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The aim of this paper is to characterize the notion of aspect in theworkspace and in the joint space for parallel manipulators. In opposite to theserial manipulators, the parallel manipulators can admit not only multipleinverse kinematic solutions, but also multiple direct kinematic solutions. Thenotion of aspect introduced for serial manipulators in [Borrel 86], andredefined for parallel manipulators with only one inverse kinematic solution in[Wenger 1997], is redefined for general fully parallel manipulators. TwoJacobian matrices appear in the kinematic relations between the joint-rate andthe Cartesian-velocity vectors, which are called the "inverse kinematics" andthe "direct kinematics" matrices. The study of these matrices allow torespectively define the parallel and the serial singularities. The notion ofworking modes is introduced to separate inverse kinematic solutions. Thus, wecan find out domains of the workspace and the joint space exempt ofsingularity. Application of this study is the moveability analysis in theworkspace of the manipulator as well as path-planing and control. This study isillustrated in this paper with a RR-RRR planar parallel manipulator.

Working Modes and Aspects in Fully-Parallel Manipulator