A screw theory basis for quantitative and graphical design tools that define layout of actuators to minimize parasitic errors in parallel flexure systems

In this paper we introduce a visual approach for placing actuators within multi-axis parallel flexure systems such that position and orientation errors are minimized. A stiffness matrix, which links twists and wrenches, is used to generate geometric shapes that guide designers in selecting optimal actuator locations and orientations. The geometric shapes, called actuation spaces, enable designers to (i) visualize the regions wherein actuators should be placed so as to minimize errors, (ii) guide designers in selecting these actuators to maximize the decoupling of actuator inputs, and (iii) determine actuator forces and displacements for actuating specific degrees of freedom. These new principles, the means to practice them, and a comparison of theory verses measured behavior, are demonstrated within a case study.