Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations

The paper presents a new structural synthesis approach of fully-isotropic translational parallel robotic manipulators (TPMs) based on the theory of linear transformations. A TPM is a 3-DOF (degree of freedom) parallel mechanism whose output link, called platform, can achieve three independent orthogonal translational motions with respect to the fixed base. The manipulators presented in this paper have three legs connecting the moving platform and the base (fixed platform). Only one kinematic pair per leg is actuated by a linear motor situated on the fixed base. A one-to-one correspondence exists between the actuated joint space and the operational space of the moving platform. The Jacobian matrix of fully-isotropic TPMs presented in this paper is the identity 3 × 3 diagonal matrix throughout the entire workspace. The synthesis method proposed in this paper allows us to obtain all structural solutions of fully-isotropic TPMs in a systematic manner. Overconstrained/isostatic solutions with elementary/complex and identical/different legs are obtained. Fully-isotropic TPMs have the advantage of simple command and important energy-saving due to the fact that, for a unidirectional translation, only one motor works as in a serial translational manipulator.