Structural synthesis of fully-isotropic parallel robots with Schِnflies motions via theory of linear transformations and evolutionary morphology

The paper presents structural synthesis of fully-isotropic parallel robotic manipulators (PMs) with Schِnflies motions. The moving platform of a parallel manipulator with Schِnflies 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 and the evolutionary morphology. 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 4 × 4 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. The synthesis method proposed in this paper allows us to obtain structural solutions of PMSMs with decoupled and uncoupled motions, along with the fully-isotropic solutions in a systematic manner. Overconstrained/isostatic solutions with elementary/complex and identical/different legs are obtained. Uncoupled and fully-isotropic PMSMs have the advantage of simple command and important energy-saving due to the fact that, for a unidirectional motion, only one motor works as in a serial translational manipulator.