Fully-Isotropic Over-Constrained Parallel Wrists with Two Degrees of Freedom

In this paper we present singularity-free fully-isotropic parallel wrists (PWs) with two degrees of freedom. The mobile platform has 2 rotations (2R) driven by two rotary actuators mounted on the base. A method is proposed for structural synthesis of 2R-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 external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of 2R-PWs with uncoupled motions is a diagonal 2×2 matrix. We use the condition number and the manipulability ellipsoids for their performance analysis. The Jacobian matrix of fully-isotropic 2R-PWs presented in this paper is the identity 2×2 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 singularity-free parallel wrists fully-isotropic throughout their entire workspace.

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