Reducible compositions of spherical four-bar linkages with a spherical coupler component

We use the output angle of a spherical four-bar linkage C as the input angle of a second four-bar linkage D, where the two frame links are assumed in aligned position as well as the follower of C and the input link of D. We determine all cases, where the relation between the input angle of the input link of C and the output angle of the follower of D is reducible and where none of the components produces a transmission, which equals that of a single spherical coupler. The problem under consideration is of importance for the classification of flexible 3 × 3 complexes.