Editing Inverse kinematics (section)

==Robotics==
In robotics, inverse kinematics makes use of the [[kinematics]] equations to determine the joint parameters that provide a desired configuration (position and rotation) for each of the robot's [[Robot end effector|end-effectors]].<ref>{{cite book | last = Paul  | first = Richard  | title = Robot manipulators: mathematics, programming, and control : the computer control of robot manipulators  | publisher = MIT Press, Cambridge, MA  | year = 1981  | url = https://books.google.com/books?id=UzZ3LAYqvRkC  | isbn =978-0-262-16082-7
}}</ref> This is important because robot tasks are performed with the end effectors, while control effort applies to the joints. Determining the movement of a robot so that its end-effectors move from an initial configuration to a desired configuration is known as [[motion planning]].  Inverse kinematics transforms the motion plan into joint [[actuator]] trajectories for the robot.<ref name=":0" /> Similar formulas determine the positions of the skeleton of an [[character animation|animated character]] that is to move in a particular way in a film, or of a vehicle such as a car or boat containing the camera which is shooting a scene of a film. Once a vehicle's motions are known, they can be used to determine the constantly-changing viewpoint for computer-generated imagery of objects in the landscape such as buildings, so that these objects change in [[Perspective (graphical)|perspective]] while themselves not appearing to move as the vehicle-borne camera goes past them.

The movement of a [[kinematic chain]], whether it is a robot or an animated character, is modeled by the kinematics equations of the chain.  These equations define the configuration of the chain in terms of its joint parameters.  [[Forward kinematics]] uses the joint parameters to compute the configuration of the chain, and inverse kinematics reverses this calculation to determine the joint parameters that achieve a desired configuration.<ref>J. M. McCarthy, 1990, ''Introduction to Theoretical Kinematics,'' MIT Press, Cambridge, MA.</ref><ref name=Uicker2003>J. J. Uicker, G. R. Pennock, and J. E. Shigley, 2003, '''Theory of Machines and Mechanisms,''' Oxford University Press, New York.</ref><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>