Synthesis of Actuation Spaces of Multi-Axis Parallel Flexure Mechanisms Based on Screw Theory

This paper introduces an approach for synthesis of actuation spaces of multi-axis parallel flexure mechanisms. The concept of actuation space, first proposed by J. Hopkins and M. Culpepper, is developed from constraint and freedom space, which are two fundamental concepts in constraint-based method. Within the framework of screw theory, actuation and constraint can be represented mathematically by a wrench, and freedom can be depicted by a twist. A Compliance matrix is provided to set the relationship between constraint wrenches and actuation forces in view that such an important rule as “actuation forces are linear independent of constraint wrenches”. Developed from this design rule, a synthesis criterion of actuation space of flexure systems is promoted to select suitable actuators. As a result, this synthesis criterion enable designers to (i) formulate the actuation space systematically in the format of screws or screw system, (ii) determine actuator placement according to the requirement of minimizing the interference between actuation forces and constraint wrenches. Synthesis procedures and selective examples are discussed in details.