Fully-isotropic Three-degree-of-freedom Parallel Wrists

This paper presents the structural synthesis of fully-isotropic parallel wrists (PWs) with three degrees of freedom. The mobile platform has 3 rotations (3R) driven by three actuators mounted on the fixed base. A method is proposed for structural synthesis of 3R-PWs with uncoupled motions and fully-isotropic based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the operational velocity space of the moving platform. The Jacobian matrix mapping the three vector spaces of 3R-PWs with uncoupled motions is a 3 times 3 diagonal matrix. We use the condition number and the manipulability ellipsoids for their performance analysis. The Jacobian matrix of the fully-isotropic 3R-PWs presented in this paper is the 3 times 3 identity matrix throughout their 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 fully-isotropic three-degree-of-freedom parallel wrists.