Editing Inverse kinematics (section)

{{short description|Computing joint values of a kinematic chain from a known end position}}
[[File:FWDvsINV Kinematics HighResTransp.png|thumb|upright=1.6|Forward vs. inverse kinematics]]

In [[computer animation]] and [[robotics]], '''inverse kinematics''' is the mathematical process of calculating the variable [[Kinematic pair|joint]] parameters needed to place the end of a [[kinematic chain]], such as a robot [[Manipulator (device)|manipulator]] or [[skeletal animation|animation character's skeleton]], in a given position and orientation relative to the start of the chain. Given joint parameters, the position and orientation of the chain's end, e.g. the hand of the character or robot, can typically be calculated directly using multiple applications of [[Trigonometric functions|trigonometric formulas]], a process known as [[forward kinematics]]. However, the reverse operation is, in general, much more challenging.<ref>[https://web.archive.org/web/20160924184009/http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD0680036 Donald L. Pieper, The kinematics of manipulators under computer control]. PhD thesis, Stanford University, Department of Mechanical Engineering, October 24, 1968.</ref><ref name=":0">{{Cite book |last1=Lynch |first1=Kevin M. |url=https://books.google.com/books?id=5NzFDgAAQBAJ |title=Modern Robotics |last2=Park |first2=Frank C. |date=2017-05-25 |publisher=Cambridge University Press |isbn=978-1-107-15630-2 |language=en}}</ref><ref>{{Cite book |last1=Siciliano |first1=Bruno |url=https://books.google.com/books?id=QbgKkAEACAAJ |title=Springer Handbook of Robotics |last2=Khatib |first2=Oussama |date=2016-06-27 |publisher=Springer International Publishing |isbn=978-3-319-32550-7 |language=en}}</ref>

Inverse kinematics is also used to recover the movements of an object in the world from some other data, such as a film of those movements, or a film of the world as seen by a camera which is itself making those movements. This occurs, for example, where a human actor's filmed movements are to be [[motion capture|duplicated by an animated character]].