附錄KinematicsanddynamicsofmachineryOneprincpleaimofkinemaricsistocreatthedesignedmotionsofthesubjectmechanicalpartsandthenmathematicallycomputethepositions,velocities,andaccelerations,whichthosemotionswillcreatontheparts.Since,formostearthboundmechanicalsystems,themassremainsessentiallyconstantwithtime，definingtheaccelerationsasafunctionoftimethenalsodefinesthedynamicforcesasafunctionoftime.Stress，inturn,willbeafunctionofbothappliedandinerialsforces.sinceengineeringdesignischargedwithcreatingsystemswhichwillnotfailduringtheirexpectedservicelife，thegoalistokeepstresseswithinacceptablelimitsforthematerialschosenandtheenvironmentalconditionsencountered.Thisobviselyrequiesthatallsystemforcesbedefinedandkeptwithindesiredlimits.Inmechinery,thelargestforcesencounteredareoftenthoseduetothedynamicsofthemachineitself.Thesedynamicforcesareproportionaltoacceletation,whichbringsusbacktokinematics,thefoundationofmechanicaldesign.Verybasicandearlydecisionsinthedesignprocessinvovlingkinematicswiiprovetroublesomeandperformbadly.Anymechanicalsystemcanbeclassifiedaccordingtothenumberofdegreeoffreedomwhichitpossesses.thesystemsDOFisequaltothenumberofindependentparameterswhichareneededtouniquelydefineitsposioninspaceatanyinstantoftime.Arigidbodyfreetomovewithinareferenceframewill,inthegeneralcase,havecomplexmotoin,whichissimultaneouscombinationofrotationandtranslation.Inthree-dimensionalspace,theremayberotationaboutanyaxisandalsosimultaneoustranslationwhichcanberesoledintocomponentionalongthreeaxes,inaplane,ortwo-dimentionalspace,complexmotionbecomesacombinationofsimultaneousalongtwoaxesintheplane.Forsimplicity,wewilllimitourpresentdiscusstionstothecaseofplanarmotion:Purerotationthebodypessessesonepoint(centerofrotation)whichhasnomotionwithrespecttothestationaryframeofreference.Allotherpointsonthebodydescribearcsaboutthatcenter.Areferencelinedrawnonthebodythroughthecenterchangesonlyitsangulaiorientation.Puretranslationallpointsonthebodydescribeparallelpaths.Areferencelinedrawnonthebodychangesitslinearposionbutdoesnotchangeitsangularoriention.Complexmotionasimulaneouscombinationofrotionandtranslationm.anyreferencelinedrawnonthebodywillchangebothitslinearpisitionanditsangularorientation.Pointsonthebodywilltravelnon-parallelpaths,andtherewillbe,ateveryinstant,acenterofrotation,whichwillcontinuouslychangelocation.Linkagesarethebacisbuildingblocksofallmechanisms.Allcommonformsofmechanismscams,gears,belts,chainsareinfactvariationsoflinkages.Linkagesaremadeupoflinksandkinematicpairs.Alinkisan(assumed)rigidbodywhichpossessesatleasttwoormorelinks(attheirnodes),whichconnectionallowssomemotion,orpotentialmotion，betweentheconnectedlinks.Thetermlowerpairisusedtidescribejiontswithsurfacecontact,aswithapinsurroundedbyahole.Thetermhigherpairisusedtodescribejiontswithpointorlinecontact,butifthereisanyclerancebetweenpinandhole(astheremustbeformotion),so-calledsurfacecontactinthepinjiontactuallybecomeslinecontact,asthepincontactsactuallyhascontactonlyatdiscretepoints,whicharethetopsofthesurfacesasperities.Themainpracticaladvantageoflowerpairsoverhigherpairsistheirbetterabilitytotraplubricantbetweentheirenvlopingsurface.Thisieespeciallytruefortherotatingpinjoint.Thelubricantismoreeasilysqueezedoutofahigherpair.assresult,thepinjointispreferredforlowwearandlonglife.Whendesigningmachinery,wemustfirstdoacompletekinematicanalysisofourdesign,inordertoobtaininformationabouttheaccelerationofthemovingparts.wenextwantteusenewtonssecondlawtocaculatethedynamicforces,buttodosoweneedtoknowthemassesofallthemovingpartswhichhavetheseknownacceletations.Thesepartsdonotexityet!aswithanydesigninordertomakeafirstpassatthecaculation.wewillthenhavetoitneratetobetteranbettersolutionsaswegeneratemoreinformation.Afirstestimateofyourpartsmassescanbeobtainedbyassumingsomereasonableshapesandsizeforallthepartsandchoosingapproriatematerials.Thencaculatethevolumeofeachpartandmultipyitsvolumebymaterialsmassdensity(notweightdensity)toobtainafirstapproximationofitsmass.thesemassvaluescanthenbeusedinNewtonsequation.Howwillweknowwhetherourchosensizesandshapesoflinksareevenacceptable,letaloneoptimalunfortunately,wewillnotknowuntillwehavecarriedthecomputationsallthewaythroughacompletestressanddeflectionanalysisoftheparts.Ititoftenthecase,especiallywithlong,thinelementssuchasshaftsorslenderlinks,thatthedeflectionsoftheparts,redesignthem,andrepeattheforce,stress,anddeflectionanalysis.designis,unavoidably,aniterativeprocess.Itisalsoworthnothingthat,unlikeastaticforcesituationinwhichafaileddesignmightbefixedbyaddingmoremasstotheparttostrenthenit,todosoinadynamicforcesituationcanhaveadeleteriouseffect.moremasswiththesameaccelerationwillgenerateevenhigherforcesandthushigherstresses!themachinedesigeroftenneedtoremovemass(intherightplaces)formpartsinordertoreducethestessesanddeflectionsduetoF=ma,thusthedesignerneedstohaveagoodunderstandingofbothmaterialpropertiesandstessanddeflectionanalysistoproperlyshapeandsizepartsforminimummasswhilemaximzingthestrengthandstiffnessneededtowithstandthedynamicforces.Oneoftheprimaryconsiderationsindesigninganymachineorstrucreisthatthestrengthmustbesufficientlygreaterthanthestresstoassurebothsafetyandreliability.Toassurethatmechanicalpartsdonotfailinservice,itisnecessarytolearnwhytheysometimesdofail.Thenweshallbeabletorelatethestresseswiththestrenthstoachievesafety.Ideally,indesigninganymachineelement，theengineershouldhaveathisdisposalshouldhavebeenmadeonspecimentshavingthesameheattreatment,surfaceroughness,andsizeastheelementheprossestodesign；andthetestsshouldbemadeunderexactlythesameloadingconditionsasthepartwillexperienceinservice.thismeansthat,ifthepartistoexperienceabendingandtorsion，itshouldbetestedundercombinedbendingandtorsion.Suchtestswillprovideveryusefulandpreciseinformation.theytelltheengineerwhatfactorofsafetytouseandwhatthereliabilityisforagivenservicelife.wheneversuchdataareavailablefordesignpurposes，theengineercanbeassurethatheisdoingthebestjustifiediffailureofthepartmayendangerhumanlife,orifthepartismanufacturedinsufficientlylargequantities.Automobilesandrefrigrerators,forexample,haveverygoodreliabilitiesbecausethepartsaremadeinsuchlargequantitiesthattheycanbethoroughlytestedinadvanceofmanufacture,thecostofmakingtheseisverylowwhenitisdividedbythetotalnumberofpartsmanufactrued.Youcannowappreciatethefollowingfourdesigncategories:(1)failureofthepartwouldendangerhumanlife,orthepartismadeinextremelylargequantities；consequently,anelaboratetestingprogramisjustifiedduringdesign.(2)thepartismadeinlargeenoughquantitiessothatamoderateseruesoftestsisfeasible.(3)Thepartismadeinsuchsmallquantitiesthattestingisnotjustifiedatall；orthedesignmustbecompletedsorapidllythatthereisnotenoughtimefortesting.(4)Theparthasalreadybeendesigned,manufactured,andtestedandfoundtobeunsatisfactory.Analysisisrequiredtounderstandwhythepartisunsatisfactoryandwhattodotoimproveit.Itiswiththelastthreecategoriesthatweshallbemostlyconcerned.thismeansthatthedesignerwillusuallyhaveonlypublishedvaluesofyieldstrenth,ultimatestrength,andpercentageelongation.withthismeagerinformationtheengieerisexpectedtodesignagainststaticanddynamicloads,biaxialandtriaxialstressstates,highandlowtemperatures，andlargeandsmallparts!Thedatausuallyavailablefordesignhavebeenobtainedfromthesimpletensiontest,wheretheloadwasappliedgraduallyandthestraingiventimetodevelop.Yetthesesamedatamustbeusedindesigningpartswithcomplicateddynamicloadsappliedthousandsoftimesperminute.Nowondermachinepartssometimesfail.Tosumup,thefundamentalproblemofthedesigneristousethesimpletensiontestdataandrelatethemtothestrengthofthepart，