Synthesis of Compliant Mechanisms for Path Generation using Genetic Algorithm

[+] Author and Article Information
Anupam Saxena

Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India

J. Mech. Des 127(4), 745-752 (Sep 29, 2004) (8 pages) doi:10.1115/1.1899178 History: Received April 29, 2004; Revised September 29, 2004

In this paper is described a procedure to synthesize the optimal topology, shape, and size of compliant continua for a given nonlinear output path. The path is prescribed using a finite number of distinct precision points much in accordance with the synthesis for path generation in traditional kinematics. Geometrically nonlinear analysis is employed to model large displacements of the constituent members. It is also essential to employ nonlinear analysis to allow the output port to negotiate the prescribed path accurately. The topology synthesis problem is addressed in its original binary form in that the corresponding design variables are only allowed to assume values of “0” for no material and “1” for the material present at a site in the design region. Shape and size design variables are modeled using continuous functions. Owing to the discrete nature of topology design variables, since gradient based optimization methods cannot be employed, a genetic algorithm is used that utilizes only the objective values to approach an optimum solution. A notable advantage of a genetic algorithm over its gradient based counterparts is the implicit circumvention of nonconvergence in the large displacement analysis, which is another reason why a genetic algorithm is chosen for optimization. The least squared objective is used to compare the design and desired output responses. To allow a user to specify preference for a precision point, individual multiple least squared objectives, same in number as the precision points are used. The multiple objectives are solved using Nondominated Sorting in Genetic Algorithm (NSGA-II) to yield a set of pareto optimal solutions. Thus, multiple solutions for compliant mechanisms can be obtained such that a mechanism can traverse one or some precision points among those specified more precisely. To traverse the entire path, a solution that minimizes the sum of individual least square objectives may be chosen. Synthesis examples are presented to demonstrate the usefulness of the proposed method that is capable of generating a solution that can be manufactured as is without requiring any interpretation.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Problem definition

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Figure 2

Regions of node placement when nodal positions are treated as design variables

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Figure 3

Topology, size, and shape synthesis of compliant pliers with five-point path generation specification (a) designvariables, (b) optimal solution minimizing (Q1−P1).(Q1−P1); (c) solution minimizing (Q2−P2).(Q2−P2); (d)–(e) solutions minimizing (Q3−P3).(Q3−P3) and (Q4−P4).(Q4−P4); (f) that minimizing the sum of all individual objectives; (g) output deformation history for all solutions

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Figure 4

(a) ABS prototype of the mechanism in Fig. 3; (b) output port in undeformed position (first precision point); (c)–(d) output port near third and fifth precision points respectively

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Figure 5

(a) Schematic of Chebyshev’s straight line mechanism (b) design specifications for topology, size, and shape optimization.

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Figure 6

Topology, size, and shape synthesis of fully compliant Chebyshev’s straight line mechanism with five-point path generation specification; (a) optimal solution minimizing (Q1−P1).(Q1−P1); (b) solution minimizing (Q2−P2).(Q2−P2); (c)–(d) solutions minimizing (Q3−P3).(Q3−P3) and (Q4−P4).(Q4−P4); (e) that minimizing the sum of all individual objectives; (f) output deformation history for all solutions

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Figure 7

ABS prototype of the mechanism in Fig. 6; (a) output port in undeformed position; (b)–(e) output port passing through second, third, fourth, and fifth precision points, respectively

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Figure 8

Synthesis of a compliant mechanism for an approximate L-shaped path; (a) design region; (b) optimal solution; (c) output response




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