Characteristic tetrahedron of wrench singularities for parallel manipulators with three legs

Abstract

A new analysis of wrench singularities is presented for spatial parallel platform manipulators consisting of three legs, with up to two actuators each, and connected to the mobile platform by spherical joints. The analysis also applies to some related manipulators with six legs, such as the 6-3 Gough-Stewart platform. The characteristic tetrahedron is introduced to identify wrench singularities, i.e. configurations where the platform can move infinitesimally with all actuators locked. An important theorem is presented that provides a geometric interpretation of wrench singularities: a manipulator is at a wrench singularity if and only if the characteristic tetrahedron is singular. All cases in which the tetrahedron becomes singular are enumerated, which leads to a classification of wrench singularities. This method is easy to visualize and presents an alternative to standard approaches using line geometry.