Singularity analysis for six practicable 5-DoF fully-symmetrical parallel manipulators

Fully-symmetrical 5-DoF 3R2T parallel manipulator may be adopted in motion simulation for a spinal column. However, kinematics of these manipulators has not been studied very well because of their short history. Furthermore, the study of kinematics leads inevitably to the problem of singular configuration. Nowadays, there are six theoretically practicable manipulators among existent nearly seventy manipulators. Singularity for the six manipulators is illustrated with screw theory and Grassmann geometry in this study. The singularity classification defined by Fang and Tsai are adopted for its convenience for comprehension. In the singular analysis, methods to avoid them are also presented. In the rear part of the paper, singular configuration for a prototype 5-RRR(RR) is analyzed and illustrated as a mechanism example in detail with both symbol expression and numerical figure.