# Arm solution

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{{short description|Calculations needed to move a robot arm to a given position and orientation}}

In the engineering field of [robotics](/source/robotics), an '''arm solution''' is a set of calculations that allow the real-time computation of the [control](/source/Robot_control) commands needed to place the end of a [robotic arm](/source/robotic_arm) at a desired position and orientation in space.

A typical [industrial robot](/source/industrial_robot) is built with fixed length segments that are connected either at [joints](/source/Mechanical_joint) whose angles can be controlled, or along [linear slides](/source/Linear_actuator) whose length can be controlled. If each angle and slide distance is known, the position and orientation of the end of the robot arm relative to its base can be computed efficiently with simple [trigonometry](/source/trigonometry). 

Going the other way — calculating the angles and slides needed to achieve a desired position and orientation — is much harder. The mathematical procedure for doing this is called an '''arm solution'''. For some robot designs, such as the [Stanford arm](/source/Stanford_arm), [Vicarm](/source/Vicarm_Inc.) [SCARA robot](/source/SCARA_robot) or [cartesian coordinate robot](/source/cartesian_coordinate_robot)s, this can be done in [closed form](/source/Closed-form_expression). Other robot designs require an [iterative](/source/iterative_method) solution, which requires more computer resources.

==See also==
*[321 kinematic structure](/source/321_kinematic_structure)
* [Inverse kinematics](/source/Inverse_kinematics)
* [Motion planning](/source/Motion_planning)

==External links==
* [http://infolab.stanford.edu/pub/voy/museum/pictures/display/1-Robot.htm infolab.stanford.edu] - The Stanford Arm (1969), with a configuration such that the mathematical computations (arm solutions) were simplified to speed up computations
* [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.

Category:Robot kinematics
Category:Trigonometry

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