| Summary: | The goal of this thesis is to develop an efficient finite element model of a particular micro-positioning(MP) system, known as the 3RRR Mechanism. MP systems are capable of delivering accurate and controllable motion in the micro-metre to sub-micrometre range. Conventional mechanisms, which are often composed of rigid links with pinned connections are prone to friction, backlash and stiction, which are magnified at small displacements. As such MP systems utilize a new structure known as the compliant mechanism. The structure of most compliant mechanisms is based on conventional mechanisms; however they are monolithic devices which utilize flexible elements, instead of pins, to transform the input to a useful output position.
One common flexible element found in compliant mechanisms is the right circular flexure hinge. The seminal work on flexure hinges was done by Paros and Weisbord(1965), the basis of which was to calculate compliance (the reciprocal of stiffness) in order to characterize the behaviour of the hinge when loaded. However they essentially modelled the flexure hinge as a 1-D beam, when it is in fact 3-D in nature. Researchers completing finite element models of MP systems and flexure hinges have extended the model to 2-D elements, still resulting in poor results when compared to experimental data.
The task of completing a full 3-D finite element model of a MP system, let alone a right circular flexure hinge, is a major computational effort. For instance, a full 3-D model of the 3RRR mechanism would require over 1,000,000 degrees of freedom(DOF) dedicated to the flexure hinges alone. A 2-D model requires approximately 45,000 DOF in total; however, this number is still regarded as large.
Given these facts, a new technique called the Equivalent Beam Methodology(EBM) has been developed to model the 3-D stiffness of any right circular flexure hinge with a low number of DOF. This method essentially maps the 3-D stiffness of the hinge to a number of 1-D beam elements. For comparison, the finite element model of the 3RRR mechanism which incorporates the beams of the EBM has under 300 DOF in total, and is more accurate than the 2-D model. This method is extremely accurate, easy to use, and has a very low number of DOF, which makes it suitable to many advanced finite element modelling analyses such as topographic optimization, dynamic and modal analysis.
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