# 321 kinematic structure

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{{Short description|Robot arm design that allows inverse arm solution in closed form}}
[[File:Scheinman MIT Arm.agr.jpg|thumb|[Victor Scheinman](/source/Victor_Scheinman)'s MIT Arm, built for MIT's Artificial Intelligence Lab {{Circa|1972}}, the first arm designed with a 321 kinematic structure]]
'''321 kinematic structure''' is a design method for [robot](/source/robot)ic arms ([serial manipulator](/source/serial_manipulator)s), invented by Donald L. Pieper and used in most commercially produced robotic arms. The [inverse kinematics](/source/inverse_kinematics) of serial manipulators with six [revolute joint](/source/revolute_joint)s, and with three consecutive joints intersecting, can be solved in [closed form](/source/Closed-form_expression), i.e. a set of equations can be written that give the joint positions required to place the end of the arm in a particular position and orientation.<ref>[https://web.archive.org/web/20160924184009/http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD0680036 D. L. Pieper, The kinematics of manipulators under computer control]. PhD thesis, Stanford University, Department of Mechanical Engineering, 1968.</ref> An arm design that does not follow these design rules typically requires an [iterative algorithm](/source/iterative_algorithm) to solve the inverse kinematics problem.

The 321 design is an example of a 6R wrist-partitioned manipulator: the three wrist joints intersect, the two shoulder and elbow joints are parallel, the first joint intersects the first shoulder joint [orthogonal](/source/orthogonal)ly (at a right angle). Many other industrial robots, such as the [PUMA](/source/Programmable_Universal_Machine_for_Assembly), have a kinematic structure that deviates a little bit from the 321 structure. The offsets move the singular positions of the robot away from places in the workspace where they are likely to cause problems.

==References==
{{reflist}}

==External links==
*[https://web.archive.org/web/20100106074814/http://www.roble.info/robotics/serial/html/SerialRobots-1se4.html 321 Kinematic Structure]

Category:Robot kinematics

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Adapted from the Wikipedia article [321 kinematic structure](https://en.wikipedia.org/wiki/321_kinematic_structure) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/321_kinematic_structure?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.