A displacement analysis of spatial five-link 3R-2C mechanisms—I. On the closures of the RCRCR mechanism

Closed form expressions for the RCRCR mechanism are obtained from dual equations which were derived using spherical trigonometry [1].

An alternative form of the degree four input-output displacement equation obtained by Yang [2] is derived. However, it is demonstrated that the RCRCR mechanism has generally a maximum of eight closures. This result is consistent with the analysis presented in Parts 2 and 3 where eight closures are obtained for both the RRCRC and RCRRC mechanisms.

The analysis for the RCRCR, RRCRC and RCRRC mechanisms is illustrated by plottings of numerical values of linkage variables which were obtained using data common to each inversion.