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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}}

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 ==

== 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}}   

[[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}}

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}}

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 ==

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[[Category:Mechanics]]

[[Category:Classical mechanics]]