Table Of ContentSpringer 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
