5.2 Elements of Multibody Systems

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1、5.2ElementsofMultibodySystems915.2ElementsofMultibodySystemsAmultibodysystemiscomposedofrigidbodies,ofjointsandofforceele-ments.Anotherimportantelementcalledthecarrierbodywillbeexplainedfurtherbelow.Jointsandforceelementshaveincommonthattheyconnectbodiesandthattheyexertforcesofequalmagnitudeandopp

2、ositedirectiononthetwoconnectedbodies.Thedifferencebetweenjointsandforceelementsisthenatureoftheseforces.Inaforceelementtheforcevector(directionandmagnitude)isaknownfunctionofthepositionsand/orthevelocitiesofthetwobodiesconnectedbytheforceelement.Thesimplestforceelementsarespringsanddampers.Theyare

3、passiveelements.Alsoactiveforceelements(actuators)areadmittedinwhichtheforceisdeterminedbyagivencontrollawfromobservedpositionandvelocityvariables.Theessentialfeatureofforceelementsisthattheydonotcreatekinematicalconstraints.Incontrast,theforceexertedontwobodiesbyajointconnectingthesebodiesisapure

4、kinematicalconstraintforce.Itiscausedbyfrictionlessrigid-bodycontacts.Itcannotbeexpressedasfunctionofpositionandvelocityvariables.Constraintforcesdonotentertheequationsofmotionbecausetheyhavezerovirtualworkandzerovirtualpower.Notethefollowingdefinitionofjoint.Thejointconnectingtwobodiesisthecomplet

5、esystemofrigid-bodycontactsbetweenthesebodies.Thisdefinitionhastheconsequencethattwobodiescannotbeconnectedbymorethanonejoint.Whatthismeansisillus-tratedinFig.5.1.Thetwobodiesarenotconnectedbytwosphericaljointsbutbyasinglejoint.Thisjointisarevolutejointwithasinglejointvariable.Notealsothefollowingc

6、onvention.Asinglejointcannotinterconnectmorethantwobodies.WhatthismeansisillustratedinFigs.5.2a,b.ThethreebodiesinFig.5.2aaremountedonasingleshaft.ThisshaftproducestworevolutejointsasisshowninFig.5.2b.Dependingonthenatureofconstraintsthedegreeoffreedomfofajointisanynumber1≤f≤5.Figures5.3a–eshowase

7、xamplesfivejointswhichhave,inthisorder,thedegreesoffreedomf=1,2,3,4and5.InFig.5.3ctwoplanesurfaces,oneoneachbody,areincontact.InFig.5.3doneoftheFig.5.1.RevolutejointconnectingFig.5.2.Thebodiesin(a)arecon-twobodies