Research Papers

Using Rigid-Body Mechanism Topologies to Design Shape-Changing Compliant Mechanisms

[+] Author and Article Information
Kai Zhao

Magna Seating of America,
Novi, MI 48335
e-mail: kzhaond@gmail.com

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 January 28, 2015; final manuscript received April 27, 2015; published online August 18, 2015. Assoc. Editor: Pierre M. Larochelle.

J. Mechanisms Robotics 8(1), 011014 (Aug 18, 2015) (9 pages) Paper No: JMR-15-1017; doi: 10.1115/1.4030585 History: Received January 28, 2015

This paper uses rigid-body mechanism topologies to synthesize fully distributed compliant mechanisms that approximate a shape change defined by a set of morphing curves in different positions. For a shape-change problem, a rigid-body mechanism solution is generated first to provide the base topology. This base topology defines a preselected design space for the structural optimization in one of two ways so as to obtain a compliant mechanism solution that is typically superior to the local minimum solutions obtained from searching more expansive design spaces. In the first strategy, the dimensional synthesis directly determines the optimal size and shape of the distributed compliant mechanism having exactly the base topology. In the second strategy, an initial mesh network established from the base topology is used to generate different topologies (in addition to the base), and an improved design domain parameterization scheme ensures that only topologies with well-connected structures are evaluated. The deformation of each generated compliant mechanism is evaluated using geometrically nonlinear finite element analysis (FEA). A two-objective genetic algorithm (GA) is employed to find a group of viable designs that trade off minimizing shape matching error with minimizing maximum stress. The procedure's utility is demonstrated with three practical examples—the first two approximating open-curve profiles of an adaptive antenna and the third approximating closed-curve profiles of a morphing wing.

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Fig. 1

(a) A set of two desired shapes. (b) Generated morphing chain with three segments. (c) Solution 1DOF rigid-body mechanism.

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Fig. 2

Two rigid-body mechanisms with different topologies that solve the same shape-change problem defined in Fig. 1(a). In mechanism (b), node 1 is the input node. Nodes 2, 3, and 4 are the fixed nodes. Nodes 5, 6, 7, and 8 are the output nodes. Nodes 9, 10, and 11 are the interconnect nodes.

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Fig. 3

Comparison of different initial mesh networks generated for the shape-change problem shown in Fig. 1(a). (a) A ground structure network. (b) A network with active points (recreated from Ref. [2]). (c) A network defined by the base topology shown in Fig. 2(b).

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Fig. 4

(a) The optimized topology (recreated from Ref. [2]) to approximate the shape change in Fig. 1(a) cannot be defined by the load path representation. (b) A substructure demonstrating contradictory representations of the load path approach.

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Fig. 5

Two examples identifying the connection status of interconnect nodes. The numbers in parentheses and square brackets indicate the direct and indirect connections, respectively, between the interconnect node and the essential nodes. The substructures (dashed lines) related to nodes 9 and 10 in (a) and nodes 9, 10, and 11 in (b) are invalid.

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Fig. 6

Compliant mechanism solution reported in Ref. [2] with a matching error of 0.469 mm for the shape-change problem in Fig. 1(a)

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Fig. 7

Pareto front for the synthesis of compliant mechanisms using the rigid-body mechanism topology in Fig. 2(b)

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Fig. 8

The solution mechanism that has a matching error of 0.542 mm and maximum stress of 33.5 MPa

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Fig. 9

A 1DOF rigid-body mechanism to approximate three open-curve profiles. An initial network established by this base topology has one input, three fixed, two output, and two interconnect nodes.

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Fig. 10

Pareto front for the synthesis of compliant mechanisms using the rigid-body mechanism topology in Fig. 9

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Fig. 11

Compliant mechanism synthesized using the rigid-body mechanism topology in Fig. 9. (a) The matching error of the first target shape is 0.396 mm. (b) The matching error of the second target shape is 0.47 mm.

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Fig. 12

Compliant mechanism synthesized from the network in Fig. 3(a). (a) The matching error of the first target profile is 0.52 mm. (b) The matching error of the second target profile is 0.81 mm.

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Fig. 13

(a) A set of three airfoil shapes in different positions. (b) Solution 1DOF rigid-body mechanism [7]. (c) An initial mesh network defined by the topology in (b).

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Fig. 14

Pareto front for the synthesis of a compliant morphing wing using the rigid-body mechanism topology shown in Fig. 13(b)

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Fig. 15

Compliant mechanism synthesized from the initial mesh network shown in Fig. 13(c). (a) The matching error of the first target shape is 7.58 mm. (b) The matching error of the second target shape is 11.22 mm.




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