Displacement analysis of the general spatial 7-link 7R mechanism

Abstract This paper derives the 16th degree polynomial input-output equation in the ten-half-angle of the output angular displacement for the general spatial 7-link 7R mechanism. The input-output equation is expressed in the form of an 8 × 8 determinant equated to zero and the formulae to determine other angular displacements are expressed in closed form. The results are verified by numerical examples. The detailed analysis is performed using a new vector theory for the analysis of spatial mechanisms, which was developed on the basis of the vector analysis theory and dual-number algebra and the recursive notation presented by J. Duffy.