Fully-isotropic parallel manipulators with Schonflies motions and complex legs with rhombus loops

This paper presents a new family of fully-isotropic parallel manipulators with Schonflies motions and complex legs containing up to m rhombus loops. 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 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 4x4 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 14 m(4) solutions of fully-isotropic PMSMs introduced in this paper is presented for the first time in the literature. These solutions are derived from a family of 7m(4) PMSMS with decoupled motions and complex legs with rhombus loops also presented for the first time.