Connectivity-Three Mechanical Couplings and the Algebraic Complexes They Trace

The subject of this paper is the degree of the algebraic line complexes traced by mechanisms consisting of three connectivity-1 couplings arranged in series. A theorem which gives the degree is presented and proved. The theorem is applied to the eight mechanisms consisting only of single kinematic pairs (revolute and prismatic). In the discussions of some of these mechanisms the degree is determined independently of the proof of the theorem. The theorem is also applied to the mechanisms of some commercial robotic manipulators.