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Research Papers

Multiple-Criteria Kinematic Optimization for the Design of Spherical Serial Mechanisms Using Genetic Algorithms

[+] Author and Article Information
Xiaoli Zhang

Division of Engineering and Physics, Wilkes University, Wilkes-Barre, PA 18766xiaoli.zhang@wilkes.edu

Carl A. Nelson1

Department of Mechanical Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588; Department of Surgery, Center for Advanced Surgical Technology, University of Nebraska Medical Center, Omaha, NE 68198cnelson5@unl.edu

1

Corresponding author.

J. Mech. Des 133(1), 011005 (Jan 03, 2011) (11 pages) doi:10.1115/1.4003138 History: Received September 04, 2009; Revised November 09, 2010; Published January 03, 2011; Online January 03, 2011

A new kinematic design methodology is presented for optimization of spherical serial mechanisms. First, a new index, combining global manipulability and the uniformity of manipulability over the workspace, is presented to improve the synthesis results. This method integrates multiple criteria (workspace size, the new manipulability index, and mechanism size) linearly in one objective function. All these criteria are optimized simultaneously to lead to a solution with better performance. By changing the priorities of each criterion, different sets of desirable kinematic performance can be expressed. An adaptation of the method using a multiobjective Pareto front is also illustrated. The optimization result for a spherical bevel-geared mechanism using a genetic algorithm demonstrated that the proposed method effectively improves the quality of the optimum solution and provides insight into the workings of the mechanism. In addition, this flexible and adaptable methodology also presents a general optimization approach for linkage synthesis.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 12

Fitness value of CoBRASurge using Yoshikawa’s manipulability index

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Figure 13

Pareto frontier for CoBRASurge

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Figure 14

Pareto frontier for S and Ws

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Figure 15

Pareto frontier for S and UDg

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Figure 16

Pareto frontier for Ws and UDg

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Figure 17

Scatter matrix illustrating the correlations between the objective functions

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Figure 18

Scatter matrix between the objective functions and the design variables

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Figure 4

Functional schematic of the spherical bevel-geared mechanism

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Figure 5

Equivalent open-loop chain of the spherical bevel-geared mechanism

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Figure 6

Fitness convergence of a typical GA evolution

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Figure 7

Yoshikawa’s manipulability of CoBRASurge

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Figure 8

Standard deviation of Yoshikawa’s manipulability

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Figure 11

Fitness value of CoBRASurge using consistent manipulability index

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Figure 1

A typical spherical serial mechanism

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Figure 2

Workspace analysis for a typical spherical serial mechanism

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Figure 3

GA operations in a typical optimization procedure

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Figure 9

Consistent manipulability of CoBRASurge

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Figure 10

Workspace of CoBRASurge

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