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Research Papers

Research on Position Analysis of a Kind of Nine-Link Barranov Truss

[+] Author and Article Information
Pin Wang

 Beijing University of Posts and Telecommunications, Beijing 100876, P.R.C.wpbupt@126.com

Qizheng Liao

 Beijing University of Posts and Telecommunications, Beijing 100876, P.R.C.qzliao@bupt.edu.cn

Yufeng Zhuang

 Beijing University of Posts and Telecommunications, Beijing 100876, P.R.C.zhuangyf@bupt.edu.cn

Shimin Wei

 Beijing University of Posts and Telecommunications, Beijing 100876, P.R.C.wsmly@bupt.edu.cn

J. Mech. Des 130(1), 011005 (Dec 07, 2007) (6 pages) doi:10.1115/1.2803256 History: Received May 29, 2006; Revised March 02, 2007; Published December 07, 2007

The position analysis of a nine-link Barranov truss is finished by using Dixon resultants together with Sylvester resultants. Above all, using vector method in complex plane to construct four constraint equations and transform them into complex exponential form, then three constraint equations are used to construct a 6×6 Dixon matrix, which contains two variables to be eliminated. We extract the greatest common divisor (GCD) of two columns of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the fourth constraint equation can be used to construct a Sylvester resultant. A 50deg univariate polynomial equation is obtained from the determinant of Sylvester resultant. Other variables can be computed by Euclidean algorithm and Gaussian elimination. Lastly, a numerical example confirms that the analytical solution number of the Barranov truss is 50. It is the first time to complete analytical solutions of this kind of Barranov truss.

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References

Figures

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Figure 3

Assembly configuration of the tenth group of solution in Table 2

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Figure 4

Assembly configuration of the 11th group of solution in Table 2

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Figure 5

Assembly configuration of the 15th group of solution in Table 2

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Figure 1

Structure of nine-link Barranov truss

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Figure 2

Assembly configuration of the seventh group of solution in Table 2

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Figure 6

Assembly configuration of the 18th group of solution in Table 2

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Figure 7

Assembly configuration of the 20th group of solution in Table 2

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Figure 8

Assembly configuration of the 21st group of solution in Table 2

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Figure 9

Assembly configuration of the 24th group of solution in Table 2

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Figure 10

Assembly configuration of the 25th group of solution in Table 2

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Figure 11

Assembly configuration of the 26th group of solution in Table 2

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Figure 12

Assembly configuration of the 27th group of solution in Table 2

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Figure 13

Assembly configuration of the 28th group of solution in Table 2

Tables

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