Abstract At the present time a large portion of the literature associated with mechanism synthesis is devoted to methods based on numerical algorithms. It is interesting to note, however, that geometric synthesis procedures often allow a deeper insight into the significance of kinematic motions than is provided through numerical procedures. for this reason the authors have developed synthesis methods based on projective geometry. The method is applied to the design of the RSCR mechanism for three finitely spaced positions. The method is illustrated by means of an example problem.