Abstract: First, screw theory, product of exponential formulas and Jacobian matrix are introduced. Then definitions are given about active force wrench, inertial force wrench, partial velocity twist, generalized active force, and generalized inertial force according to screw
theory. After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.

Key words: screw theory, partial velocity twist, open-chain manipulator, Kane dynamic equation, uniformly valid, asymptotic solution, turning point