Singularity-free fully-isotropic parallel manipulators with Schonflies motions

In this paper we present a new family of singularity-free fully-isotropic parallel manipulators with Schonflies motions. The moving platform of a parallel manipulator with Schonflies motions (PMSM) has four degrees of freedom, which are three independent translations and one rotation about an axis of fixed direction. A method is proposed for structural synthesis of fully-isotropic PMSMs based on the theory of linear transformations. 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 fully-isotropic PMSMs presented in this paper is the identity 4times4 matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware, the family of 8750 solutions of singularity-free fully-isotropic PMSMs introduced in this paper is presented for the first time in the literature. These solutions are derived from a family of PMSMs with decoupled motions and elementary legs also presented for the first time