Forward kinematic problem and constant orientation workspace of 5-RP̲RRR (3T2R) parallel mechanisms

This paper investigates some kinematic properties of a five-degree-of-freedom parallel mechanism generating the 3T2R motion and comprising five identical limbs of the RP̲UR type. In this study, two classes of simplified designs are proposed whose forward kinematic problems have either a univariate or a closed-form solution. The principal contributions of this study are the solution of the forward kinematic problem for some simplified designs—which may have more solutions than the FKP of the general 6-DOF Stewart platform with 40 solutions—and the determination of the constant orientation workspace based on algebraic geometry (Bohemian domes).