Multibody Dynamics: Computational Methods and Applications

218 Pages·2013·4.839 MB·English

by  A. L. Schwab, D. M. Fintelman, O. den Braver (auth.), Jean-Claude Samin, Paul Fisette (eds.)

Multibody Dynamics
Computational Methods in Applied Sciences
Volume28
SeriesEditor
E.Oñate
InternationalCenterforNumericalMethodsinEngineering(CIMNE)
TechnicalUniversityofCatalonia(UPC)
EdificioC-1,CampusNorteUPC
GranCapitán,s/n
08034Barcelona,Spain
[e-mail]
www.cimne.com
Forfurthervolumes:
www.springer.com/series/6899
Jean-Claude Samin (cid:2) Paul Fisette
Editors
Multibody
Dynamics
Computational Methods
and Applications
Editors
Jean-ClaudeSamin PaulFisette
InstituteforMechanics,MaterialsandCivil InstituteforMechanics,MaterialsandCivil
Engineering Engineering
UniversitécatholiquedeLouvain(UCL) UniversitécatholiquedeLouvain(UCL)
Louvain-la-Neuve,Belgium Louvain-la-Neuve,Belgium
ISSN1871-3033 ComputationalMethodsinAppliedSciences
ISBN978-94-007-5403-4 ISBN978-94-007-5404-1(eBook)
DOI10.1007/978-94-007-5404-1
SpringerDordrechtHeidelbergNewYorkLondon
LibraryofCongressControlNumber:2012950804
©SpringerScience+BusinessMediaDordrecht2013
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection
with reviews or scholarly analysis or material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of
this publication or parts thereof is permitted only under the provisions of the Copyright Law of the
Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.
PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations
areliabletoprosecutionundertherespectiveCopyrightLaw.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpub-
lication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforany
errorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespect
tothematerialcontainedherein.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Preface
MultibodyDynamicsisanexcitingareaofComputationalMechanicswhichmerges
andblendsvariousdisciplinesinordertoprovidemethodsandtoolsforthevirtual
prototyping of complex mechanical systems. Multibody dynamics plays a central
rolethesedaysinthemodeling,analysis,simulationandoptimizationofmechanical
andmechatronicsystemsinavarietyoffieldsandforawiderangeofscientificand
industrialapplications,someofwhichareillustratedbelow.
Asnewmethodsandproceduresarebeingproposedatafastpaceinacademia,
researchlaboratoriesandindustry,itisbecomingimportanttoprovideresearchers
v
vi Preface
inmultibodydynamicswithappropriatevenuesforexchangingideasandresults.To
answertheseneeds,theECCOMASThematicConferenceonMultibodyDynamics
was initiated in Lisbon in 2003, and continued in Madrid in 2005, Milan in 2007
andWarsawin2009.Continuingthisverysuccessfulseries,the2011editionofthe
ECCOMAS Thematic Conference on Multibody Dynamics was held in Brussels,
BelgiumandorganizedbytheUniversitécatholiquedeLouvain,from4thto7thJuly
2011.Morethan250participantswereattendingtheconferencewhichprovideda
forumforfruitfuldiscussionandtechnicalexchanges.
This book contains the contributions of participants selected by the organizers
that reflect the State-of-Art in the application of Multibody Dynamics to different
areasofengineering.Thechaptersofthisbookareenlargedandrevisedversionsof
thecommunications,deliveredattheconference,whichwereenhancedintermsof
self-containmentandtutorialqualitybytheauthors.Theresultisacomprehensive
textthatconstitutesavaluablereferenceforresearchersanddesignengineerswhich
helps to appraise the potential for the application of multibody dynamics method-
ologiestoawiderangeofareasofscientificandengineeringrelevance.
Louvain-la-Neuve,Belgium Jean-ClaudeSamin
PaulFisette
Contents
SpeedSkatingModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
A.L.Schwab,D.M.Fintelman,andO.denBraver
Contact Modellingin Multibody Systems by Means of a Boundary
ElementCo-simulationandaDIRICHLET-to-NEUMANNAlgorithm 25
JánosZierathandChristophWoernle
TrajectoryControlofSerialandParallelFlexibleManipulatorsUsing
ModelInversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
RobertSeifried,MarkusBurkhardt,andAlexanderHeld
A3DShearDeformableFiniteElementBasedontheAbsoluteNodal
CoordinateFormulation . . . . . . . . . . . . . . . . . . . . . . . . . 77
KarinNachbagauer,PeterGruber,andJohannesGerstmayr
AVariationalApproachtoMultirateIntegrationforConstrainedSystems 97
SigridLeyendeckerandSinaOber-Blöbaum
SymbolicSensitivityAnalysisofMultibodySystems . . . . . . . . . . . . 123
JoydeepM.BanerjeeandJohnMcPhee
Efficient Coarse-Grained Molecular Simulations in the Multibody
DynamicsScheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
MohammadPoursinaandKurtS.Anderson
Efficiency and Precise Interaction for Multibody Simulations in
AugmentedReality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
LorenzoMaritiandPierPaoloValentini
ModellingofContactBetweenStiffBodiesinAutomotiveTransmission
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
GeoffreyVirlez,OlivierBrüls,NicolasPoulet,EmmanuelTromme,and
PierreDuysinx
vii
Speed Skating Modeling
A.L.Schwab,D.M.Fintelman,andO.denBraver
Abstract Advice about the optimal coordination pattern for an individual speed
skater to reach their optimal performance, could well be addressed by simulation
and optimization of a biomechanical model of speed skating. But before getting
to this optimization approach one needs a model that matches observed behavior.
In this chapter we present a simple 2-dimensional model of speed skating on the
straights which mimics observed kinematic and force data. The primary features
of the model are: the skater is modeledas three pointmasses, only motionsin the
horizontalplaneareconsidered,airdragforceswhicharequadraticinthevelocity
andcoulombtypeicefrictionforcesattheskatesareincluded,andidealizedcontact
oftheskateontheiceismodeledbyaholonomicconstraintintheverticaldirection
and a non-holonomic constraint in the lateral direction. Using the measured leg
extension(relativemotionsoftheskateswithrespecttotheupperbody)weareable
to predict reasonable well the speed skater motions, even if we do not fit for that.
Themodelseemstohavethekeytermsforinvestigationsofspeedskating.
1 Introduction
The coordinationpatternof speedskatingappears to becompletelydifferent from
allothertypesofhumanpropulsion.Inmostpatternsofhumanlocomotion,humans
generateforcesbypushingagainsttheenvironmentintheoppositedesireddirection
(cid:2)
A.L.Schwab( )
LaboratoryforEngineeringMechanics,DelftUniversityofTechnology,Mekelweg2,
2628CDDelft,TheNetherlands
e-mail:[e-mail]
D.M.Fintelman
SchoolofSportandExerciseSciences,UniversityofBirmingham,Edgbaston,B152TT,
Birmingham,UK
e-mail:[e-mail]
O.denBraver
BioMechanicalEngineering,DelftUniversityofTechnology,Mekelweg2,2628CDDelft,
TheNetherlands
J.-C.Samin,P.Fisette(eds.),MultibodyDynamics, 1
ComputationalMethodsinAppliedSciences28,
DOI10.1007/978-94-007-5404-1_1,©SpringerScience+BusinessMediaDordrecht2013
2 A.L.Schwabetal.
Fig.1 Phasesofastroke:push-offphase,glidephaseandrepositionphase[1]
ofmotion.Inspeedskatinghumansgenerateforcesbypushinginsidewarddirec-
tion. When we take a closer look at speed skating the straights we observe that
a skating stroke can be divided in three phases: the glide, push-off and reposition
phase,see Fig. 1. In the push-off phase the skate movessidewards with respect to
thecenterofmass(COM)ofthebodytillnearfulllegextension.Inthereposition
phasethelegisretractedinthedirectionofthecenterofmassofthebody.During
the glide phase the body is supported over one leg that remains at nearly constant
height(ankletohipdistance).Doublesupport,wherebothskatesareontheice,only
existsinthefirstpartoftheglidephaseofonelegandinthesecondpartofpush-off
phaseoftheotherleg.Thiscoordinationpatternwithsidewardpush-offresultsina
sinus-waveliketrajectoryoftheupperbodyontheice[4].
Fromtheseobservationsanumberofquestionsarise.Ofthemanypossibleco-
ordinationpatterns,thatispositionandorientationoftheskateswithrespecttothe
upperbody,whydoskatersusethisparticularone?Whatistheoptimalcoordina-
tionpatternforanindividualspeedskatertoreachtheiroptimalperformance?How
dospeedskaterscreateforwardpoweronice?Whyarespeedskaterssteeringback
to their body at the end of the push-off? What is the effect of anthropometric dif-
ferencesonthecoordinationpatternofaspeedskater(likethedifferencebetweena
tallDutchskaterandasmallJapaneseskater)?Allthesequestionsarehighlydepen-
dentonthecoordinationpatternofthespeedskaterandcouldwellbeaddressedby
simulationandoptimizationofabiomechanicalmodelofspeedskating.Butbefore
getting to this optimization approach one needs a model that reasonable matches
observedbehavior.
Currently, there exist three speed skating models [1, 6, 10]. The first models
of speed skating were initiated by Gerrit Jan van Ingen Schenau [12] and further
developed by researchers at the VU University Amsterdam [6]. By using power
balances of the human and the environment useful information about the posture,
athlete physiology and environmental parameters on the performance is obtained.
Disadvantagesofthesemodelsarethatthevalidationisdifficultanditisimpossible
toinvestigatedifferencesincoordinationpattern.
AmorerecentmodelwasdevelopedbyOtten[10],inwhichforwardandinverse
dynamicsarecombined.Themodeliscomplexandincludesupto19rigidbodies
and160muscles.Themodelisabletosimulateskatingandcangiveinsightinthe
forces/moments in the joints. Limitations of the model are that the kinematics in
SpeedSkatingModeling 3
the model are manually tuned and that the model is not driven and validated with
measurements of speed skaters. Unfortunately, no information about this model is
availableintheopenliterature,whichmakesithardtoreview.
The most recent speed skater model is developed by Allinger and van den
Bogert [1]. they developed a simple, one point mass, inverse dynamics model of
a speed skater which is driven by individual strokes. The main limitations of the
modelarethatthemodelisdrivenbyapresumedlegfunctionintimeandthatthe
modelisnotvalidatedwithforcemeasurements.Furthermore,theeffectoftheas-
sumptions on the model (e.g. constant height) are not investigated. On the other
handthemodelispossiblyaccurateandveryusefulforoptimizationthecoordina-
tionpatternofspeedskating.
Although three biomechanical models exist, none of these models is shown to
accuratelypredictobservedforcesandmotions.Whichispartlyduetothelackof
experimentalkinematicdataandforcedataonstrokelevel.
In this chapter, we present a 2-dimensional inverse dynamics model on the
straightswhichhasminimalcomplexity.Themodelisbasedonthreelumpedmasses
and is validated with observed in-plane (horizontal) kinematics and forces at the
skates. In the future, this model can be used to provide individual advice to elite
speedskatersabouttheircoordinationpatterntoreachtheiroptimalperformance.
2 Methods
Wemeasuredintimethe2-dimensionalin-plane(horizontal)positions(x,y)ofthe
twoskatesandtheupperbody,thenormalforcesandlateralforcesatthetwoskates
andleanangleoftheskates.Wedevelopeda2-dimensionalinversedynamicmodel
of a skater. The model is driven by the measured leg extensions, that is relative
motions of the skates with respect to the upper body and absolute orientation of
theskateswithrespecttotheice.Theupperbodymotionstogetherwiththeforces
exertedontheicebytheskatesarecalculatedfromthemodel.
Aschematicofour2-dimensionalmodelisshowninFig.2.Themodelconsists
ofthreepointmasses:lumpedmassesatthebodyandthetwoskates.Thetotalmass
of the system is distributed over the three bodies by a constant mass distribution
coefficient.Themotionsofthearmsareneglected.Wedonotconsiderthevertical
motionoftheupperbody,sinceexperimentsshowthattheupperbodyisatnearly
constant height [3]. Air friction and ice friction are taken into account. Idealized
contactoftheskateontheiceismodeledbyaholonomicconstraintinthevertical
directionandanon-holonomicconstraintinthelateraldirection.
Values for the mass distribution and air friction are found experimentally. The
best agreement between the measurements and model can be achieved if we use
accuratevaluesfortheseparameters.Thereforeweconstructedanobjectivefunction
J andminimizedtheerrorbetweenthemeasurementsandmodel.Detailsonthe
min
objectivefunctioncanbefoundinAppendix8.3.