The Inverse Kinematics of a Three-Cylindric Robot

Abstract

This article presents solutions to the inverse kinematic prob lems of a three-axis robot with three cylindric joints. Since a cylindric joint has two degrees of freedom, the end effector will have six degrees of freedom in general. Therefore, the robot can position and orient the end effector at a specified location within the work space. An important feature of the robot is that the rotational components of the end effector displacement are completely decoupled from the translational components of displacement. This eliminates the need for compensation from the orienting mechanism when position ing the end effector. The inverse of a 3 × 3 dual-Jacobian matrix is introduced and used to obtain closed-form solutions to the inverse velocity and acceleration problems. This is believed to be an original contribution to the robotics litera ture, and it is hoped that the method will provide a meaning ful alternative to existing methods for formulating the inverse kinematic problems of robots. For illustrative purposes, we include a potential application of the three-cylindric robot as a flexible worktable that could be used in a cooperating multiple-robot work cell.