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Research Papers: Design of Mechanisms and Robotic Systems

Turning Functions in Optimal Synthesis of Mechanisms

[+] Author and Article Information
Fernando Nadal

Department of Mechanical Engineering,
University of Málaga,
C/Dr. Ortiz Ramos S/N,
Málaga 29071, Spain
e-mail: fnm@uma.es

Juan A. Cabrera

Mem. ASME
Department of Mechanical Engineering,
University of Málaga,
C/Dr. Ortiz Ramos S/N,
Málaga 29071, Spain
e-mail: jcabrera@uma.es

Alex Bataller

Department of Mechanical Engineering,
University of Málaga,
C/Dr. Ortiz Ramos S/N,
Málaga 29071, Spain
e-mail: alex@uma.es

Juan J. Castillo

Mem. ASME
Department of Mechanical Engineering,
University of Málaga,
C/Dr. Ortiz Ramos S/N,
Málaga 29071, Spain
e-mail: juancas@uma.es

Antonio Ortiz

Department of Mechanical Engineering,
University of Málaga,
C/Dr. Ortiz Ramos S/N,
Málaga 29071, Spain
e-mail: aortizf@uma.es

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 10, 2014; final manuscript received February 5, 2015; published online March 10, 2015. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 137(6), 062302 (Jun 01, 2015) (10 pages) Paper No: MD-14-1336; doi: 10.1115/1.4029825 History: Received June 10, 2014; Revised February 05, 2015; Online March 10, 2015

In this paper, we describe the use of turning functions to compare errors between the coupler and the target paths. The main reason to use turning functions is that the measured error does not depend on the mechanism scale or the position and rotation of the fixed link. Therefore, the searching space for the optimization algorithm is reduced. To carry out mechanism synthesis, we use an evolutionary algorithm. The effectiveness of the proposed method has been demonstrated in five synthesis examples.

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References

Figures

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Fig. 1

(a) Polygonal shape F. (b) Turning function of shape F.

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Fig. 4

Four-bar mechanism with its design variables

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Fig. 5

Algorithm to evaluate the e2 function

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Fig. 6

Scheme of the MUMSA algorithm

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Fig. 12

The best path traced by the coupler with the proposed method and two bibliography examples for case 3

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Fig. 13

Error distribution when the MUMSA algorithm is running 100 times for case 3. Histogram bar plot.

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Fig. 14

Statistical parameter at 1000 iterations of the MUMSA algorithm for the best population for case 3

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Fig. 15

The best path traced by the coupler with the proposed method and one bibliography example for case 4

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Fig. 11

Paths of the proposed and transformed mechanism for case 2

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Fig. 7

Paths of the proposed and transformed mechanism for case 1

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Fig. 8

The best path traced by the coupler with the proposed method and two bibliography examples for case 1

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Fig. 9

Error distribution when the MUMSA algorithm is running 100 times for case 1. Histogram bar plot.

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Fig. 10

Statistical parameter at 100 iterations of the MUMSA algorithm for the best population

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Fig. 16

The best path traced by the coupler with the proposed method and one bibliography example for case 5

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