Kinematic analyses of a 1T2R and a 1T3R parallel mechanisms with closed-form position solutions

Two parallel mechanisms, a 1T2R (one translational motion and 2-DOF rotational motions) and a 1T3R (one translational motion and 3-DOF spherical motion), are proposed. The 1T2R mechanism consists of three sub chains. Specifically, the middle sub chain has a similar joint arrangement with a PRR serial mechanism. Two revolute joints located at the top plate are driven by two closed-chain linkages. Similarly, the 1T3R mechanism employs the same concept as the 1T2R mechanism. The 1T3R has one more closed linkage to actuate the distal revolute joint of a PRRR serial sub chain in the middle. Due to these linkage arrangements, both of these two mechanisms have closed-form forward and inverse position solutions. Kinematic modeling of these two mechanisms is performed and their kinematic analyses are investigated with respect to their workspace and kinematic isotropic characteristics. Finally, to verify the motion capability of the mechanisms, their simulators are developed.