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In order to solve the problem of kinematics modeling of parallel mechanism with sub closed-chains (PMHSC), definition of the mechanism was made. The concept of general screw was derived by discussing the motion relationship of planar four-bar linkage, and its inner connection with instantaneous equivalent screw of so-called general kinematic pair was explained. Based on the concept, the relative velocity and acceleration of any two bars in a sub closed-chain with multi-DOF were obtained, and the result was arranged to the form by using general screw. Combining the new screw representation of sub closed-chain with conventional screw form of relative motion of two rigid bodies that connected directly with a joint, the first and second order influence coefficients of single kinematic serial limb with sub closed-chain were obtained, the discussion was conducted from the serial with one sub closed-chain to multi ones. It revealed that the elements corresponding to the sub closed-chain contained the general screw, especially in the second order influence coefficient matrix, which was consisted of two parts, no longer the lie bracket form of two screws as usual. Furthermore, the universal formula that depicted the mapping from general input velocity and acceleration to screw velocity and acceleration of terminal body of PMHSC was derived. Simulation verification was conducted by using two parallel mechanisms. The first one was 6-(PRRR) US type that had planar PRRR closed loop in each leg, it’s a 1-DOF sub closed-chain; and the second one was 5-UPS/(RPRRR) RS type which had a 2-DOF sub closed-chain in the special limb. The results prove that the method discussed is correct.