Closed-Form Direct Kinematics Solution of a New Parallel Minimanipulator

Abstract

Closed-form direct kinematics solution of a new three-limbed six-degree-of-freedom minimanipulator is presented. Five-bar linkages and inextensible limbs are used in synthesis of the minimanipulator to improve its positional resolution and stiffness. All of the minimanipulator actuators are base-mounted. Kinematic inversion is used to reduce the direct kinematics of the mimimanipulator to an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the moving platform. Hence, the maximum number of assembly configurations for the minimanipulator is sixteen. Furthermore, it is proved that the sixteen solutions are eight pairs of reflected configurations with respect to the plane passing through the lower ends of the three limbs. A numerical example is also presented and the results are verified by an inverse kinematics analysis.