Resolving Redundancy of Series Kinematic Chains through Imaginary Links

A new approach of redundancy resolution for dexterous robots intended for the operations in clustered areas is proposed. These robots are modeled by series kinematic chains with a high number of degrees of freedom and are described by underdetermined systems of kinematic equations. The inverse problem has therefore an infinite number of solutions. The basic idea of the proposed approach is to for complement this system with some simple geometrical equations, which take the real existing decrease of the robot flexibility because of the tasks and/or workspace properties into consideration. That is done by the addition of a corresponding number of imaginary links to the redundant open kinematic chain. The resulted multi-loop kinematic structure is no more redundant. It has a simple structure and for many practical relevant kinematic chains with parallel and/or perpendicular joint axes admit an exact symbolic solution of the inverse kinematics in a closed form.