Investigation of Parallel Manipulators Using Linear Complex Approximation

Abstract

This investigation deals with singularity analysis of parallel manipulators and their instantaneous behavior while in or close to a singular configuration. The method presented utilizes line geometry tools and screw theory to describe a manipulator in a given position. Then, this description is used to obtain the closest linear complex, presented by its screw coordinates, to the set of governing lines of the manipulator. The linear complex axis and pitch provide additional information and a better physical understanding of the type of singularity and the motion the manipulator tends to perform in a singular point and in its neighborhood. Examples of Hunt’s, Fichter’s and 3-UPU singularities, along with a few selected examples taken from Merlet’s work [1], are presented and analyzed using this method.