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Screw and Lie Group Theory in Multibody Dynamics Recursive Algorithms and Equations of Motion of Tree-Topology Systems
Multibody Syst Dyn DOI 10.1007/s11044-017-9583-6 Screw and Lie group theory in multibody dynamics Recursive algorithms and equations of motion of tree-topology systems Andreas Müller1 Received: 12 November 2016 / Accepted: 16 June 2017 © The Author(s) 2017. This article is published with open access at Springerlink.com Abstract Screw and Lie group theory allows for user-friendly modeling of multibody sys- tems (MBS), and at the same they give rise to computationally efficient recursive algo- rithms. The inherent frame invariance of such formulations allows to use arbitrary reference frames within the kinematics modeling (rather than obeying modeling conventions such as the Denavit–Hartenberg convention) and to avoid introduction of joint frames. The com- putational efficiency is owed to a representation of twists, accelerations, and wrenches that minimizes the computational effort. This can be directly carried over to dynamics formula- tions. In this paper, recursive O(n) Newton–Euler algorithms are derived for the four most frequently used representations of twists, and their specific features are discussed. These for- mulations are related to the corresponding algorithms that were presented in the literature. Two forms of MBS motion equations are derived in closed form using the Lie group formu- lation: the so-called Euler–Jourdain or “projection” equations, of which Kane’s equations are a special case, and the Lagrange equations. The recursive kinematics formulations are readily extended to higher orders in order to compute derivatives of the motions equations. To this end, recursive formulations for the acceleration and jerk are derived. It is briefly discussed how this can be employed for derivation of the linearized motion equations and their time derivatives. -
An Historical Review of the Theoretical Development of Rigid Body Displacements from Rodrigues Parameters to the finite Twist
Mechanism and Machine Theory Mechanism and Machine Theory 41 (2006) 41–52 www.elsevier.com/locate/mechmt An historical review of the theoretical development of rigid body displacements from Rodrigues parameters to the finite twist Jian S. Dai * Department of Mechanical Engineering, School of Physical Sciences and Engineering, King’s College London, University of London, Strand, London WC2R2LS, UK Received 5 November 2004; received in revised form 30 March 2005; accepted 28 April 2005 Available online 1 July 2005 Abstract The development of the finite twist or the finite screw displacement has attracted much attention in the field of theoretical kinematics and the proposed q-pitch with the tangent of half the rotation angle has dem- onstrated an elegant use in the study of rigid body displacements. This development can be dated back to RodriguesÕ formulae derived in 1840 with Rodrigues parameters resulting from the tangent of half the rota- tion angle being integrated with the components of the rotation axis. This paper traces the work back to the time when Rodrigues parameters were discovered and follows the theoretical development of rigid body displacements from the early 19th century to the late 20th century. The paper reviews the work from Chasles motion to CayleyÕs formula and then to HamiltonÕs quaternions and Rodrigues parameterization and relates the work to Clifford biquaternions and to StudyÕs dual angle proposed in the late 19th century. The review of the work from these mathematicians concentrates on the description and the representation of the displacement and transformation of a rigid body, and on the mathematical formulation and its progress. -
JAMES Maccullagh (1809-1847)
Hidden gems and Forgotten People ULSTER HISTORY CIRCLE JAMES MacCULLAGH (1809-1847) James MacCullagh, the eldest of twelve children, was born in the townland of Landahussy in the parish of Upper Badoney, Co. Tyrone in 1809. He was to become one of Ireland and Europe's most significant mathematicians and physicists. He entered Trinity College, Dublin aged just 15 years and became a fellow in 1832. He was accepted as a member of the Royal Irish Academy in 1833 before attaining the position of Professor of Mathematics in 1834. He was an inspiring teacher who influenced a generation of students, some of whom were to make their own contributions to the subjects. He held the position of Chair of Mathematics from 1835 to 1843 and later Professor of Natural and Experimental Philosophy from 1843 to 1847. In 1838 James MacCullagh was awarded the Royal Irish Academy's Cunningham Medal for his work 'On the laws of crystalline reflexion'. In 1842, a year prior to his becoming a fellow of the Royal Society, London, he was awarded their Copley Medal for his work 'On surfaces of the second order'. He devoted much of the remainder of his life to the work of the Royal Irish Academy. James MacCullagh's interests went beyond mathematical physics. He played a key role in building up the Academy's collection of Irish antiquities, now housed in the National Museum of Ireland. Although not a wealthy man, he purchased the early 12th century Cross of Cong, using what was at that time, his life savings. In August 1847 he stood unsuccessfully as a parliamentary candidate for one of the Dublin University seats. -
James Clerk Maxwell
James Clerk Maxwell JAMES CLERK MAXWELL Perspectives on his Life and Work Edited by raymond flood mark mccartney and andrew whitaker 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2013942195 ISBN 978–0–19–966437–5 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. -
The Cambridge Mathematical Journal and Its Descendants: the Linchpin of a Research Community in the Early and Mid-Victorian Age ✩
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 31 (2004) 455–497 www.elsevier.com/locate/hm The Cambridge Mathematical Journal and its descendants: the linchpin of a research community in the early and mid-Victorian Age ✩ Tony Crilly ∗ Middlesex University Business School, Hendon, London NW4 4BT, UK Received 29 October 2002; revised 12 November 2003; accepted 8 March 2004 Abstract The Cambridge Mathematical Journal and its successors, the Cambridge and Dublin Mathematical Journal,and the Quarterly Journal of Pure and Applied Mathematics, were a vital link in the establishment of a research ethos in British mathematics in the period 1837–1870. From the beginning, the tension between academic objectives and economic viability shaped the often precarious existence of this line of communication between practitioners. Utilizing archival material, this paper presents episodes in the setting up and maintenance of these journals during their formative years. 2004 Elsevier Inc. All rights reserved. Résumé Dans la période 1837–1870, le Cambridge Mathematical Journal et les revues qui lui ont succédé, le Cambridge and Dublin Mathematical Journal et le Quarterly Journal of Pure and Applied Mathematics, ont joué un rôle essentiel pour promouvoir une culture de recherche dans les mathématiques britanniques. Dès le début, la tension entre les objectifs intellectuels et la rentabilité économique marqua l’existence, souvent précaire, de ce moyen de communication entre professionnels. Sur la base de documents d’archives, cet article présente les épisodes importants dans la création et l’existence de ces revues. 2004 Elsevier Inc. -
Alexander Dalgarno: from Atomic and Molecular Physics to Astronomy and Aeronomy Ewine F
RETROSPECTIVE Alexander Dalgarno: From atomic and molecular physics to astronomy and aeronomy Ewine F. van Dishoecka,1, Tom Hartquistb, and Amiel Sternbergc Massey, who offered Alex a fellowship toward aLeiden Observatory, Leiden University, 2300 RA Leiden, The Netherlands; bSchool of Physics a doctorate in atomic physics. Alex accepted and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom; and cSchool of Physics and made the switch to physics. This episode & Astronomy, Tel Aviv University, Ramat Aviv 69978, Israel highlights the importance of spotting talent at an early age. Alex himself excelled at nurturing early career researchers, and the AsSirDavidBateswrotein1988,“There is from the combination of his seminal insight “Dalgarno scientific family tree” contains no greater figure than Alex Dalgarno in the and unparalleled, boundless, and sustained 70 graduate students and 36 postdocs. Alex history of atomic-molecular-optical [AMO] productivity. His long career is described in guided and mentored all of them with the physics, and its applications” (1). Prof. Alex- his autobiographical article “A serendipitous utmost thoughtfulness and care. ander Dalgarno (Harvard) passed away peace- journey” (2) and in the books written in his After completing his doctorate in 1951, fully on April 9, 2015 at age 87 in the presence – honor (1, 3 5). Alex was offered a Lecturer position in Ap- of his long-term companion, Fern Creelan. Alex, a twin and the youngest of five plied Mathematics at the Queen’s University During a career spanning 60 years, Alex children, was born in London in 1928 and of Belfast. Together with David Bates, he built produced about 750 publications covering a grew up during the Second World War. -
STORM: Screw Theory Toolbox for Robot Manipulator and Mechanisms
2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) October 25-29, 2020, Las Vegas, NV, USA (Virtual) STORM: Screw Theory Toolbox For Robot Manipulator and Mechanisms Keerthi Sagar*, Vishal Ramadoss*, Dimiter Zlatanov and Matteo Zoppi Abstract— Screw theory is a powerful mathematical tool in Cartesian three-space. It is crucial for designers to under- for the kinematic analysis of mechanisms and has become stand the geometric pattern of the underlying screw system a cornerstone of modern kinematics. Although screw theory defined in the mechanism or a robot and to have a visual has rooted itself as a core concept, there is a lack of generic software tools for visualization of the geometric pattern of the reference of them. Existing frameworks [14], [15], [16] target screw elements. This paper presents STORM, an educational the design of kinematic mechanisms from computational and research oriented framework for analysis and visualization point of view with position, velocity kinematics and iden- of reciprocal screw systems for a class of robot manipulator tification of different assembly configurations. A practical and mechanisms. This platform has been developed as a way to bridge the gap between theory and practice of application of screw theory in the constraint and motion analysis for robot mechanisms. STORM utilizes an abstracted software architecture that enables the user to study different structures of robot manipulators. The example case studies demonstrate the potential to perform analysis on mechanisms, visualize the screw entities and conveniently add new models and analyses. I. INTRODUCTION Machine theory, design and kinematic analysis of robots, rigid body dynamics and geometric mechanics– all have a common denominator, namely screw theory which lays the mathematical foundation in a geometric perspective. -
Chapter 1 Introduction and Overview
Chapter 1 Introduction and Overview ‘ 1.1 Purpose of this book This book is devoted to the kinematic and mechanical issues that arise when robotic mecha- nisms make multiple contacts with physical objects. Such situations occur in robotic grasp- ing, workpiece fixturing, and the quasi-static locomotion of multilegged robots. Figures 1.1(a,b) show a many jointed multi-fingered robotic hand. Such a hand can both grasp and manipulate a wide variety of objects. A grasp is used to affix the object securely within the hand, which itself is typically attached to a robotic arm. Complex robotic hands can imple- ment a wide variety of grasps, from precision grasps, where only only the finger tips touch the grasped object (Figure 1.1(a)), to power grasps, where the finger mechanisms may make multiple contacts with the grasped object (Figure 1.1(b)) in order to provide a highly secure grasp. Once grasped, the object can then be securely transported by the robotic system as part of a more complex manipulation operation. In the context of grasping, the joints in the finger mechanisms serve two purposes. First, the torques generated at each actuated finger joint allow the contact forces between the finger surface and the grasped object to be actively varied in order to maintain a secure grasp. Second, they allow the fingertips to be repositioned so that the hand can grasp a very wide variety of objects with a range of grasping postures. Beyond grasping, these fingers’ degrees of freedom potentially allow the hand to manipulate, or reorient, the grasped object within the hand. -
Modern Library and Information Science
MCQs for LIS ABBREVIATIONS, ACRONYMS 1. What is the full form of IATLIS? (a) International Association of Trade Unions of Library & Information Science (b) Indian Association of Teachers in Library & Information Science (c) Indian Airlines Technical Lower Intelligence Services (d) Indian Air Traffic Light Information and Signal 2. IIA founded in USA in 1968 stands for (a) Integrated Industry Association (b) Information Industry Association (c) Integrated Illiteracy eradication Association (d) Institute of Information Association 3. BSO in classification stands for (a) Basic Subject of Organisation (b) Broad System of Ordering (c) Bibliography of Subject Ordering (d) Bibliographic Subject Organisation 4. IPR stands for (a) Indian Press Registration (b) Intellectual Property Right (c) International Property Right (d) Indian Property Regulations 5. NAAC stands for (a) National Accreditation and Authority Council (b) Northern Accreditation and Authorities Committee (c) National Assessment and Accreditation Council (d) Northern Assessment and Accreditation Council 6. ACRL 1 Dr . K.Kamila & Dr. B.Das MCQs for LIS (a) Association of College and Research Libraries (b) All College and Research Libraries (c) Academic Community Research Libraries 7. CILIP (a) Chartered Institute of Library and Information Professionals (b) Community Institute for Library and Information Programmes (c) College level Institute for Library and Information Programmes (d) Centre for Indian Library and Information Professionals 8. SCONUL (a) Society of College National and University Libraries (previously Standing Conference of National and University Libraries) (b) School College National and University Libraries (c) Special Council for National and University Libraries (d) None of these 9. NISCAIR (a) National Institute of Science Communication and Information Resources (b) National Institute of Scientific Cultural and Industrial Research (c) National Institute of Social Cultural and Industrial Research (d) None of the above 10. -
“It Took a Global Conflict”— the Second World War and Probability in British
Keynames: M. S. Bartlett, D.G. Kendall, stochastic processes, World War II Wordcount: 17,843 words “It took a global conflict”— the Second World War and Probability in British Mathematics John Aldrich Economics Department University of Southampton Southampton SO17 1BJ UK e-mail: [email protected] Abstract In the twentieth century probability became a “respectable” branch of mathematics. This paper describes how in Britain the transformation came after the Second World War and was due largely to David Kendall and Maurice Bartlett who met and worked together in the war and afterwards worked on stochastic processes. Their interests later diverged and, while Bartlett stayed in applied probability, Kendall took an increasingly pure line. March 2020 Probability played no part in a respectable mathematics course, and it took a global conflict to change both British mathematics and D. G. Kendall. Kingman “Obituary: David George Kendall” Introduction In the twentieth century probability is said to have become a “respectable” or “bona fide” branch of mathematics, the transformation occurring at different times in different countries.1 In Britain it came after the Second World War with research on stochastic processes by Maurice Stevenson Bartlett (1910-2002; FRS 1961) and David George Kendall (1918-2007; FRS 1964).2 They also contributed as teachers, especially Kendall who was the “effective beginning of the probability tradition in this country”—his pupils and his pupils’ pupils are “everywhere” reported Bingham (1996: 185). Bartlett and Kendall had full careers—extending beyond retirement in 1975 and ‘85— but I concentrate on the years of setting-up, 1940-55. -
Gerry Roche "A Memoir"
A Survivor’s Story: a memoir of a life lived in the shadow of a youthful brush with psychiatry by Gerry Roche And the end of all our exploring Will be to arrive where we started And know the place for the first time. TS Eliot: Four Quartets Contents Introduction 4 Chapter 1 : Ground Zero 7 1971: Lecturing, Depression, Drinking, John of Gods, … Chapter 2 : Zero minus one 21 1945-71: Childhood, School, University … Chapter 3 : Zero’s aftermath: destination ‘cold turkey’ 41 1971-81: MSc., Lecturing, Sculpting, Medication-free, Building Restoration, …… Chapter 4 : After ‘cold turkey’: the cake 68 1981-92: Tibet, India, Log Cabin Building, … Chapter 5 : And then the icing on the cake 105 1992-96: China, Karakoram, more Building, Ethiopia, ... Chapter 6 : And then the cognac … (and the bitter 150 lemon) 1996-2012: MPhil, Iran, Japan, PhD, more Building, Syria ... (and prostate cancer) … Chapter 7 : A Coda 201 2012-15: award of PhD … Armenia, Korea, … Postscript : Stigma: an inerasable, unexpungeable, 215 indestructible, indelible stain. Appendix: : Medical interventions on the grounds of 226 ‘best interests’ Endnotes 233 2 I wish to dedicate this memoir to my sons Philip and Peter and to their mother (and my-ex-wife) Mette, with love and thanks. I wish to give a special word of thanks to Ms. Maureen Cronin, Mr. Brian McDonnell, Mr. Charles O’Brien and Ms. Jill Breivik who assisted me in editing this memoir. 3 Introduction A cure is not overcoming anything, a cure is learning to live with what your are, and with what the past has made you, with what you've made of yourself with your own past .1 The story that I tell is of a journey, or perhaps more of an enforced wandering or a detour occasioned by what, at the time, seemed as inconsequential as the taking of a short break. -
Back Matter (PDF)
INDEX TO THE PHILOSOPHICAL TRANSACTIONS (10 FOR THE YEAR 1895. A. Abbott (E. C.) (see Gadow and A bbott). B. B lackman (F. F.). Experimental Researches on Vegetable Assimilation and Respiration.—No. I. On a New Method for Investigating the Carbonic Acid Exchanges of Plants, 485. -No. II. On the Paths of Gaseous Exchange between Aerial Leaves and the Atmosphere, 503. B ourne (G. G.). On the Structure and Affinities of P allas. With some Observa tions on the Structure of Xenia and Heteroxenia,455. Boice (K.). A Contribution to the Study of Descending Degenerations in the Brain and Spinal Cord, and on the Seat of Origin and Paths of Conduction of the Fits in Absinthe Epilepsy, 321. C. Catamites, the roots of, 683 (see W illiamson and Scott). CoebeHum, degenerations consequent on experimental lesions of the, 633 (sec R ussell). Coal-measures, further observations on the fossil plants of the, 683, 703 (see Williamson and Scott). C celomic fluid of Lumbricus terrestrisin relation to a protective mechanism, on the, 383 (see Kenu). Cynodontia from the Karroo llocks, on the skeleton in new, 59 (see S eeley). D. D ixon (H. H.) and J oey (J .). On the Ascent of Sap, 563. MDCCCXCV.—B. 5 X 878 INDEX. E. Echinoderm larva}, the effect of environment on the development of, 577 (see V ernon). Evolution of the vertebral column of fishes, on the, 163 (see Gadow and A bbott). F. Fishes, on the evolution of the vertebral column of, 163 (see Gadow and A bbott). Foraminifera,contributions to the life-history of the, 401 (see L ister).