Type synthesis of 3-DOF translational compliant parallel mechanisms

In this paper, we apply screw theory to the type synthesis of compliant parallel mechanisms (PMs). Compliant PMs are formed by a moving stage supported by three or more limbs each of which is a serial chain of flexure joints and rigid bodies. They achieve movement through the deformation of flexure joints and have been widely used in precision machinery. As an important task in the conceptual design stage, the goal of type synthesis is to determine the chain of each limb as well as their relationship when they are assembled in parallel for a prescribed motion pattern. Our approach starts with a category of commonly used flexure primitives and flexure elements whose freedom and constraint spaces are characterized by twists and wrenches in screw theory. Following the well-studied synthesis procedure for rigid body PMs, we propose a synthesis procedure for compliant PMs via screw theory. This procedure consists of four basic steps: decomposition of the screw system of the constraint space, type synthesis of limbs, assembling limbs and design of flexure joints. As an example, we demonstrate the procedure for synthesizing compliant PMs for three degree-of-freedom (DOF) translational motions. Tables of limbs, types and geometric conditions for the assemblies of these limbs are presented. The paper provides a catalogue of compliant PM designs with three translational motions. At last, we provide a case study of applying finite element simulation to validate one of the synthesized designs.