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.
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Project supported by the National Natural Science Foundation of China (Nos. 50378083 and 50638050), and the Research Foundation for the Doctoral Program of Higher Education of China (No. 20050335097)
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Lu, Jy., Luo, Yz. & Li, N. Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD. J. Zhejiang Univ. - Sci. A 8, 1091–1100 (2007). https://doi.org/10.1631/jzus.2007.A1091
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DOI: https://doi.org/10.1631/jzus.2007.A1091
Key words
- Pin-jointed mechanisms
- Criteria for stability of equilibrium
- Criteria for mobility
- Potential energy function
- Equilibrium matrix
- Singular value decomposition (SVD) method