P. Merlet, D. Daney Determination of the wrench-closure workspace of 6-DOF paral lel cable-driven mechanisms 315 G. Gogu Fully-isotropic hexapods 323 P. Last, J. Hesselbach A new calibration stategy for a class of parallel mechanisms 331 M. Krefft, J. Hesselbach The dynamic optimization of PKM 339 . Contents ix - Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com J.A. Snyman On non-assembly in the optimal synthesis of serial manipulators performing prescribed tasks 349 Design of Mechanisms W.A. Khan, S. Caro, D. Pasini, J. Angeles Complexity analysis for the conceptual design of robotic archi tecture 359 D.V. Lee, S.A. Velinsky Robust three-dimensional non-contacting angular motion sensor 369 K. Brunnthaler, H P. Schr¨ocker, M. Husty Synthesis of spherical four-bar mechanisms using spherical kine matic mapping 377 R. Vertechy, V. Parenti-Castelli Synthesis of 2-DOF spherical fully parallel mechanisms 385 G.S. Soh, J.M. McCarthy Constraint synthesis for planar n-R robots 395 T. Bruckmann, A. Pott, M. Hiller Calculating force distributions for redundantly actuated tendon 403 P. Boning, S. Dubowsky A study of minimal sensor topologies for space robots 413 M. Callegari, M C. Palpacelli Kinematics and optimization of the translating 3-CCR/3-RCC parallel mechanisms 423 Motion Synthesis and Mobility C C. Lee, J.M. Herv´e Pseudo-planar motion generators 435 S. Krut, F. Pierrot, O. Company On PKM with articulated travelling-plate and large tilting angles 445 C.R. Diez-Mart´ınez, J.M. Rico, J.J. Cervantes-S´anchez, J. Gallardo Mobility and connectivity in multiloop linkages 455 K. Tcho´n, J. Jakubiak Jacobian inverse kinematics algorithms with variable steplength for mobile manipulators 465 x -based Stewart platforms Contents Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com J. Zamora-Esquivel, E. Bayro-Corrochano Kinematics and grasping using conformal geometric algebra 473 R. Subramanian, K. Kazerounian Application of kinematics tools in the study of internal mobility of protein molecules 481 O. Altuzarra, C. Pinto, V. Petuya, A. Hernandez Motion pattern singularity in lower mobility parallel manipula tors 489 Author Index 497 Contents xi Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com Methods in Kinematics J. Andrade-Cetto, F. Thomas Wire-based tracking using mutual information G. Nawratil C. Innocenti, D. Paganelli Determining the 3×3 rotation matrices that satisfy three linear equations in the direction cosines P.M. Larochelle A polar decomposition based displacement metric for a finite region of SE(n) J P. Merlet, P. Donelan On the regularity of the inverse Jacobian of parallel robots P. Fanghella, C. Galletti, E. Giannotti Parallel robots that change their group of motion A.P. Murray, B.M. Korte, J.P. Schmiedeler Approximating planar, morphing curves with rigid-body linkages M. Zoppi, D. Zlatanov, R. Molfino On the velocity analysis of non-parallel closed chain mechanisms 3 15 23 33 41 49 57 65 The control number as index for Stewart Gough platforms Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com [...]... Approximation in line space: applications in robot kinematics and surface reconstruction, Advances in Robot Kinematics: Analysis & Control (J Lenarcic, M Husty, eds.), pp 403–412, Kluwer Salisbury, J.K and Craig, J.J (1982), Articulated Hands: Force Control and Kinematic Issues, Int J of Robotics Research, vol 1, no 1, pp 4–17 Wolf, A., and Shoham, M (2003), Investigations of Parallel Manipulators Using Linear... here of interest too because infinite real Rodrigues parameters are associated to finite real 3 × 3 rotation matrices, and ii) in case one or more solutions at infinity exist, these algorithms might fail to determine even the finite solutions After exemplifying the recurrence in kinematics of the addressed three-equation set in the direction cosines, this paper presents an original procedure to find all... three-equation set in nine direction cosines is the unifying factor behind a number of seemingly different kinematics problems, such as those epitomized in Fig 1 Although these problems have already been solved in the literature by ad-hoc algorithms, they could be also worked out by determining all 3 × 3 rotation matrices satisfying three linear conditions in the direction cosines In this respect, the... direction cosines, Rodrigues parameters 1 Introduction A whole class of problems of spatial kinematics can be solved by determining all 3 × 3 rotation matrices whose nine direction cosines obey three given linear equations Owing to the orthogonality constraints among the direction cosines, these problems are equivalent to solving a set of nine equations: three linear and six quadratic Rather than tackling right... exerted on the moving object by the measuring device itself This paper shows how, by introducing a rotating base, the number of wires can be reduced to three, and singularities can be avoided by using an active sensing strategy This also permits reducing wire interference problems and the pulling force exerted by the device The proposed sensing strategy minimizes the uncertainty in the location of... (eds.), Advances in Robot Kinematics, 23 – 32 © 2006 Springer Printed in the Netherlands Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com 24 C Innocenti and D Paganelli Figure 1 a) Fully-parallel spherical wrist; b) rigid body supported at six points by six planes not always suitable to the case at hand The reason is twofold: i) they are unable to find real solutions at infinity,... three supporting planes not parallel to the same line, three of these equations can be linearly solved for the components of vector s, and their expressions inserted into the remaining three equations Therefore a linear three-equation set that has the nine direction cosines of matrix R as only unknowns is obtained once more Other kinematics problems susceptible of being reduced to the same linear formulation... the outline of the procedure that has been presented – without investigating its singularities – in Roth, 1993 It is worth noting that Eq (11) is unable to yield solutions at infinity Things keep manageable if an infinite pγ satisfies Eq (5) for some values of pα and pβ, as Eq (11) has a degree lower than eight and its roots convey information on finite solutions only Regrettably, should an infinite... usual Kalman gain 4 Information Gain This section builds from basic principles a metric for the expected information gain as a result of performing a given action, and develops from it, a strategy for controlling the base orientation The aim is to rotate the base in the direction that most reduces the uncertainty in the entire pose state estimate, by using the information that should be gained from future... another kinematics problem, which consists in finding any possible positions of a rigid body C supported at six given points Pi ( i =1, ,6) by six fixed planes (Innocenti, 1994; Wampler, 2006) The coordinate vector wi of each point Pi is known with respect to a reference frame S’ attached to C Each supporting plane is defined with respect to the fixed frame S by the coordinate vector vi of a point Qi lying . ADVANCES IN ROBOT KINEMATICS Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com Advances in Robot Kinematics Edited by I Jo ef Stefan Institute Ljubljana,. book in the series of Advances in Robot Kinematics. Two were produced as workshop proceedings, Springer published one book in 1991 and since 1994 Kluwer published a book every two years without interruptions practice of robot kinematics and treat the motion of robots, in particular robot manipulators, without regard to how this motion is produced or con- trolled. Each book of Advances in Robot Kinematics