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.

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Keywords Algebraic screw pair, Griffis’duffy platform, NA jacobian
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Robinson, J.D. (James D.), & Hayes, M.J.D. (2012). Velocity level kinematic analysis of serial ŋA-chains. In Latest Advances in Robot Kinematics (pp. 389–396). doi:10.1007/978-94-007-4620-6_49