Truss transformation method to obtain the non-overconstrained forms of 3D overconstrained linkages

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 5R linkage, respectively. Further discussion on fabrication errors is carried out to demonstrate the tolerance on the mobility of the non-overconstrained forms.

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