The paper presents T1R3-type fully-isotropic redundantly-actuated parallel manipulators (PMs) with four degrees of freedom. The mobile platform has one independent translation (T1) and three independent rotations (R3). A method is proposed for structural synthesis of fully-isotropic redundantly-actuated TlR3-type PMs 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 fully-isotropic T1R3-type PMs presented in this paper is 4×4 identity 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. Redundant actuation is used to obtain fully-isotropic solutions. As far as we are aware, this paper presents for the first time in the literature the use of redundancy to design fully-isotropic T1R3-type PMs.
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