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Research Papers

Simultaneous Topological and Dimensional Synthesis of Planar Morphing Mechanisms

[+] Author and Article Information
Lawrence W. Funke

Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: lfunke@nd.edu

James P. Schmiedeler

Fellow ASME
Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: schmiedeler.4@nd.edu

1Corresponding author.

Manuscript received October 13, 2016; final manuscript received January 13, 2017; published online March 9, 2017. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 9(2), 021009 (Mar 09, 2017) (9 pages) Paper No: JMR-16-1306; doi: 10.1115/1.4035878 History: Received October 13, 2016; Revised January 13, 2017

This paper presents a general method to perform simultaneous topological and dimensional synthesis for planar rigid-body morphing mechanisms. The synthesis is framed as a multi-objective optimization problem for which the first objective is to minimize the error in matching the desired shapes. The second objective is typically to minimize the actuating force/moment required to move the mechanism, but different applications may require a different choice. All the possible topologies are enumerated for morphing mechanism designs with a specified number of degrees of freedom (DOF), and infeasible topologies are removed from the search space. A multi-objective genetic algorithm (GA) is then used to simultaneously handle the discrete nature of the topological optimization and the continuous nature of the dimensional optimization. In this way, candidate solutions from any of the feasible topologies enumerated can be evaluated and compared. Ultimately, the method yields a sizable population of viable solutions, often of different topologies, so that the designer can manage engineering tradeoffs in selecting the best mechanism. Three examples illustrate the strengths of this method. The first examines the advantages gained by considering and optimizing across all the topologies simultaneously. The second and third demonstrate the method's versatility by incorporating prismatic joints into the morphing chain to allow for morphing between shapes that have significant changes in both shape and arc length.

FIGURES IN THIS ARTICLE
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Copyright © 2017 by ASME
Topics: Chain , Design , Topology , Errors
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References

Figures

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Fig. 1

Example 1DOF closed morphing mechanism

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Fig. 2

Example 3DOF fixed-end morphing mechanism

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Fig. 3

Example 2DOF open morphing mechanism

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Fig. 4

Target profile set for the example in Sec. 4

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Fig. 5

Plots showing the percent increase in matching error and maximum required actuating moment for each mechanism in the suitable design region for the example in Sec. 4. The symbols represent different topology permutations. (a) 1DOF solutions for the restricted topology case and (b) 1DOF solutions for the general topology case.

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Fig. 6

Sample solution mechanisms for the example in Sec. 4, shown in configurations closest to the first design profile: (a) topology permutation denoted by squares (□) in Fig. 5(a), (b) topology permutation denoted by circles (o) in Fig. 5(b), (c) topology permutation denoted by left facing triangles (◁) in Fig. 5(b), and (d) topology permutation denoted by x marks (x) in Fig. 5(b)

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Fig. 7

Target profile set for the example in Sec. 5

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Fig. 8

Plots showing the percent increase in matching error and the average maximum required actuating moment for each mechanism in the suitable design region for the example in Sec. 5. Each symbol is a different topology permutation. (a) 1DOF solutions, (b) 2DOF solutions, and (c) 3DOF solutions.

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Fig. 9

3DOF solution mechanism from the topology permutation denoted by circles (o) in Fig. 8(c) for the example in Sec. 5, shown in its configuration closest to the first design profile

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Fig. 10

Target profile set for the example in Sec. 6

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Fig. 11

Plots showing the percent increase in matching error and the average maximum required actuating moment for each mechanism in the suitable design region for the example in Sec. 6. Each symbol is a different topology permutation. (a) 1DOF solutions, (b) 2DOF solutions, and (c) 3DOF solutions.

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Fig. 12

2DOF solution from the topology permutation denoted by squares (□) in Fig. 11(b) for the example in Sec. 6, shown in its configuration closest to the first design profile

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