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Abstract
This thesis deals with computerbased 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 groundstructure 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 crosssectional 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 nonlinearity in the kinematics.
This should be considered for the analysis of mechanisms since the displacements of mechanisms are
intrinsically large. The consideration of geometric nonlinearity, however, causes numerical difficulties
relating to the nonconvexity 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. Graphtheoretical enumeration [Paper 1]
2. Gradientbased local optimization [Paper 2]
3. Branch and bound global optimization [Paper 3]
4. Pathgeneration 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 gradientbased local optimization. With respect to design variables, only crosssectional
areas are used in the first and second papers, whereas both crosssectional areas and nodal positions are
simultaneously optimized in the third and fourth papers.
Original language  English 

Place of Publication  Kgs. Lyngby, Denmark 

Publisher  Technical University of Denmark 
Number of pages  32 
Publication status  Published  2004 
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 1 Finished

Generation of Articulated Mechanisms by Optimization Techniques  Matrix Inequalities and Global Search
Kawamoto, A., Bendsøe, M. P., Sigmund, O., Klit, P., Eberhard, P. & Klarbring, A.
18/03/2005 → 18/03/2005
Project: PhD