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Line 27: + + + + − 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.+ − − 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, [https://books.google.com/books?id=jv9mQyjRIw4C&dq=geometric+design+of+linkages&pg=PA231 ''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]]. Line 40:
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KS update 1.3
'''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, or objects, and systems of bodies, or groups of objects, without looking at the cause of this motion.<ref>
{{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
* {{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
|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&q=kinematics |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&q=mechanics+kinetics |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}}
* {{cite book |title=Kinematics |author=Joseph Stiles Beggs |page=1 |url=https://books.google.com/books?id=y6iJ1NIYSmgC&q=kinematics |isbn=0-89116-355-7 |year=1983 |publisher=Taylor & Francis}}
* {{cite book |title=Elements of Mechanics Including Kinematics, Kinetics and Statics|author=Thomas Wallace Wright |url=https://books.google.com/books?id=-LwLAAAAYAAJ&q=mechanics+kinetics |at=Chapter 1 |year=1896 |publisher=E and FN Spon}}</ref>
== Etymology ==
The word was [[Translation|translated]] from [[French language|French]]. [[André-Marie Ampère|A.M. Ampère]] used the word ''cinématique''.<ref>{{cite book
| last = Ampère
| last = Ampère
| first = André-Marie
| first = André-Marie
|title=Mechanical Systems, Classical Models: Particle Mechanics |chapter=Kinematics |page=287 |chapter-url=https://books.google.com/books?id=k4H2AjWh9qQC&pg=PA287 |author=P. P. Teodorescu |isbn=978-1-4020-5441-9 |year=2007 |publisher=Springer}}
|title=Mechanical Systems, Classical Models: Particle Mechanics |chapter=Kinematics |page=287 |chapter-url=https://books.google.com/books?id=k4H2AjWh9qQC&pg=PA287 |author=P. P. Teodorescu |isbn=978-1-4020-5441-9 |year=2007 |publisher=Springer}}
</ref>
</ref>
== Overview ==
To describe [[motion]], kinematics studies the [[Path|paths]] of [[Point (geometry)|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 body|celestial bodies]] and systems.{{cn|date=December 2024}}
== Applications ==
[[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|mathematical functions]]. 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 of relativistic space and time.{{cn|date=December 2024}}
Mathematicians have developed a science of kinematic geometry, which uses [[time]] as a [[parameter]].{{cn|date=December 2024}} Some geometric transformations, called the ''rigid transformations'', have been developed to describe the movement of components of a mechanical system. Such transformations simplify the derivation of its equations of motion and is central to dynamic analysis.{{cn|date=December 2024}}
Kinematic analysis is the process of measuring the kinematic quantities{{clarification|date=December 2024}} used to describe motion.{{cn|date=December 2024}} In engineering, kinematic analysis may be used to find the range of movement for a given mechanism. Reversely, kinematic synthesis enables the design of 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&dq=geometric+design+of+linkages&pg=PA231 ''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.{{clarification|date=December 2024}}{{cn|date=December 2024}}
== Kinematics Media ==
== Kinematics Media ==
File:Relative velocity.svg|Relative velocities between two particles in classical mechanics.
File:Relative velocity.svg|Relative velocities between two particles in classical mechanics.
File:Velocity Time physics graph.jpg|Velocity Time physics graph
File:Velocity Time physics graph.svg|Velocity Time physics graph
File:Nonuniform circular motion.svg|Nonuniform circular motion
File:Nonuniform circular motion.svg|Nonuniform circular motion