| Central to many manipulator positional control schemes is a requirement to invert the forward kinematic equations which model the given manipulator. It is shown in this thesis that for manipulator types where a common wrist center exists, a simplified Jacobian form is feasible and its inversion can be used in place of inverse kinematic solutions for positional control. The Jacobian simplification is obtained by decoupling of the wrist member from the positional member, resulting in a Jacobian inversion involving the solution of two sets of three equations with three unknowns. Within the development of the alternate Jacobian form, a technique for substituting incremental rotations with incremental translations is introduced yielding better insight into the Jacobian structure. A requirement for small moves is validated with a discussion of a proposed positional control strategy and a comprehensive example is presented as a summary of the results. |
