Topology and Dimensional Synthesis of Compliant Mechanisms Using Discrete Optimization

[+] Author and Article Information
Kerr-Jia Lu

Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052kjlu@gwu.edu

Sridhar Kota

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109kota@umich.edu

J. Mech. Des 128(5), 1080-1091 (Oct 30, 2005) (12 pages) doi:10.1115/1.2216729 History: Received February 08, 2005; Revised October 30, 2005

A unified approach to topology and dimensional synthesis of compliant mechanisms is presented in this paper as a discrete optimization problem employing both discrete (topology) and continuous (size) variables. The synthesis scheme features a design parameterization method that treats load paths as discrete design variables to represent various topologies, thereby ensuring structural connectivity among the input, output, and ground supports. The load path synthesis approach overcomes certain design issues, such as “gray areas” and disconnected structures, inherent in previous design schemes. Additionally, multiple gradations of structural resolution and a variety of configurations can be generated without increasing the number of design variables. By treating topology synthesis as a discrete optimization problem, the synthesis approach is incorporated in a genetic algorithm to search for feasible topologies for single-input single-output compliant mechanisms. Two design examples, commonly seen in the compliant mechanisms literature, are included to illustrate the synthesis procedure and to benchmark the performance. The results show that the load path synthesis approach can effectively generate well-connected compliant mechanism designs that are free of gray areas.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 14

A prototype of the compliant gripper in its inactive mode (left) and gripping mode (right)

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Figure 15

(a) A hypothetical SISO problem with three fixed points and ten interconnect points. (b) The maxPathLength(=4) imposes an upper bound on the length of pathSeq and pDim.

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Figure 16

A fully ground structure with mesh resolution and complexity comparable with the load path representation in Fig. 1

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Figure 1

(a)–(c) Disconnected structures associated with the homogenization parameterization. (d)–(f) Disconnected structures associated with the ground structure parameterization.

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Figure 2

A compliant gripper example to illustrate the different load paths in a structure

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Figure 3

Direct and indirect load paths between the essential points

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Figure 4

(a) A fully connected graph representing a SISO compliant mechanism; (b) a partially connected graph derived from (a) by ‘turning off’ some of the paths (setting pTop to zero). Their corresponding topology information is shown in Table 2.

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Figure 5

Different interConLocations render different geometries in the compliant mechanisms (a) and (b), although their topologies are identical

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Figure 6

Two variations of the design in Fig. 5 with different in-plane beam dimensions

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Figure 7

Design domain for the displacement amplifier. Due to symmetry about the y-axis, only the right half is modeled in the synthesis process.

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Figure 8

A displacement amplifier with loaded geometric advantage of 27 (right half of the design) based on linear analysis

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Figure 9

The full model of the displacement amplifier in its inactive mode (left) and amplifying mode (right)

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Figure 10

The design domain for a compliant gripper. Due to symmetry about the x-axis, only the upper half is modeled in the synthesis process.

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Figure 11

A compliant gripper obtained from the load path approach (upper half of the gripper)

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Figure 12

A compliant gripper obtained from the load path approach after moving the fixed point from (0,20) to (10,30) and re-run the program

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Figure 13

The full model of the compliant gripper in its inactive mode (left) and gripping mode (right)



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