Direct and inverse kinematics of a highly parallel manipulator

A model of a parallel mechanism called the Double Tetrahedron was constructed. The model displayed more mobility than predicted. The increased mobility of the model was attributed to extra rotary joints inadvertently created by the design of the mechanism.;The mobility and workspace of this newly created mechanism, dubbed Tetradon, are examined qualitatively. The movement of Tetradon is described by the rigid body rotation and translation of one tetrahedron relative to another. A method to calculate Tetradon's joint coordinates based on this rotation and translation is presented. The underconstrained solution for Tetradon and the constrained solution for a modified version of Tetradon are given.;With a view toward applying Tetradon as a positioning mechanism, three different ways in which to calculate the direct kinematics of Tetradon are presented.;Complementing the direct kinematic solutions, a solution to the inverse kinematics of Tetradon is presented. A Newton-Gauss approximation scheme is applied to a set of constrained objective functions. The objective functions are used to maintain the intersection of the six edge pairs in the mechanism.