used herein the term u201c work joint u201d should be understood to mean one or more work joints as the application would require for a linkage naturally in a closed form the work joints 52 may be actual joints 16 not virtual joints 54 an example of a linkage where the effector is not the final link is a stewart gough platform for example as used in flight simulators and the like where intermediate joints in the chain support the platform referring still to fig2 the mathematical description of the articulated linkage 12 in a preferred embodiment may describe the position of each joint 16 as a mathematical screw t i where the subscript i represents the number of the joint 16 discussed above referring momentarily to fig3 a mathematical screw provides for a screw axis 56 having a defined orientation in three space and a pitch 58 describing the axial separation between periodic loops of a helical trajectory 59 around the axis 56 for a typical revolute joint the pitch 58 will be zero and for a prismatic joint the reciprocal of the pitch will be zero the mathematical screw t i may be defined for example by plucker coordinates providing for a vector 61 aligned with axis 56 for example a unit vector defined by three scalars and extending from an axis point 60 defined by three point coordinate scalars.