Table Of ContentJaime Gallardo-Alvarado
Kinematic
Analysis of Parallel
Manipulators by
Algebraic Screw
Theory
Kinematic Analysis of Parallel Manipulators
by Algebraic Screw Theory
Jaime Gallardo-Alvarado
Kinematic Analysis
of Parallel Manipulators
by Algebraic Screw Theory
123
JaimeGallardo-Alvarado
DepartmentofMechanicalEngineering
InstitutoTecnologicodeCelaya
Celaya,Mexico
ISBN978-3-319-31124-1 ISBN978-3-319-31126-5 (eBook)
DOI10.1007/978-3-319-31126-5
LibraryofCongressControlNumber:2016939238
©SpringerInternationalPublishingSwitzerland2016
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Preface
Robotics is a prolific and intensive research field whose applications have had
a highly positive impact on both academia and industry. While old and modern
theoriesareappliedtosolvechallengingproblemsandimproveexistingsolutions,
mathematical models are currently used in the design, simulation, and control
of industrial robots. Certainly, the possibilities offered by robot manipulators are
immense,causingthevarietyofrobotdesignstocontinuetogrow,whichdemands
efficient and confident mathematical methods of analysis. It is noticeable that
despite the diversity of journals and books concerned with the study of robot
manipulators, there are particular issues that deserve to be deeply investigated
or in some cases elucidated in the light of modern kinematics; these include
singularitiesandhigher-orderkinematicanalysesofrobotmanipulators.Inthisarea,
contributionsapproachingthejerkandhyper-jerkanalysesofrobotmanipulatorsvia
screwtheoryareratherscarce,perhapsbecauseofthelackofpracticalapplications
or the lack of credibility about the validity of the equations in screw form of the
acceleration analysis of kinematic chains introduced almost two decades ago. In
thisbook,relevantfundamentalsofscrewtheoryconcerningtheso-calledfirst-order
kinematic analysis of a rigid body are carefully reviewed through the introduction
ofpropositionsthatareconfirmedthroughdetailedandexplicitproofs.Inaddition,
the acceleration, jerk, and hyper-jerk analyses of a rigid body are exhaustively
investigatedbytakingadvantageofthemethodoutlinedforthefirst-orderkinematic
analysis. Because of the recent successful introduction of parallel manipulators in
the industry, those mechanical devices are selected as the means to exemplify the
application of screw theory exposed in this book. With the material provided in
this book, readers can extend screw theory into the kinematics of optional order
of a rigid body and apply it to the analysis of parallel manipulators. Illustrative
examples and exercises to reinforce learning are provided. Of particular note, the
kinematics of emblematic parallel manipulators, such as the Delta robot as well
as the original Gough and Stewart platforms, are revisited. In addition to screw
theory, we apply new methods devoted to simplifying the corresponding forward
displacementanalysis,achallengingtaskformostparallelmanipulators.
vii
viii Preface
Thematerialpresentedinthisbookisbasedonresearchpublishedbytheauthor
over the last 20 years, including his doctoral dissertation developed at Instituto
TecnológicodelaLaguna,México,underthesupervisionofProf.JoséMaríaRico-
Martínez. To the author’s best knowledge, this is one of the first books devoted
to the higher-order kinematic analyses of a rigid body by screw theory and its
application to the study of mechanisms possessing parallel kinematic structures.
Theauthorisconfidentabouttheusefulnessofthematerialprovidedinthisbook,
whichrepresentsanexcellentargumenttoensurethatscrewtheoryisnotconfined
totheso-calledfirst-orderkinematicanalysis.Thematerialpresentedhereprovides
toolsforengineers,researchers,andstudentsdealingwiththekinematicsofparallel
manipulators.Asaconsiderationforreadersunfamiliarwithscrewtheory,thebook
contains a reasonable quantity of examples. Furthermore, as an unusual outcome,
fullanswerstoselectedexercisesareprovidedattheendofthevolume.
Celaya,GTO,Mexico JaimeGallardo-Alvarado
May2016
Acknowledgments
The author wishes to thank the support of two Mexican institutions: the Consejo
Nacional de Ciencia y Tecnología (CONACYT) and the Tecnológico Nacional
de México (TecNM). The author is especially indebted to Michael Luby, Editor,
Mechanical Engineering, Springer, for his advice and guidance in the preparation
of the final text. Also, Nicole Lowary and Brian Halm are to be thanked for the
assistancetheyprovidedduringthepublicationofthisbook.
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