Advances in Robot Kinematics: Mechanisms and Motion

500 Pages·2006·25.217 MB·English

by  J. Andrade-Cetto, F. Thomas (auth.), Jadran Lennarčič, B. Roth (eds.)

ADVANCES IN ROBOTKINEMATICS
Advances in Robot Kinematics
Mechanisms and Motion
Edited by
JADRANLENAR (cid:253)I(cid:253)
Jožef Stefan Institute
Ljubljana, Slovenia
and
B. ROTH
Stanford University
California, U.S.A.
AC.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 AADordrecht, 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
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and executed on a computer system, for exclusive use by the purchaser of the work.
Printed in the Netherlands.
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
results should interest researchers, teachers and students, in fields of
engineering and mathematics related to robot theory, design, control and
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
theirresultsatthetenthinternationalsymposiumonAdvancesinRobot
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
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
Approximatingplanar,morphingcurveswithrigid-bodylinkages 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
viii Contents
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 parallel 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
manipulators using a virtual-chain approach 123
A. De Santis, P. Pierro, B. Siciliano
The multiple virtual end-effectors approach for human-robot
interaction 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
motions 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
Allsingularitiesofthe9-DOFDLRmedicalrobotsetupfor
minimally 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
Contents ix
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
manipulators 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
SingularityofaclassofGough-Stewartplatformswiththree
concurrent joints 265
T.K. Tanev
Singularity analysis of a 4-DOF parallel manipulator using
geometric 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
parallel 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
x Contents
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
architecture 359
D.V. Lee, S.A. Velinsky
Robust three-dimensional non-contacting angular motion sensor 369
K. Brunnthaler, H.-P. Schro¨cker, M. Husty
Synthesis of spherical four-bar mechanisms using spherical
kinematic 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-based Stewart platforms 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
OnPKMwitharticulatedtravelling-plateandlargetiltingangles 445
C.R. Diez-Mart´ınez, J.M. Rico, J.J. Cervantes-Sa´nchez,
J.Gallardo
Mobility and connectivity in multiloop linkages 455
K. Tchon´, J. Jakubiak
Jacobian inverse kinematics algorithms with variable steplength
for mobile manipulators 465
Contents xi
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
manipulators 489
Author Index 497
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
Determiningthe3×3rotationmatricesthatsatisfythree
linearequationsin 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