Truss transformation method to obtain the non-overconstrained forms of 3D overconstrained linkages. (August 2016)

• Record Type: Journal Article
• Authors: Yang, Fufu; Chen, Yan; Kang, Rongjie; Ma, Jiayao
• Is Part Of: Mechanism and machine theory. Volume 102(2016:Aug.)
• Page Start: 149
• Page End: 166
• Publication Date: 2016-08
• Subjects: Overconstrained linkage -- Truss structure -- Bennett linkage -- Myard 5R linkage; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2016.04.005
• Languages: English
• ISSNs: 0094-114X

Abstract

Abstract: In order to widen the engineering application of 3D overconstrained linkages, their strict overconstrained geometric conditions are expected to be eliminated for improvement of fabrication error tolerance so as to facilitate mass production, which requests to find the non-overconstrained forms of the overconstrained linkages. In this paper, a general truss transformation method is proposed by taking the truss form of overconstrained linkage as an intermedium. According to Maxwell's rule and rank of the equilibrium matrix, the redundant bars in the truss form of the overconstrained linkage are detected and removed to obtain a non-overconstrained linkage, while their kinematic equivalence is well kept. Adopting this method, the results show that RSSR linkage and RRSRR linkages are the non-overconstrained forms of Bennett linkage and Myard 5 R linkage, respectively. Further discussion on fabrication errors is carried out to demonstrate the tolerance on the mobility of the non-overconstrained forms. Highlights: A truss method is proposed to find the non-overstrained forms of linkages. Non-overconstrained forms of overconstrained linkages are obtained. Non-overconstrained forms and original linkages are kinematically equivalent. The non-overconstrained form of Bennett linkage is a RSSR linkage. Non-overconstrained forms own greater fault-tolerance capability.