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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
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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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+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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