Beam-based analysis of flexure mechanisms: increasing computational efficiency, accuracy and design freedom

Abstract

The use of beam elements with constant cross-section limits the design freedom. This thesis presents a formulation for beam elements with a varying cross-section, to allow for the analysis of non-prismatic flexures. Design optimizations of several flexure joints shows that this extra design freedom can result in significantly better flexure joints.Flexure joints contain parts which connect the flexures to each other. Although these socalled frame parts are intended to be very stiff, their compliance can significantly decrease the overall support stiffness of the flexure joints, reducing the performance. An accurate evaluation of the performance requires the stiffness of the frame parts to be modelled. However, frame parts typically have complex shapes, such that they can barely be modelled using beam elements. This thesis formulates a superelement by which complex shaped parts can be modelled efficiently. Examples show that flexure joints can be modelled efficiently and accurately by using the superelement to model frame parts and using beam elements to model the flexures.Very complex flexure-based mechanisms can be analysed more efficiently and more accurately by using the methods and elements that are introduced in this thesis. This may help the development of new flexure mechanisms, increasing the potential for using flexure mechanisms in practice.