Maximally Regular Planar Non Fully Parallel Manipulators

This paper presents a new family of maximally regular planar non fully parallel manipulators (PPMs). The moving platform has three planar degrees of freedom, which are two planar translations and one rotation around an axis perpendicular to the plane of translations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of the maximally regular PPMs is a 3×3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the maximally regular parallel robots perform very well with regard to force and motion transmission capabilities. The new kinematic criteria, used for structural synthesis, are based on the recent formulae proposed by the author for mobility, connectivity, redundancy and overconstraint of parallel robots. These kinematic criteria allow us to get new families of over constrained and non overconstrained maximally regular parallel robots with planar motion of the moving platform. The non fully-parallel solutions are presented for the first time in the literature.