Mechanism Design: Enumeration of Kinematic Structures According to Function (Mechanical and Aerospace Engineering Series)

311 Pages·2000·12.69 MB·English

by  Lung-Wen Tsai

Mechanism Design
Enumeration of
Kinematic Structures
According to Function
Mechanical Engineering Series
Frank Kreith - Series Editor
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Mechanism Design
Enumeration of
Kinematic Structures
According to Function
Lung-Wen Tsai
Presidential Chair Professor
Department of Mechanical Engineering
Bourns College of Engineering
University of California, Riverside
CRC Press
Boca Raton London New York Washington, D.C.
ON THE COVER:
A 4-speed automatic transmission. (Courtesy of General Motors, Warren, MI.)
Library of Congress Cataloging-in-Publication Data
Tsai, Lung-Wen.
Mechanism design : enumeration of kinematic structures according to function /
Lung-Wen Tsai
p. cm.--(Mechanical engineering series)
Includes bibliographical references and index.
ISBN 0-8493-0901-8
1. Machinery, Kinematics of. 2. Machine design. I. Title. II. Advanced topics in
mechanical engineering series.
TJ175 .T78 2000
621.8′11--dc21 00-056415

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International Standard Book Number 0-8493-0901-8
Library of Congress Card Number 00-056415
Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
Printed on acid-free paper
Preface
This textbook has evolved from class notes used for a course in systematic design
of mechanisms that the author has taught for over a decade. Although it is written
primarilyforseniorandfirst-yeargraduatelevelstudentsinengineering,itisequally
valuableforpracticingengineers,particularlyformechanismandmachinedesigners.
Traditionally, mechanisms are created by the designer’s intuition, ingenuity, and
experience. This ad hoc approach, however, cannot ensure the identification of all
feasibledesignalternatives,nordoesitnecessarilyleadtoanoptimumdesign. Two
approaches have been developed to alleviate the problem. The first involves the
development of atlases of mechanisms grouped according to function for use as a
primary source of ideas. The second makes use of a symbolic representation of
the kinematic structure and the combinatorial analysis as a tool for enumeration of
mechanisms.
This textbook introduces a systematic methodology for the creation and classifi-
cation of mechanisms. The approach is partly analytical and partly algorithmic. It
isbasedontheideathat,duringtheconceptualdesignphase,someofthefunctional
requirementsofadesiredmechanismcanbetransformedintostructuralcharacteris-
ticsthatcanbeemployedforsystematicenumerationofmechanisms. Thekinematic
structureofamechanismcontainstheessentialinformationaboutwhichlinkiscon-
nectedtowhichotherlinkbywhattypeofjoint. Usinggraphtheory,combinatorial
analysis,andcomputeralgorithms,kinematicstructuresofthesamenature,i.e.,the
samethenumberofdegreesoffreedom,typeofmotion(planarorspatial),andcom-
plexitycanbeenumeratedinanessentiallysystematicandunbiasedmanner. Then
each mechanism structure is sketched and evaluated with respect to the remaining
functionalrequirements. Thisresultsinaclassoffeasiblemechanismsthatcanbe
subjecttodimensionalsynthesis,kinematicanddynamicanalyses,designoptimiza-
tion,anddesigndetailing.
Thistextbookisorganizedasfollows:
Chapter1providesabriefreviewofthedesignprocessandasystematicmethod-
ologyforcreationofmechanisms. Someterminologiesrelatedtothekinematicsof
mechanismaredefined. Mechanismsareclassifiedaccordingtothenatureofmotion
intoplanar,spherical,andspatialmechanisms.
Chapter2isconcernedwiththebasicconceptsofgraphtheory,whichisessentialfor
structuralanalysisandstructuralsynthesisofmechanisms. Thismaterialisextremely
importantsincethedesignmethodologyemploysgraphstorepresentthemechanism
structureandmechanismstructuresareenumeratedwiththeaidofgraphtheory.
Chapter3introducesseveralmethodsofrepresentationofthekinematicstructure
of mechanisms. The kinematic structure, which contains the essential information
aboutwhichlinkisconnectedtowhichotherlinksbywhattypesofjoint,willbeused
forenumerationofmechanisms.
Chapter4examinesthestructuralcharacteristicsofmechanisms. Thecorrespon-
dence between graph and mechanism is established, from which several important
mechanismstructuralcharacteristicsarederived. Thedegreesoffreedomofamecha-
nism,theloop-mobilitycriterion,theconceptofstructuralisomorphism,andvarious
methodsofidentificationofstructuralisomorphismaredescribed.
Chapter5dealswiththeenumerationofgraphsofkinematicchains. Systematic
algorithmsfortheenumerationofcontractedandconventionalgraphsarepresented.
Atlases of contracted graphs and conventional graphs are developed. Using these
atlases,anenormousnumberofmechanismscanbedeveloped.
Chapter6describesageneralprocedurefortheenumerationandclassificationof
mechanisms. Planar bar linkages, geared mechanisms, cam mechanisms, spherical
mechanisms,andspatialmechanismsareenumeratedandclassifiedaccordingtothe
numberofdegreesoffreedom,thenumberofindependentloops,etc.
Chapter7coverstheenumerationandclassificationofepicyclicgeartrains(EGTs).
ThestructuralcharacteristicsofEGTsareidentified. Variousmethodsofenumeration
including Buchsbaum and Freudenstein’s method, the genetic graph approach, and
theparentbarlinkagemethodarediscussed. Furthermore,thetheoryoffundamental
circuitsisintroducedforthespeed-ratioanalysisofEGTs.
Chapters 8 and 9 offer several conceptual design examples to demonstrate the
powerofthemethodology. Chapter8concentratesontheenumerationofautomotive
mechanisms, whereas Chapter 9 involves the enumeration of robotic mechanisms.
Atlasesofparallelmanipulatorsandroboticwristmechanismsaredeveloped.
AppendixApresentsanalgorithmforsolvingasystemofmlinearequationsinn
unknowns. Anesteddo-loopsalgorithmservesasthebasisforsystematicenumera-
tionofmechanisms. AppendixBprovidesanatlasofcontractedgraphshavingtwoto
fourindependentloops. AppendixCiscomprisedofanatlasofgraphsofkinematic
chainshavinguptothreeindependentloopsandeightlinks. AppendixDoffersan
atlas of planar linkages with one, two, and three degrees of freedom. Appendix E
contains an atlas of spatial one-dof, single-loop kinematic chains. Appendix F in-
cludesanatlasofepicyclicgeartrainsclassifiedaccordingtothenumberofdegreesof
freedom,thenumberofindependentloops,andthevertexdegreelisting. AppendixG
furnishestheschematicdiagramsandclutchingsequencesofsomecommonlyused
epicyclictransmissiongeartrains.
Prerequisitesforreadersofthistextbookincludethebasicconceptsofcombinato-
rialanalysis,graphtheory,matrixtheory,andthekinematicsofmechanismsthatare
usuallytaughtattheundergraduatelevel. ThomasEdisonsaid,“geniusisonepercent
inspirationandninety-ninepercentperspiration.” Inspirationcanoccurmorereadily
whenperspirationisproperlydirectedandfocused. Themethodologypresentedin
this book is intended to help designers better organize the perspiration so that the
inspirationcantakeplaceearlyinthedesignprocess. Forthosewhoarewillingto
try,therewardsshouldbewellworthit.
TheauthorwishestoexpresshissincereappreciationtoDr.BernardRoth,hisfor-
merPh.D.advisoratStanfordUniversity,andDr. FerdinandFreudenstein,Professor
EmeritusatColumbiaUniversity,fortheirlifelongadviceandencouragement. Ama-
jorportionofthematerialpresentedinthistextbookisderivedfromDr.Freudenstein
andhisformerstudents’researchresults. Othersaretakenfromtheauthor’sresearch
incollaborationwithprofessionalcolleagues,TingLiuandRolandMaki,andwithhis
former students, Sun-Lai Chang, Goutam Chatterjee, Dar-Zen Chen, Hsin-I Hsieh,
Chen-ChouLin, RichardStamper, andFarhadTahmasebi. Theireffortsaregreatly
appreciated. Lastly, the author appreciates the patience and sacrifice of his family
members, Lung-ChuTsai, JuleAnnTsai, andDavidJeanchungTsai, overthepast
fewyearswhilethetextbookwasbeingwritten.
Lung-WenTsai
Riverside,California
The Author
Lung-WenTsaiisaPresidentialChairProfessorintheDepartmentofMechanical
EngineeringattheUniversityofCaliforniainRiverside. HeobtainedhisB.S.degree
in mechanical engineering from the National Taiwan University in Taipei, Taiwan;
M.S.degreeinengineeringsciencefromtheStateUniversityofNewYork(SUNY)
inBuffalo,NewYork;andPh.D.inmechanicalengineeringfromStanfordUniversity
inStanford,California.
From1973to1978,Dr.TsaiwasaresearchanddevelopmentengineerforHewlett
PackardresponsibleforthedesignofinstrumentationtaperecordersandX-Yplotters.
From1978to1986hewasaseniorstaffresearchengineerforGeneralMotorsand
ledprojectsinthedevelopmentofvariable-strokeenginemechanisms,variable-valve
timingmechanisms,activeenginebalancingdevices,automatictransmissionmech-
anisms,andkinematicsofrobotmanipulators. Hismostrecentpositionwaswiththe
UniversityofMarylandinCollegeParkfrom1986toJuly2000whereheestablished
anationallyrecognizedresearchandeducationprograminmechanismsandmachine
theory,automotiveengineering,androbotmanipulators. Dr.TsaijoinedtheDepart-
ment of Mechanical Engineering at the University of California at Riverside in the
Fallof2000.
Dr.TsaiisaregisteredprofessionalengineerinCalifornia,aFellowoftheASME,
andamemberoftheSAE.HeisChiefEditorfortheASMEJournalofMechanical
DesignandChairmanofthe2000ASMEInternationalDesignEngineeringTechnical
ConferencesandtheComputerinEngineeringConference. Dr.Tsaihaspublished
onebookonrobotanalysis(RobotAnalysis: TheMechanicsofSerialandParallel
Manipulators,JohnWiley&Sons,NewYork,1999)andmorethan100journaland
conferenceproceedingspapers. Heistherecipientofnumerousawards,includingthe
1984ASMEMechanismCommitteebestpaperaward,1989and1991AMRProcter&
GambleAwards,1985ASMEMelvilleMedal,1986GMJohnCampbellAward,1988
SAE Arch Colwell Merit Award, and 1993 AMR South-Pointing-Chariot Rotating
Trophy.