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Research Papers

Topology Optimization of Large Motion Rigid Body Mechanisms With Nonlinear Kinematics

[+] Author and Article Information
Kai Sedlaczek

Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany

Peter Eberhard

Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germanyeberhard@itm.uni-stuttgart.de

J. Comput. Nonlinear Dynam 4(2), 021011 (Mar 10, 2009) (8 pages) doi:10.1115/1.3079786 History: Received February 28, 2008; Revised July 24, 2008; Published March 10, 2009

The modern design process of mechanical structures is increasingly influenced by highly sophisticated methods of topology optimization that can automatically synthesize optimal design variants. However, the typically finite-element-based methods are limited to design tasks with comparably small deflections and simple kinematics. They are not directly applicable to the difficult development process of large motion mechanisms, which remains mainly a manual task based on the engineer’s experience, intuition, and ingenuity. There, optimization techniques are only, if at all, used in the process of dimensional synthesis, where the geometrical properties and the orientation of individual links of a fixed mechanism topology are determined. In this work, two different approaches to optimization-based topology synthesis of large motion rigid body mechanisms are presented and investigated. The goal is to automatically synthesize a combination of linkage topology and joint types that represent the most suitable mechanism layout for a particular task. The first approach is based on a trusslike ground structure that represents an overdetermined system of rigid bars from which the most appropriate topology can be extracted from this ground structure by means of gradient-based optimization algorithms. In the second approach, a genetic algorithm is used to solve the intrinsically combinatorial problem of topology synthesis. Along with several examples, both approaches are explained, their functionality is shown, and their advantages, limitations, and their capability to improve the overall design process is discussed.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Ground structure representation of a four-bar mechanism

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Figure 2

Illustration of a (kinematically undetermined) solution of the test problem with a maximum number of Nρ=10 bars (initial position)

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Figure 3

Solution of the test problem with a maximum number of Nρ=10 bars (final position)

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Figure 4

An example six-link mechanism and its extended (node and edge labeled) graph representation

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Figure 5

The basic procedure for GA-based topology optimization of planar rigid body mechanisms

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Figure 6

The best mechanisms found by the evolutionary process. For the elliptic target trajectory, the maximum number of links were set to four (left). For the conchoidal (middle) as well as for the cycloidal path (right), the maximum number was set to six.

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Figure 7

(a) Illustration of the pick-and-place task and (b) the corresponding synthesis problem. (c) compares the desired path and the trajectory of the best design that was created automatically by the GA approach. Its schematic representation is shown in (d).

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