Xian - Wen Kong and Clement M Gosselin Kinematics and Singularity Analysis of a Novel Type of 3 - CRR 3 - DOF Translational Parallel Manipulator

A new three-degrees-of-freedom (3-DOF) translational parallel manipulator (TPM) with linear actuators, i.e., 3-CRR TPM, is first proposed. The rotation singularity analysis, the inverse kinematics, the forward kinematics, and the kinematic singularity analysis of the 3CRR TPM are then performed. The analysis shows that the proposed TPM has the following kinematic merits over previous TPMs. (1) The forward displacement analysis can be performed by solving a set of linear equations. (2) The Jacobian matrix of the TPM is constant. The inverse of the Jacobian matrix can be pre-calculated, and there is no need to calculate repeatedly the inverse of the Jacobian matrix in performing the forward displacement analysis and forward velocity analysis. (3) There is no rotation singularity. (4) There is no uncertainty singularity. (5) The TPM has a fewer number of links or joints. The geometric condition for a 3-CRR TPM to be isotropic is also revealed. Two additional kinematic merits exist for the isotropic 3-CRR TPM. The first is that an isotropic 3-CRR TPM is isotropic in its whole workspace. The second is that no calculation is needed in order to pre-determine the inverse of the Jacobian matrix. Finally, preliminary design considerations are presented. KEY WORDS—translational parallel manipulator, kinematics, singularity analysis, isotropic manipulator, screw theory, parallel mechanism