Design and kinematics of a three-legged parallel manipulator

This paper investigates the kinematics and stiffness of an isotropic three-legged manipulator having six degrees of freedom. Rotary motors at the base rotate the tool by using the extensible legs as drive shafts. The manipulator has the positional stiffness of a parallel manipulator and the rotational stiffness of a serial manipulator. Low inertia results from having only three legs and having three motors fixed at the base. The inverse kinematics are obtained in closed form. Singularities are characterized for the case of concentric u-joints at the tool. These singularities yield the constraint singularities of a related 3-universal-prismatic-universal translational manipulator.