Colloquia

Summary

Flexure mechanisms offer a great alternative for conventional hinges and linear guides in high precision applications. They provide highly predictable and repeatable movement, but generally have a low support stiffness. The SPACAR program developed at the Faculty of Engineering Technology of the University of Twente is specialized in modelling the behaviour of such flexure mechanisms. It is often desirable to optimize the design of a flexure mechanism. The optimization method should provide the best possible design, while complying with the set bounds and constraints. The property that defines the performance of the design is defined as the objective function, which for flexure mechanisms is often the first parasitic eigen frequency or support stiffness. Succesful optimizations of in SPACAR modelled mechanisms have been performed. This was usually done with the Nelder-Mead optimization algorithm. This is an easy to implement and gradient free algorithm. However it is slow compared to gradient based algorithms and above 6-8 design variables, the algorithm is not viable.

In this research, optimization with gradient based algorithms is explored, in which finite differences are used to determine gradients. One key aspect was improving the accuracy of the finite differences. Maintaining continiously differentiables functions for the objective function and all constraints throughout the design space was also an important consideration.

The resulting optimization approach is demonstrated on a reinforced cartwheel hinge, which was succesfully optimized with 25 design variables.