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Technical Brief

Using Rigid-Body Mechanism Topologies to Design Path Generating 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 28, 2015; published online September 25, 2015. Assoc. Editor: Pierre M. Larochelle.

J. Mechanisms Robotics 8(1), 014506 (Sep 25, 2015) Paper No: JMR-15-1018; doi: 10.1115/1.4030623 History: Received January 28, 2015

For a path generation problem, this paper uses the base topology of a single degree-of-freedom (DOF) rigid-body mechanism solution to synthesize fully distributed compliant mechanisms that can trace the same path. Two different strategies are proposed to employ the base topology in the structural optimization so that its design space size can be intelligently reduced from an arbitrary complexity. In the first strategy, dimensional synthesis directly determines the optimal size and shape of the compliant mechanism solution while maintaining the exact base topology. In the second, the base topology establishes an initial mesh network to determine the optimal topology and dimensions simultaneously. To increase the possibility of converging to an optimal design, the objective metrics to evaluate the path generation ability are computed in a novel manner. A section-by-section analysis with a rigid-body transformation is implemented to examine the full path of each candidate mechanism. A two-objective genetic algorithm (GA) is employed to find a group of viable designs that tradeoff minimizing the average Euclidean distance between the desired and actual paths with minimizing the peak distance between corresponding points on those paths. Two synthesis examples generating straight-line and curved paths are presented to demonstrate the procedure's utility.

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References

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Figures

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Fig. 1

Flowchart for synthesizing fully distributed compliant mechanisms for path generation

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Fig. 2

Three rigid-body mechanisms that can trace straight lines. (a) A four-bar mechanism. Nodes 1, 2, and 3 are the input, fixed, and output nodes, respectively. Nodes 4 and 5 are the interconnect nodes. (b) A six-bar mechanism. (c) An eight-bar mechanism.

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Fig. 3

(a) The topology is disconnected since the input node (node 1) is not connected to the output node (node 3). (b) The substructures (dashed lines) related to nodes 5, 8, 9, and 10 are invalid and must be removed from the topology.

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Fig. 4

(a) The dashed line with points F1,...,Fn is the full path generated by a compliant mechanism. The solid line with points T1,...,T5 is the target path. (b) The generated path is shifted to minimize the distance metric D15 relative to the target path. (c) Section F612 from point F6 to F12 of the generated path has the smallest error Dmin. The distance between F12 and T12 is the peak error Dp.

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Fig. 5

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

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Fig. 6

(a) The solution mechanism that has an average matching error of 0.225 mm and peak error of 1.518 mm in its undeformed position before the rigid-body transformation. (b) Animation of the solution mechanism to trace the target line. (c) Comparison between the generated path of the solution mechanism and the target path.

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Fig. 7

(a) Solution 1DOF rigid-body mechanism with a rotary actuator. (b) An initial mesh network defined by the topology in (a).

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Fig. 8

Pareto front for the synthesis of compliant mechanisms using the rigid-body mechanism topology in Fig. 7(a)

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Fig. 9

(a) The solution mechanism that has an average error of 0.448 mm and peak error of 3.412 mm in its undeformed position before the rigid-body transformation. (b) Animation of the solution mechanism to trace the target line. (c) Comparison between the generated path of the solution mechanism in (b) and the target path.

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Fig. 10

Prototype of the compliant mechanism solution (Fig. 9) in its (a) undeformed position, (b) top-end position, and (c) bottom-end position

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Fig. 11

(a) Solution 1DOF rigid-body mechanism with a linear actuator. (b) An initial mesh network defined by the topology in (a).

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Fig. 12

Pareto front for the synthesis of compliant mechanisms using the rigid-body mechanism topology in Fig. 11(a)

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Fig. 13

(a) The solution mechanism that has an average matching error of 0.215 mm and peak error of 0.422 mm in its undeformed position before the rigid-body transformation. (b) Animation of the solution mechanism to trace the target curve. (c) Comparison between the generated path of the solution mechanism in (b) and the target path.

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Fig. 14

Prototype of the solution mechanism (Fig. 13) in its (a) undeformed position, (b) right-end position, and (c) left-end position

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