EXACT DISPLACEMENT ANALYSIS OF XCCC SPATIAL MECHANISMS BY THE DIRECTION COSINE MATRIX-METHOD

A method of exact displacement analysis of four-link spatial mechanisms has been developed and successfully applied for four-link spatial mechanisms of RGGR, RGCR, RRGG, and RRGC. The results using this method were exact solutions without requiring numerical or iterative schemes and was called as the direction cosine matrix method. In this paper this method of displacement analysis is extended to the XCCC group of four-link mechanisms. The cylindrical joint has two degrees of freedom, translating as well as rotating. Therefore the analysis is focused on the calculation of the rotating angle as well as the length change. In the development, direction cosine matrices are used by introducing two types of coordinates, the global and the local. The direction cosine matrix has a unique property that each element in the matrix is equal to its own cofactor. Since most mechanisms of this group are bent mechanisms, the analysis of the bent link is also included. © 1990.