Automatic kinematic alignment of flexures in parallel mechanisms

Compliant mechanisms offer a number of benefits over sliding joint based mechanisms; however, their design is more complicated. As a result multiple design methods have been developed to assist with the design of compliant mechanisms. The kinematic FACT method assists in the manual design of mechanisms but has seen limited use in computational optimization. This research presents an alternative kinematics based computational optimization approach towards the automatic placement of a chosen set of flexures in 3D space such that a desired constraint space is obtained while minimizing the redundancy of constraints within a parallel spatial mechanism. A continuous measure for vector space misalignment is developed and utilized in a cost function optimization to manipulate the coordinate frame transformation of screws associated with flexural building blocks. This continuous measure is also used to formulate constraints for the cost function optimization. The approach is tested in three design cases within a limited design volume: a spherical hinge composed of wire flexures, a single rotation degree of freedom (DOF) hinge composed of leaf flexures and a parallel mechanism with three non-intersecting rotational DOFs consisting of wire flexures. The flexures are introduced and optimized sequentially and kinematically valid designs are obtained. This research is a stepping stone towards the development of a more general automatic 3D building block based synthesis approach for compliant mechanisms.