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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.7 P.1091~1100

10.1631/jzus.2007.A1091


Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD


Author(s):  LU Jin-yu, LUO Yao-zhi, LI Na

Affiliation(s):  Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   luoyz@zju.edu.cn

Key Words:  Pin-jointed mechanisms, Criteria for stability of equilibrium, Criteria for mobility, Potential energy function, Equilibrium matrix, Singular value decomposition (SVD) method


LU Jin-yu, LUO Yao-zhi, LI Na. Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD[J]. Journal of Zhejiang University Science A, 2007, 8(7): 1091~1100.

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author="LU Jin-yu, LUO Yao-zhi, LI Na",
journal="Journal of Zhejiang University Science A",
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pages="1091~1100",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1091"
}

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%T Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD
%A LU Jin-yu
%A LUO Yao-zhi
%A LI Na
%J Journal of Zhejiang University SCIENCE A
%V 8
%N 7
%P 1091~1100
%@ 1673-565X
%D 2007
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A1091

TY - JOUR
T1 - Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD
A1 - LU Jin-yu
A1 - LUO Yao-zhi
A1 - LI Na
J0 - Journal of Zhejiang University Science A
VL - 8
IS - 7
SP - 1091
EP - 1100
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2007.A1091


Abstract: 
Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new criterion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[8] Maxwell, J.C., 1890. On the Calculation of the Equilibrium and Stiffness of Frames. Cambridge University Press, Cambridge, UK.

[9] Pellegrino, S., 1990. Analysis of pre-stressed mechanisms. Int. J. Solids Struct., 26(12):1329-1350.

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[11] Pellegrino, S. (Ed.), 2001. Deployable Structures. CISM Course and Lectures No. 412. Springer, Wien, New York.

[12] Pellegrino, S., Calladine, C.R., 1986. Matrix analysis of statically and kinematically indeterminate frameworks. Int. J. Solids Struct., 22(4):409-428.

[13] Tarnai, T., Szabó, J., 2000. On the exact equation of inextensional, kinematically indeterminate assemblies. Comp. Struct., 75(2):145-155.

[14] Tarnai, T., Szabó, J., 2002. Rigidity and Stability of Prestressed Infinitesimal Mechanisms. In: Drew, H.R., Pellegrino, S. (Eds.), New Approaches to Structural Mechanics, Shells and Biological Structures. Kluwer, Dordrecht, p.245-256.

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