Fully-isotropic over-constrained planar parallel manipulators

In this paper we present singularity-free fully-isotropic planar parallel manipulators (PPMs) with three degrees of mobility. The moving platform has three planar degrees of freedom (DoFs), which are two planar translations and one rotation around the axis perpendicular to the plane of translations. A method is proposed for structural synthesis of four families of fully-isotropic PPMs 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 PPMs presented in this paper is the identity 3 × 3 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 this paper presents for the first time solutions of singularity-free fully-isotropic PPMs.