321 kinematic structure

<p>321 kinematic structure is a design method for <a href="/facts/Robot/S5mDzWYk">robotic</a> arms (<a href="/facts/Serial_manipulator/KflAgqNM">serial manipulators</a>), invented by Donald L. Pieper and used in most commercially produced robotic arms. The <a href="/facts/Inverse_kinematics/VzEVGnNy">inverse kinematics</a> of serial manipulators with six <a href="/facts/Revolute_joint/GvmPuln9">revolute joints</a>, and with three consecutive joints intersecting, can be solved in <a href="/facts/Closed-form_expression/y0xCXlSk">closed form</a>, 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. An arm design that does not follow these design rules typically requires an <a href="/facts/Iterative_algorithm/uKMAJhEh">iterative algorithm</a> to solve the inverse kinematics problem.
</p><p>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 <a href="/facts/Orthogonal/JVIjYPog">orthogonally</a> (at a right angle). Many other industrial robots, such as the <a href="/facts/Programmable_Universal_Machine_for_Assembly/NYqcuxkh">PUMA</a>, 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.
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321 kinematic structure