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Journal of Mechanical Design | Volume 131 | Issue 5 | Research Paper
Research Papers

Geometric Optimization of Spatial Compliant Mechanisms Using Three-Dimensional Wide Curves

[+] Author and Article Information
Hong Zhou

Department of Mechanical and Industrial Engineering, Texas A&M University-Kingsville, Kingsville, TX 78363hong.zhou@tamuk.edu

Kwun-Lon Ting

Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38505kting@tntech.edu

J. Mech. Des 131(5), 051002 (Apr 03, 2009) (7 pages) doi:10.1115/1.3086792 History: Received April 18, 2008; Revised January 07, 2009; Published April 03, 2009
Article
References
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Citing Articles

A three-dimensional wide curve is a spatial curve with variable cross sections. This paper introduces a geometric optimization method for spatial compliant mechanisms by using three-dimensional wide curves. In this paper, every material connection in a spatial compliant mechanism is represented by a three-dimensional wide curve and the whole spatial compliant mechanism is modeled as a set of connected three-dimensional wide curves. The geometric optimization of a spatial compliant mechanism is considered as the generation and optimal selection of the control parameters of the corresponding three-dimensional parametric wide curves. The deformation and performance of spatial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The optimization problem is solved by the MATLAB constrained nonlinear programming algorithm.
Copyright © 2009 by American Society of Mechanical Engineers
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References

1
Midha, A., Norton, T. W., and Howell, L. L., 1994, “On the Nomenclature, Classification, and Abstractions of Compliant Mechanisms,” ASME J. Mech. Des.  [CrossRef], 116 (1), pp. 270–279.
2
Ananthasuresh, G. K., and Kota, S., 1995, “Designing Compliant Mechanisms,” Mech. Eng. (Am. Soc. Mech. Eng.), 117 (11), pp. 93–96.
3
Howell, L. L., 2001, "Compliant Mechanisms", Wiley, New York.
4
Kota, S., Ananthasuresh, G. K., Crary, S. B., and Wise, K. D., 1994, “Design and Fabrication of Microelectromechanical Systems,” ASME J. Mech. Des.  [CrossRef], 116 (4), pp. 1081–1088.
5
Ananthasuresh, G. K., 2003, "Optimal Synthesis Methods for MEMS", Kluwer Academic, Boston, MA.
6
Bendsøe, M. P., and Sigmund, O., 2002, "Topology Optimization", Springer, New York.
7
Hetrick, J. A., and Kota, S., 1999, “An Energy Formulation for Parametric Size and Shape Optimization of Compliant Mechanisms,” ASME J. Mech. Des.  [CrossRef], 121 (2), pp. 229–234.
8
Xu, D., and Ananthasuresh, G. K., 2003, “Freeform Skeletal Shape Optimization of Compliant Mechanisms,” ASME J. Mech. Des.  [CrossRef], 125 (2), pp. 253–261.
9
Zhou, H., and Ting, K. L., 2006, “Shape and Size Synthesis of Compliant Mechanisms Using Wide Curve Theory,” ASME J. Mech. Des.  [CrossRef], 128 (3), pp. 551–558.
10
Lan, C. C., and Cheng, Y. J., 2008, “Distributed Shape Optimization of Compliant Mechanisms Using Intrinsic Functions,” ASME J. Mech. Des.  [CrossRef], 130 (7), p. 072304.
11
Salomon, D., 1999, "Computer Graphics and Geometric Modeling", Springer, New York.
12
Farin, G., 2001, "Curves and Surfaces for CAGD: A Practical Guide", Academic, New York.
13
Mestetskii, L. M., 2000, “Fat Curves and Representation of Planar Figures,” Comput. Graph.  [CrossRef], 24 (1), pp. 9–21.
14
2006, “Optimization Toolbox for Use With MATLAB ,” User’s Guide, Version 3, MathWorks, Inc.
15
Weisstein, E. W., 2002, “Plane-Plane Intersection,” MathWorld—A Wolfram Web Resource.
16
Crisfield, M. A., 1997, "Non-Linear Finite Element Analysis of Solids and Structures", Wiley, New York.
17
Belytschko, T., Liu, W. K., and Moran, B., 2003, "Nonlinear Finite Elements for Continua and Structures", Wiley, New York.

Figures

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+A three-dimensional quintic wide Bezier curve
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A three-dimensional quintic wide Bezier curve
Figure 1

A three-dimensional quintic wide Bezier curve

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+A three-dimensional wide curve with curvature self-intersection
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A three-dimensional wide curve with curvature self-intersection
Figure 2

A three-dimensional wide curve with curvature self-intersection

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+A three-dimensional wide curve with loop self-intersection
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A three-dimensional wide curve with loop self-intersection
Figure 3

A three-dimensional wide curve with loop self-intersection

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+A set of consecutive cross sections of a three-dimensional wide curve
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A set of consecutive cross sections of a three-dimensional wide curve
Figure 4

A set of consecutive cross sections of a three-dimensional wide curve

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+Two space circular sections in which the distance from the center of a circular section to the intersection line is greater than its radius
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Two space circular sections in which the distance from the center of a circular section to the intersection line is greater than its radius
Figure 5

Two space circular sections in which the distance from the center of a circular section to the intersection line is greater than its radius

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+Two space circular sections in which the distances from the centers of two circular sections to the intersection line are less than their radii
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Two space circular sections in which the distances from the centers of two circular sections to the intersection line are less than their radii
Figure 6

Two space circular sections in which the distances from the centers of two circular sections to the intersection line are less than their radii

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+Two space circular sections with interference
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Two space circular sections with interference
Figure 7

Two space circular sections with interference

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+The topology, loading and supporting positions, and design domain in example 1
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The topology, loading and supporting positions, and design domain in example 1
Figure 8

The topology, loading and supporting positions, and design domain in example 1

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+The control spheres of the structure in example 1
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The control spheres of the structure in example 1
Figure 9

The control spheres of the structure in example 1

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+The optimal synthesis result in example 1
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The optimal synthesis result in example 1
Figure 10

The optimal synthesis result in example 1

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+The optimal synthesis result using straight uniform connections in example 1
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The optimal synthesis result using straight uniform connections in example 1
Figure 11

The optimal synthesis result using straight uniform connections in example 1

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+The topology, input and output positions, and design domain in example 2
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The topology, input and output positions, and design domain in example 2
Figure 12

The topology, input and output positions, and design domain in example 2

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+The control spheres of the compliant gripper in example 2
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The control spheres of the compliant gripper in example 2
Figure 13

The control spheres of the compliant gripper in example 2

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+The optimal synthesis result in example 2
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The optimal synthesis result in example 2
Figure 14

The optimal synthesis result in example 2

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+The optimal synthesis result using straight uniform connections in example 2
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The optimal synthesis result using straight uniform connections in example 2
Figure 15

The optimal synthesis result using straight uniform connections in example 2

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