On the kinematics of the 3-RRUR spherical parallel manipulator

In the present paper, the kinematics of a three-degree-of-freedom spherical wrist is investigated. The wrist consists of a fixed base connected to a moving platform by three identical legs, each with a RRUR chain (R and U denote a revolute pair and a universal pair, respectively). For each leg, the first R pair is to be considered actuated. Although in previous works the kinematics synthesis of this architecture was carried out, no detailed studies were presented on the kinematic issues of the wrist. This paper presents the mobility analysis, the direct and inverse position kinematics, the differential kinematics of the manipulator including inspection on the jacobian matrix and the analysis of the singularities. The geometrical condition matched in case of mechanical interference between legs is addressed, too. A numerical example of the manipulator kinematics was performed to obtain the workspace, the condition number and the mechanical inteference condition.