Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators
Author:
Wang Jing1, Gosselin Cle´ment M.1
Affiliation:
1. De´partement de Ge´nie Me´canique, Universite´ Laval, Que´bec, Que´bec, Canada, G1K 7P4
Abstract
In this paper, the singularity loci of a special class of spherical 3-DOF parallel manipulators with prismatic actuators are studied. Concise analytical expressions describing the singularity loci are obtained in the joint and in the Cartesian spaces by using the expression of the determinant of the Jacobian matrix and the inverse kinematics of the manipulators. It is well known that there exist three different types of singularities for parallel manipulators, each having a different physical interpretation. In general, the singularity of type II is located inside the Cartesian workspace and leads to the instability of the end-effector. Therefore, it is important to be able to identify the configurations associated with this type of singularity and to find their locus in the space of all configurations. For the class of manipulators studied here, the six general cases and the five special cases of singularities are discussed. It is shown that the singularity loci in the Cartesian space (defined by the three Euler angles) are six independent planes. In the joint space (defined by the length of the three input links), the singularity loci are quadric surfaces, such as hyperboloid, sphere or a degenerated line or a degenerated circle. In addition, the three-dimensional graphical representations of the singular configurations in each of the general and special cases are illustrated. The description of the singular configurations provided here has great significance for robot trajectory planning and control.
Publisher
ASME International
Subject
Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials
Reference24 articles.
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