The dynamics of a single algebraic screw pair

The algebraic screw pair, or A-pair, represents a new class of kinematic constraint that exploits the self-motions inherent to a specific configuration of Griffis-Duffy platform. Using the A-pair as a joint in a hybrid parallel-serial kinematic chain results in a sinusoidal coupling of rotation and translation between adjacent links. The resulting linkage is termed an A-chain. This paper reveals the dynamic equations of motion of a single A-pair and examines the impact of the inertial properties of the legs of the A-pair on the dynamics. A numerical example illustrates the impact of the leg effects from different perspectives and shows that while the gravity effects of the legs are significant, it may be possible to neglect the leg kinetic energy from the dynamics model.