Changes

'''Kinematics''' is the branch of [[classical mechanics]] which describes the [[motion (physics)|motion]] of points, bodies (objects) and systems of bodies (groups of objects) without looking at the cause of this motion.<ref name="Whittaker">

'''Kinematics''' is the branch of [[classical mechanics]] which describes the [[motion (physics)|motion]] of points, bodies (objects) and systems of bodies (groups of objects) without looking at the cause of this motion.<ref name="Whittaker">

{{cite book |title=A Treatise on the Analytical Dynamics of Particles and Rigid Bodies |author=Edmund Taylor Whittaker |url=http://books.google.com/books?id=epH1hCB7N2MC&printsec=frontcover&dq=inauthor:%22E+T+Whittaker%22&lr=&as_brr=0&sig=SN7_oYmNYM4QRSgjULXBU5jeQrA&source=gbs_book_other_versions_r&cad=0_2#PPA1,M1

{{cite book |title=A Treatise on the Analytical Dynamics of Particles and Rigid Bodies |author=Edmund Taylor Whittaker |url=https://books.google.com/books?id=epH1hCB7N2MC&printsec=frontcover&dq=inauthor:%22E+T+Whittaker%22&lr=&as_brr=0&sig=SN7_oYmNYM4QRSgjULXBU5jeQrA&source=gbs_book_other_versions_r&cad=0_2#PPA1,M1

|at=Chapter 1 |year=1904 |publisher=Cambridge University Press |isbn=0-521-35883-3}}</ref><ref name=Beggs>{{cite book |title=Kinematics |author=Joseph Stiles Beggs |page=1 |url=http://books.google.com/books?id=y6iJ1NIYSmgC&printsec=frontcover&dq=kinematics&lr=&as_brr=0&sig=brRJKOjqGTavFsydCzhiB3u_8MA#PPA1,M1 |isbn=0-89116-355-7 |year=1983 |publisher=Taylor & Francis}}</ref><ref name=Wright>{{cite book |title=Elements of Mechanics Including Kinematics, Kinetics and Statics|author=Thomas Wallace Wright |url=http://books.google.com/books?id=-LwLAAAAYAAJ&printsec=frontcover&dq=mechanics+kinetics&lr=&as_brr=0#PPA6,M1 |at=Chapter 1 |year=1896 |publisher=E and FN Spon}}</ref>  The term was translated from French; [[André-Marie Ampère|A.M. Ampère]] used the term ''cinématique''.<ref>{{cite book

|at=Chapter 1 |year=1904 |publisher=Cambridge University Press |isbn=0-521-35883-3}}</ref><ref name=Beggs>{{cite book |title=Kinematics |author=Joseph Stiles Beggs |page=1 |url=https://books.google.com/books?id=y6iJ1NIYSmgC&printsec=frontcover&dq=kinematics&lr=&as_brr=0&sig=brRJKOjqGTavFsydCzhiB3u_8MA#PPA1,M1 |isbn=0-89116-355-7 |year=1983 |publisher=Taylor & Francis}}</ref><ref name=Wright>{{cite book |title=Elements of Mechanics Including Kinematics, Kinetics and Statics|author=Thomas Wallace Wright |url=https://books.google.com/books?id=-LwLAAAAYAAJ&printsec=frontcover&dq=mechanics+kinetics&lr=&as_brr=0#PPA6,M1 |at=Chapter 1 |year=1896 |publisher=E and FN Spon}}</ref>  The term was translated from French; [[André-Marie Ampère|A.M. Ampère]] used the term ''cinématique''.<ref>{{cite book

   | last = Ampère

   | last = Ampère

   | first = André-Marie

   | first = André-Marie

   | title = Essai sur la Pilosophie des Sciences

   | title = Essai sur la Pilosophie des Sciences

   | publisher = Chez Bachelier

   | publisher = Chez Bachelier

   | url = http://books.google.com/books?id=j4QPAAAAQAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

   | url = https://books.google.com/books?id=j4QPAAAAQAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

}}</ref> He constructed the term form the [[Ancient Greek language|Greek]] {{lang|grc|κίνημα}}, '''kinema''' (movement, motion), derived from {{lang|grc|κινεῖν}}, '''kinein''' (to move).<ref>{{cite book

}}</ref> He constructed the term form the [[Ancient Greek language|Greek]] {{lang|grc|κίνημα}}, '''kinema''' (movement, motion), derived from {{lang|grc|κινεῖν}}, '''kinein''' (to move).<ref>{{cite book

   | last = Merz

   | last = Merz

   | year = 1903

   | year = 1903

   | pages = 5

   | pages = 5

   | url = http://books.google.com/books?id=toZJAAAAYAAJ&pg=PA5&lpg=PA5}}</ref><ref name= Bottema>{{cite book |title=Theoretical Kinematics |at=preface, p. 5 |url=http://books.google.com/books?id=f8I4yGVi9ocC&printsec=frontcover&dq=kinematics&lr=&as_brr=0&sig=YfoHn9ImufIzAEp5Kl7rEmtYBKc#PPR7,M1  |author=O. Bottema & B. Roth |isbn=0-486-66346-9 |publisher=Dover Publications |year=1990}}</ref> The study of ''kinematics'' is often referred to as the ''geometry of motion.''<ref name="various">See, for example: {{cite book

   | url = https://books.google.com/books?id=toZJAAAAYAAJ&pg=PA5&lpg=PA5}}</ref><ref name= Bottema>{{cite book |title=Theoretical Kinematics |at=preface, p. 5 |url=https://books.google.com/books?id=f8I4yGVi9ocC&printsec=frontcover&dq=kinematics&lr=&as_brr=0&sig=YfoHn9ImufIzAEp5Kl7rEmtYBKc#PPR7,M1  |author=O. Bottema & B. Roth |isbn=0-486-66346-9 |publisher=Dover Publications |year=1990}}</ref> The study of ''kinematics'' is often referred to as the ''geometry of motion.''<ref name="various">See, for example: {{cite book

|title=Engineering Mechanics: Dynamics |author=Russell C. Hibbeler |chapter=Kinematics and kinetics of a particle |url=http://books.google.com/books?id=tOFRjXB-XvMC&pg=PA298 |page=298 |isbn=0-13-607791-9 |year=2009 |edition=12th |publisher=Prentice Hall}},

|title=Engineering Mechanics: Dynamics |author=Russell C. Hibbeler |chapter=Kinematics and kinetics of a particle |url=https://books.google.com/books?id=tOFRjXB-XvMC&pg=PA298 |page=298 |isbn=0-13-607791-9 |year=2009 |edition=12th |publisher=Prentice Hall}},

{{cite book

{{cite book

|title=Dynamics of Multibody Systems |author=Ahmed A. Shabana |chapter=Reference kinematics |url=http://books.google.com/books?id=zxuG-l7J5rgC&pg=PA28 |edition=2nd |publisher=Cambridge University Press |year=2003 |isbn=978-0-521-54411-5}},

|title=Dynamics of Multibody Systems |author=Ahmed A. Shabana |chapter=Reference kinematics |url=https://books.google.com/books?id=zxuG-l7J5rgC&pg=PA28 |edition=2nd |publisher=Cambridge University Press |year=2003 |isbn=978-0-521-54411-5}},

{{cite book

{{cite book

|title=Mechanical Systems, Classical Models: Particle Mechanics |chapter=Kinematics |page=287 |url=http://books.google.com/books?id=k4H2AjWh9qQC&pg=PA287 |author=P. P. Teodorescu |isbn=1-4020-5441-6 |year=2007 |publisher=Springer}}

|title=Mechanical Systems, Classical Models: Particle Mechanics |chapter=Kinematics |page=287 |url=https://books.google.com/books?id=k4H2AjWh9qQC&pg=PA287 |author=P. P. Teodorescu |isbn=1-4020-5441-6 |year=2007 |publisher=Springer}}

</ref>

</ref>

To describe motion, kinematics studies the paths of points, [[line|lines]] and other [[geometry|geometric]] objects in [[Space (physics)|space]], and some of their properties such as [[velocity]] and [[acceleration]]. A[[astrophysics|strophysics]] uses kinematics to describe the motion of [[celestial bodies]] and systems. [[Mechanical engineering]], [[robotics]] and [[biomechanics]] use it  to describe the motion of systems composed of joined parts  such as an [[engine]], a robotic arm or the [[Human skeleton|skeleton]] of the [[human]] [[body]].<ref name="Biewener">{{cite book |title=Animal Locomotion |url=http://books.google.com/books?id=yMaN9pk8QJAC |author=A. Biewener |isbn=019850022X |publisher=Oxford University Press |year=2003}}</ref>

To describe motion, kinematics studies the paths of points, [[line|lines]] and other [[geometry|geometric]] objects in [[Space (physics)|space]], and some of their properties such as [[velocity]] and [[acceleration]]. [[Astrophysics]] uses kinematics to describe the motion of [[celestial bodies]] and systems. [[Mechanical engineering]], [[robotics]] and [[biomechanics]] use it  to describe the motion of systems composed of joined parts  such as an [[engine]], a robotic arm or the [[Human skeleton|skeleton]] of the [[human]] [[body]].<ref name="Biewener">{{cite book |title=Animal Locomotion |url=https://books.google.com/books?id=yMaN9pk8QJAC |author=A. Biewener |isbn=019850022X |publisher=Oxford University Press |year=2003}}</ref>

The study of kinematics can be abstracted into purely [[mathematical function]]s.  It is possible to represent [[rotation]] with elements of the [[unit circle]] in the [[complex plane]]. Other [[Non-Euclidean geometry#Planar algebras|planar algebras]] are used to represent the [[shear mapping]] of classical motion in [[absolute time and space]] and to represent the [[Lorentz transformation]]s of relativistic space and time.  Mathematicians have developed a science of [[Non-Euclidean geometry#Kinematic geometries|kinematic geometry]], which uses [[time]] as a parameter.

The study of kinematics can be abstracted into purely [[mathematical function]]s.  It is possible to represent [[rotation]] with elements of the [[unit circle]] in the [[complex plane]]. Other [[Non-Euclidean geometry#Planar algebras|planar algebras]] are used to represent the [[shear mapping]] of classical motion in [[absolute time and space]] and to represent the [[Lorentz transformation]]s of relativistic space and time.  Mathematicians have developed a science of [[Non-Euclidean geometry#Kinematic geometries|kinematic geometry]], which uses [[time]] as a parameter.

Certain  geometric transformations which are called  [[rigid transformation]]s have been developed to  describe the movement of components of a [[mechanical system]]. These transformations simplify the derivation of its equations of motion, and is central to [[Lagrangian mechanics|dynamic analysis]].

Certain  geometric transformations which are called  [[rigid transformation]]s have been developed to  describe the movement of components of a [[mechanical system]]. These transformations simplify the derivation of its equations of motion, and is central to [[Lagrangian mechanics|dynamic analysis]].

[[robot kinematics|Kinematic analysis]] is the process of measuring the [[Physical quantity|kinematic quantities]] used to describe motion.  In engineering, kinematic analysis may be used to find the range of movement for a given [[Mechanism (engineering)|mechanism]], and, working in reverse, [[Burmester theory|kinematic synthesis]] designs a mechanism for a desired range of motion.<ref name=McCarthy2010>J. M. McCarthy and G. S. Soh, 2010, [http://books.google.com/books?id=jv9mQyjRIw4C&pg=PA231&lpg=PA231&dq=geometric+design+of+linkages&source=bl&ots=j6TS1043qE&sig=R5ycw5DximWrQOEVshfiytflD6Q&hl=en&sa=X&ei=0Zj4TuiCFvCGsgKyvO3FAQ&ved=0CGAQ6AEwBQ#v=onepage&q=geometric%20design%20of%20linkages&f=false ''Geometric Design of Linkages,''] Springer, New York.</ref> <!-- I am not sure that these are the best examples:  The movement of a crane and the oscillations of a piston in an engine are both simple kinematic systems. The crane is a type of open kinematic chain, while the piston is part of a closed [[four-bar linkage]].--> In addition, ''kinematics'' applies algebraic geometry to the study of the [[mechanical advantage]] of a [[mechanical system]], or [[mechanism (engineering)|mechanism]].

[[robot kinematics|Kinematic analysis]] is the process of measuring the [[Physical quantity|kinematic quantities]] used to describe motion.  In engineering, kinematic analysis may be used to find the range of movement for a given [[Mechanism (engineering)|mechanism]], and, working in reverse, [[Burmester theory|kinematic synthesis]] designs a mechanism for a desired range of motion.<ref name=McCarthy2010>J. M. McCarthy and G. S. Soh, 2010, [https://books.google.com/books?id=jv9mQyjRIw4C&pg=PA231&lpg=PA231&dq=geometric+design+of+linkages&source=bl&ots=j6TS1043qE&sig=R5ycw5DximWrQOEVshfiytflD6Q&hl=en&sa=X&ei=0Zj4TuiCFvCGsgKyvO3FAQ&ved=0CGAQ6AEwBQ#v=onepage&q=geometric%20design%20of%20linkages&f=false ''Geometric Design of Linkages,''] Springer, New York.</ref> <!-- I am not sure that these are the best examples:  The movement of a crane and the oscillations of a piston in an engine are both simple kinematic systems. The crane is a type of open kinematic chain, while the piston is part of a closed [[four-bar linkage]].--> In addition, ''kinematics'' applies algebraic geometry to the study of the [[mechanical advantage]] of a [[mechanical system]], or [[mechanism (engineering)|mechanism]].

 

==References==

==References==

{{reflist}}

{{reflist}}

[[Category:Mecha

[[Category:Mechanics]]