1 Department of Mathematics, Technical University of Denmark2 Department of Applied Mathematics and Computer Science, Technical University of Denmark
This thesis deals with computer-based methodologies for designing articulated mechanisms. An articulated mechanism consists of several links (or bars) connected by joints and it gains all of its mobility from the joints. This is in contrast to a compliant mechanism which is a different type of mechanism that gains some or all of the mobility from the elasticity of its components. A truss ground-structure approach is taken for the optimization of such mechanisms. This allows for an efficient analysis of the properties of the mechanism and is a suitable basis for an optimization procedure that handles topological variations. In this thesis the technique is also extended so as to design the shape as well as the topology of the truss using cross-sectional areas and nodal positions as design variables. This leads to a technique for simultaneous type and dimensional synthesis of articulated mechanisms. A critical issue for designing articulated mechanisms is geometric non-linearity in the kinematics. This should be considered for the analysis of mechanisms since the displacements of mechanisms are intrinsically large. The consideration of geometric non-linearity, however, causes numerical difficulties relating to the non-convexity of the potential energy defining the equilibrium equations. It is thus essential to implement a numerical method that can – in a consistent way – detect a stable equilibrium point; the quality of the equilibrium analysis not only is important for itself but also directly affects the result of the associated sensitivity analysis. Another critical issue for mechanism design is the concept of mechanical degrees of freedom and this should be also considered for obtaining a proper articulated mechanism. The thesis treats this inherently discrete criterion in some detail and various ways of handling constraints related to mechanical degrees of freedom are suggested. The thesis consists of the following four parts corresponding to the four thesis papers that are the main material of the thesis: 1. Graph-theoretical enumeration [Paper 1] 2. Gradient-based local optimization [Paper 2] 3. Branch and bound global optimization [Paper 3] 4. Path-generation problems [Paper 4] In terms of the objective of the articulated mechanism design problems, the first to third papers deal with maximization of output displacement, while the fourth paper solves prescribed path generation problems. From a mathematical programming point of view, the methods proposed in the first and third papers are categorized as deterministic global optimization, while those of the second and fourth papers are categorized as gradient-based local optimization. With respect to design variables, only cross-sectional areas are used in the first and second papers, whereas both cross-sectional areas and nodal positions are simultaneously optimized in the third and fourth papers.