Type synthesis of freedom and constraint elements for design of flexure mechanisms

In this paper, we present the type synthesis of freedom and constraint elements for design of general flexure mechanisms. As an important step in the conceptual design stage, the goal of type synthesis is to qualitatively determine the topology or connectivity of flexure elements and rigid bodies in a mechanism. The synthesis procedure presented here is based on a recently emerging screw theory based approach for flexure mechanisms. We first categorize a list of commonly used atomic flexure primitives including blades, wires, notches and bellow springs etc. We then derive their twist and wrench matrices that mathematically represent their freedom and constraint spaces. The synthesis procedure rigorously follows screw algebra. Freedom elements including R-joints and P-joints are defined as basic motion elements that allow a single rotation or a single translation. By using parallel structures of these flexure primitives, eleven designs of R-joints and eight designs of P-joints are systematically synthesized. As a duality, constraint elements including P-constraints and R-constraints remove a single translation or rotation. In contract to freedom elements, we synthesized serial chains of flexure primitives and obtained six designs of P-constraints and three designs of R-constraints. These freedom and constraint elements form a catalogue of basic building blocks for designing more complex flexure mechanisms. At last we utilize four design examples to demonstrate how to synthesize hybrid structures with serial and parallel combination of these elements.