Synthesis of parallel flexure stages with decoupled actuators using sum, intersection, and difference of screw systems

Abstract

Parallel flexure systems (PFS) are used in high-precision positioning systems for a wide range of scientific, medical, and industrial applications. The controllability of the flexure system is optimized when actuators are decoupled and the output of any actuator does not affect the output of the others. In this paper, Screw Theory and Linear Algebra are used to perform the synthesis of parallel flexure systems. New procedures to compute the sum, intersection, and difference of screw systems are presented. These three operations are used to formulate the synthesis of PFS with decoupled actuators completely in terms of the freedom screw systems in combination with a graph representation of the mechanism and the implementation of constraint systems using Blanding´s rules. The methodology is illustrated with the design and redesign of three case studies: (i) a 2-DOF platform with cylindrical motion, (ii) three 3-DOF tip-tilt-piston platforms, and (iii) a 3-DOF platform with planar motion. The kinematic and static analyses for the solutions are performed analytically and then validated using finite element analyses. The designed PFS have very simple structures, high precision, and controllability.