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

We use the output angle of a spherical four-bar linkage image as the input angle of a second four-bar linkage image where the two frame links are assumed in aligned position as well as the follower of image and the input link of image. We determine all cases where the relation between the input angle of the input link of image and the output angle of the follower of image is reducible and where additionally at least one of these 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 and for the determination of all flexible octahedra in the projective extension of the Euclidean 3-space.