Mechanical Simulation with MATLAB PDF
Preview Mechanical Simulation with MATLAB
Springer Tracts in Mechanical Engineering Dan B. Marghitu Hamid Ghaednia Jing Zhao Mechanical Simulation with MATLAB® Springer Tracts in Mechanical Engineering SeriesEditors Seung-BokChoi,CollegeofEngineering,InhaUniversity,Incheon,Korea (Republicof) HaibinDuan,BeijingUniversityofAeronauticsandAstronautics,Beijing,China YiliFu,HarbinInstituteofTechnology,Harbin,China CarlosGuardiola,CMT-MotoresTermicos,PolytechnicUniversityofValencia, Valencia,Spain Jian-QiaoSun,UniversityofCalifornia,Merced,CA,USA YoungW.Kwon,NavalPostgraduateSchool,Monterey,CA,USA FranciscoCavas-Martínez,DepartamentodeEstructuras,UniversidadPolitécnica deCartagena,Cartagena,Murcia,Spain FakherChaari,NationalSchoolofEngineersofSfax,Sfax,Tunisia FrancescadiMare,InstituteofEnergyTechnology,Ruhr-UniversitätBochum, Bochum,Nordrhein-Westfalen,Germany HamidRezaKarimi,DepartmentofMechanicalEngineering,Politecnicodi Milano,Milan,Italy Springer Tracts in Mechanical Engineering (STME) publishes the latest develop- ments inMechanical Engineering - quickly, informally and withhigh quality. The intentistocoverallthemainbranchesofmechanicalengineering,boththeoretical andapplied,including: (cid:129) EngineeringDesign (cid:129) MachineryandMachineElements (cid:129) MechanicalStructuresandStressAnalysis (cid:129) AutomotiveEngineering (cid:129) EngineTechnology (cid:129) AerospaceTechnologyandAstronautics (cid:129) NanotechnologyandMicroengineering (cid:129) Control,Robotics,Mechatronics (cid:129) MEMS (cid:129) TheoreticalandAppliedMechanics (cid:129) DynamicalSystems,Control (cid:129) FluidsMechanics (cid:129) EngineeringThermodynamics,HeatandMassTransfer (cid:129) Manufacturing (cid:129) PrecisionEngineering,Instrumentation,Measurement (cid:129) MaterialsEngineering (cid:129) TribologyandSurfaceTechnology Within the scope of the series are monographs, professional books or graduate textbooks, editedvolumes aswellasoutstanding PhDthesesand books purposely devoted to support education in mechanical engineering at graduate and post-graduatelevels. IndexedbySCOPUS,zbMATH,SCImago. PleasecheckourLectureNotesinMechanicalEngineeringathttp://www.springer. com/series/11236ifyouareinterestedinconferenceproceedings. Tosubmitaproposalorforfurtherinquiries,pleasecontacttheSpringerEditor in yourregion: Ms.EllaZhang(China) Email:[email protected] PriyaVyas(India) Email:[email protected] Dr.LeontinaDiCecco(Allothercountries) Email:[email protected] AllbookspublishedintheseriesaresubmittedforconsiderationinWebofScience. Moreinformationaboutthisseriesathttps://link.springer.com/bookseries/11693 · · Dan B. Marghitu Hamid Ghaednia Jing Zhao Mechanical Simulation ® with MATLAB DanB.Marghitu HamidGhaednia MechanicalEngineeringDepartment DepartmentofOrthopedicSurgery AuburnUniversity MassachusettsGeneralHospital Auburn,AL,USA Boston,MA,USA JingZhao MechanicalEngineeringDepartment AuburnUniversity Auburn,AL,USA ISSN2195-9862 ISSN2195-9870 (electronic) SpringerTractsinMechanicalEngineering ISBN978-3-030-88101-6 ISBN978-3-030-88102-3 (eBook) https://doi.org/10.1007/978-3-030-88102-3 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface This book deals with the simulation of the mechanical behavior of engineering structures, mechanisms, and components. It presents a set of strategies and tools forformulatingthemathematicalequationsandthemethodsofsolvingthemusing MATLAB. For the same mechanical systems, it also shows how to obtain solu- tionsusingdifferentapproaches.Itthencomparestheresultsobtainedwiththetwo methods.Bycombiningfundamentalsofkinematicsanddynamicsofmechanisms withapplicationsanddifferentsolutionsinMATLABofproblemsrelatedtogears, cams, and multilink mechanisms, and by presenting the concepts in an accessible manner,thisbookisintendedtoassistadvancedundergraduateandmechanicalengi- neeringgraduatestudentsinsolvingvariouskindofdynamicalproblemsbyusing methods in MATLAB. It also offers a comprehensive, practice-oriented guide to mechanicalengineersdealingwithkinematicsanddynamicsofseveralmechanical systems. Auburn,USA DanB.Marghitu Boston,USA HamidGhaednia Auburn,USA JingZhao v Contents 1 Introduction ................................................... 1 1.1 KinematicPairs ............................................ 1 1.2 DegreesofFreedom ........................................ 3 1.3 KinematicChains .......................................... 4 1.4 TypeofDyads ............................................. 6 1.5 PositionAnalysisforLinks .................................. 9 1.6 VelocityandAccelerationAnalysisforRigidBody .............. 15 1.7 PlanarDynamicsAnalysis ................................... 22 1.8 Problems .................................................. 28 References ..................................................... 28 2 ClassicalAnalysisofaMechanismwithOneDyad ................. 31 2.1 PositionAnalysis ........................................... 31 2.2 VelocityandAccelerationAnalysis ........................... 38 2.3 DynamicForceAnalysis .................................... 44 2.4 Problems .................................................. 52 References ..................................................... 54 3 ContourAnalysisofaMechanismwithOneDyad ................. 57 3.1 ClosedContourEquations ................................... 57 3.2 ClosedContourEquationsforR-RTRMechanism ............... 61 3.3 ForceAnalysisforR-RTRMechanism ........................ 65 3.4 Problems .................................................. 70 References ..................................................... 70 4 ClassicalAnalysisofaMechanismwithTwoDyads ................ 73 4.1 PositionAnalysis ........................................... 73 4.2 VelocityandAccelerationAnalysis ........................... 78 4.3 DynamicForceAnalysis .................................... 85 4.4 Problems .................................................. 95 References ..................................................... 98 vii viii Contents 5 ContourAnalysisofaMechanismwithTwoDyads ................ 101 5.1 VelocityandAccelerationAnalysis ........................... 102 5.2 ContourDynamicForceAnalysiswithD’AlembertPrinciple ..... 107 5.2.1 ReactionForce F ................................... 107 24 5.2.2 ReactionForce F ................................... 109 23 5.2.3 ReactionForce F ................................... 110 12 5.2.4 ReactionForce F ................................... 112 03 5.2.5 ReactionForce F ................................... 113 05 5.2.6 ReactionForce F andReactionMoment M ........... 115 54 54 5.2.7 ReactionForce F andMoment M ................... 117 01 m 5.3 Problems .................................................. 119 References ..................................................... 119 6 DyadRoutinesforMechanisms .................................. 123 6.1 DriverLink ................................................ 123 6.2 PositionAnalysis ........................................... 124 6.3 VelocityAnalysis ........................................... 127 6.4 ForceAnalysis ............................................. 132 6.4.1 R-RRRMechanism .................................. 139 6.4.2 R-RTRMechanism ................................... 146 6.4.3 R-RRT-RTRMechanism .............................. 151 6.4.4 Problems ........................................... 161 References ..................................................... 162 7 EpicyclicGearTrains ........................................... 165 7.1 Introduction ............................................... 165 7.2 EpicyclicGearTrainwithOnePlanet ......................... 167 7.2.1 ClassicalMethod .................................... 168 7.2.2 ContourMethod ..................................... 170 7.3 MechanismwithEpicyclicGears ............................. 172 7.3.1 ClassicalMethod—VelocityAnalysis ................... 174 7.3.2 ContourMethod—VelocityAnalysis .................... 175 7.4 EpicyclicGearTrainwithMultiplePlanets ..................... 177 7.4.1 ClassicalMethod—VelocityAnalysis ................... 179 7.4.2 ContourMethod—VelocityAnalysis .................... 181 7.5 Problems .................................................. 183 References ..................................................... 186 8 CamandFollowerMechanism .................................. 189 8.1 KinematicsAnalysis ........................................ 190 8.2 ForceAnalysis ............................................. 195 8.3 EquivalentLinkages ........................................ 197 8.4 DifferentialMethod ......................................... 200 8.5 Problems .................................................. 201 References ..................................................... 203 Contents ix 9 DirectDynamics ............................................... 207 9.1 EquationsofMotion—SphereonaSpring ..................... 207 9.2 DynamicsofaRotatingLinkwithanElasticForce .............. 215 9.3 ImpactofaFreeLinkwithMATLAB ......................... 228 9.4 Problems .................................................. 242 References ..................................................... 243 Index ............................................................. 247 Chapter 1 Introduction Abstract Thestructureofthemechanicalsystemsisanalyzed:links,joints,degrees of freedom of the joint, degrees of freedom, independent contours, dyads. For the planarmechanismsthecontourdiagramandthedyadsareintroduced.Formulasfor kinematicsanddynamicsoftherigidbodyarepresented. 1.1 KinematicPairs Linkages are made up of links and joints and are basic elements of mechanisms androbots.Alink(elementormember)isarigidbodywithnodes.Thenodesare points at which links can be connected. Figure1.1 shows a link with two nodes, a binary link. The links with three nodes are ternary links. A kinematic pair or a jointistheconnectionbetweentwoormorelinks.Thekinematicpairsgiverelative motion between the joined elements. The degree of freedom of the kinematic pair isthenumberofindependentcoordinatesthatestablishestherelativepositionofthe joinedlinks. Ajointhas(6−i)degreesoffreedomwherei isthenumberofrestrictedrelative movements.Aplanaronedegreeoffreedomkinematicpair,c ,removes5degrees 5 offreedomandallowsonedegreeoffreedom.Theplanartwodegreesoffreedom kinematicpair,c ,hastwodegreesoffreedomandremoves4degreesoffreedom.To 4 findthedegreesoffreedomofakinematicpaironeelementisholdtobeareference linkandthepositionoftheotherelementisfoundwithrespecttothereferencelink. Figure1.2ashowsaslider(translationalorprismatic)jointthatallowsonetranslation (T)degreeoffreedombetweentheelements1and2.Figure1.2brepresentsarotating pin (rotational or revolute) joint that allows one rotational (R) degree of freedom betweenlinks1and2.Thesliderandthepinjointsarec joints.Thec jointsallow 5 5 one degrees of freedom and is called full-joint. For the two degrees of freedom joints, c , there are two independent, relative motions, translation (T) and rotation 4 (R),betweenthejoinedlinks.TwodegreesoffreedomjointsareshowninFig.1.3. Thetwodegreesoffreedomjointiscalledhalf-jointandhas4degreesofconstraint. Foraplanarsystemtherearetwokindsofjointsc andc .Ajoystick(ball-and-socket 5 4 joint,oraspherejoint)isathreedegreesoffreedomjoint(3degreesofconstraint, ©TheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerlandAG2022 1 D.B.Marghituetal.,MechanicalSimulationwithMATLAB®, SpringerTractsinMechanicalEngineering, https://doi.org/10.1007/978-3-030-88102-3_1
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