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This paper concerns kinematics and dimensional synthesis of a three universal-revolute-universal (3-URU) pure rotational parallel mechanism. The mechanism is composed of a base, a platform and three symmetric limbs consisting of U-R-U joints. This mechanism is a spatial non-overconstrained mechanism with three degrees of freedom. The joints in each limb are so arranged to perform pure rotational motion of the platform around a specific point. Equations for inverse displacement analysis and singularities were derived to investigate the relationship of the kinematic constants to the solution of the inverse kinematics and singularities. Based on the results, a dimensional synthesis procedure for the 3-URU parallel mechanism considering singularities and the workspace was proposed. A numerical example was also presented to illustrate the synthesis method.

Kinematic Analysis and Synthesis of a 3-URU Pure Rotational Parallel Mechanism with Respect to Singularity and Workspace