Velocity level kinematic analysis of serial ŋA-chains

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. The A-pair causes a sinusoidal coupling of rotation and translation between adjacent links in the kinematic chain. The resulting linkage is termed an A-chain. This paper presents a derivation of the manipulator Jacobian of n A-chains in general, and a specific 4 degree-of-freedom hybrid serial-parallel 4A-chain