A Concise Introduction to Mechanics of Rigid Bodies

2012·0.93 MB·English

by  L. Huang

A Concise Introduction to Mechanics
of Rigid Bodies

L. Huang
A Concise Introduction to
Mechanics of Rigid Bodies
Multidisciplinary Engineering
123
L.Huang
SchoolofEngineering
AucklandUniversityofTechnology
PrivateBag92006
1142Auckland
NewZealand
[email protected]
ISBN978-1-4614-0471-2 e-ISBN978-1-4614-0472-9
DOI10.1007/978-1-4614-0472-9
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2011940828
©SpringerScience+BusinessMedia,LLC2012
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ForXin,Zhongjia,and Zhongjin

Preface
Mechanics is a mature engineering subject. Why do we need another mechanics
book?
This book presents rigid-body mechanics in a compact form for a multidis-
ciplinary engineering program. Typically, such programs include mechatronics,
which covers mechanical engineering, electrical and electronic engineering, and
computer engineering, and biomechanics, which is related to human physiology,
sports, and engineering mechanics. In terms of course structure, they have the
followingfeatures:
• Awiderangeofsubjectsinvariousareasistaught.
• Limitedteachingtimeisallocatedtoeachsubject.
• Thereisasharptransitionfromfundamentaltospecializedsubjects.
Mechanics is one of the most important subjects in traditional mechanical
engineeringprograms.Itusuallytakestwosemesterstocoveralltherelevanttopics,
arranged in the following order: mechanics of particle motion (one dimension),
planar motion (two dimensions), and rigid body motion in space. In comparison,
thetimeallottedtotheteachingofmechanicsismuchshorterinamultidisciplinary
engineering program. It is hard to find a concise presentation of the material that
covers the essential principles of mechanics and that can be taught in a limited
time.
Many existing textbooksfocusalmost exclusivelyon the mechanicsof particle
and planar motions, which are easily visualized and can be readily analyzed with
geometrical and graphical methods. On the other hand, multibody dynamics in
three-dimensionalspaceisthecornerstoneofmanyspecializedcoursesinmultidis-
ciplinaryengineeringprograms(e.g.,robotics).Thereisahugegapbetweenwhatis
coveredintraditionaltextbooksonmechanicsandtherequirementsforspecialized
courses (e.g. [7] and [8]) on the motions of rigid bodies and complex systems in
three-dimensionalspace. Thusa book is needed that narrowsthe gap by focusing
onthemechanicsofrigidbodies,withparticlemotionandplanarmotionasspecial
cases.
vii
viii Preface
Themainmotivationforwritingthisbookwastoproduceaworkthatiscompact
butcomprehensiveinitscoverageoftheessentialprinciplesofrigid-bodydynamics.
Toachievethis,thefollowingapproacheswereadoptedinthebook:
• Thethree-dimensionaldynamicsofarigidbodyisdealtwithfromthebeginning
of the book to the end. Mechanics in relation to particle motion and planar
motionaretreatedasspecialcases.Thisisincontrasttothetraditional,sequential
coverageoftopics:particlemotion!motioninaline!planarmotion!three-
dimensionalmotion.
• Matrix and vector manipulationsare used extensivelyto make the presentation
concise and clear. This is in contrast to the traditional approach, which is
dominatedbyscalarandvectormanipulations.Thisisfineforlow-dimensional
motionbuttooclumsyfordescribingmotionsandmasspropertieswithrespect
to different reference frames. Matrix and vector notations can greatly simplify
mathematicalexpressionsandrevealtheessentialprinciplesgoverningmotions
in high dimensions; this is also in line with the general approach taken in
advanced specialized courses like roboticsand mechanisms. In this regard,the
reader is expected to be familiar with concepts and manipulations of vectors
andmatrices,whicharecoveredinundergraduatecourseslikelinearalgebraor
engineering mathematics. Chapter 1 of this book is designed for readers who
mightneedtoreviewthebasicsintherelevantareas.
• Theconceptsofobservationframeanddescriptionframeareintroducedandare
reflected by a set of new vector notations to define kinematic variables more
clearly.
The main parts of the book concern the description and analysis of position,
velocity and acceleration, inertial properties, and the establishment of equations
of motion throughthree main methods:Newton–Eulerformulation,D’Alembert’s
principle, and Lagrange equations. Some examples are taken from existing books
onengineeringmechanicsandbiomechanics.Theyareaddressedwiththemethod-
ologiesandapproachespresentedinthebook,andeachsteptoreachthesolutionis
painstakinglyandrigorouslyexplained.Therearenoquestionsetsforpracticeafter
each chapter since rich sourcesof questionscan be foundin manyexisting books
onmechanics(e.g.[3]and[5]).
Thoughsome importanttopicslike the impulse-momentummethod,collisions,
vibrations,andforwarddynamics(derivationofarigidbody’smotionfromforces
ortorques)arenotcoveredduetospaceconstraints,whatispresentedinthebook
should providea sufficientfoundationfor dealing with those topics. Statics is not
coveredhereeithersinceitcanbetreatedasaspecialcaseofdynamics.
Asanoteofclarification,dynamicsinthisbookmeansthestudyoftherelation
between changesin motion and the causes of those changes (forces and torques).
Insome books,thisis called kinetics,and dynamicsincludesboth kinematicsand
kinetics.
Preface ix
The book comprises the following chapters. Chapter 1 covers preliminary
mathematicalknowledgeneededtostudythebook.Itfocusesonvectorandmatrix
operations which has been discussed in [1] and [2]. Chapter 2 is on kinematics,
Chap.3isondynamics,andChap.4presentscasestudies.
Thebookissuitableforundergraduatesandpostgraduatestudentsinmultidisci-
plinaryengineeringprogramslikemechatronicsandbiomechanics.Itisalsosuitable
forstudentsinmechanicalengineeringandengineersandresearchersinterestedin
rigid-bodydynamics.