Editing Inverse kinematics (section)

==Kinematic analysis==
[[File:Modele cinematique corps humain.svg|thumb|upright|A model of the human skeleton as a kinematic chain allows positioning using inverse kinematics.]]
Kinematic analysis is one of the first steps in the design of most industrial robots. Kinematic analysis allows the designer to obtain information on the position of each component within the mechanical system. This information is necessary for subsequent dynamic analysis along with control paths.

Inverse kinematics is an example of the kinematic analysis of a constrained system of rigid bodies, or [[kinematic chain]].  The [[kinematic equations]] of a robot can be used to define the loop equations of a complex articulated system.  These loop equations are non-linear constraints on the configuration parameters of the system.  The independent parameters in these equations are known as the [[degrees of freedom (mechanics)|degrees of freedom]] of the system.

While analytical solutions to the inverse kinematics problem exist for a wide range of kinematic chains, computer modeling and animation tools often use [[Newton's method]] to solve the non-linear kinematics equations.<ref name=":0" /> When trying to find an analytical solution it is often convenient to exploit the geometry of the system and decompose it using [[Paden–Kahan subproblems|subproblems with known solutions]].<ref>{{Cite thesis |title=Kinematics and Control of Robot Manipulators |url=https://ui.adsabs.harvard.edu/abs/1985PhDT........94P |date=1985-01-01 |first=Bradley Evan |last=Paden|bibcode=1985PhDT........94P }}</ref><ref>{{Cite book |last1=Murray |first1=Richard M. |url=https://books.google.com/books?id=D_PqGKRo7oIC&q=murray+li+sastry |title=A Mathematical Introduction to Robotic Manipulation |last2=Li |first2=Zexiang |last3=Sastry |first3=S. Shankar |last4=Sastry |first4=S. Shankara |date=1994-03-22 |publisher=CRC Press |isbn=978-0-8493-7981-9 |language=en}}</ref>

Other applications of inverse kinematic algorithms include [[interactive manipulation]], [[animation control]] and [[Collision detection|collision avoidance]].