Determination of the Presence of Singularities in 6D Workspace of a Gough Parallel Manipulator

Abstract

Determining if singularities exist in the workspace of a parallel manipulator is an important step in the design of a parallel robot. Singularities are obtained when the posture-dependent determinant of the inverse jacobian matrix of the robot is equal to 0. This determinant is a complex function of the posture. We present an algorithm enabling to determine the presence of singularities in any type of workspace defined either by a geometrical object in the Euclidean space for the position of the end-effector and three ranges for the angles defining its orientation or by an hypercube in the 6-dimensional articular space. This algorithm is relatively fast and numerically robust.