Abstract: H4 mechanism corresponds to a group of parallel mechanisms with good dynamical character, the center components of their movable platforms have three translational DOFs and one rotational DOF. In this group of mechanisms there are four isomorphic sub-chain mechanisms, each sub-chain includes one (S-S)2 quadrilateral bar-suit, and the difference of these four mechanisms is in that their actuated joints or the sub-chains’ deployment between base and movable platforms are different. Based on the structure analysis of isomorphic sub-chain mechanisms, the force equilibrium equations of movable platform and sub-chain are established, and force Jacobian matrix are obtained. On which the singularities of the four mechanisms are analyzed by using line geometry method, the discriminating conditions of sub-chain singularity, platform singularity and actuator singularity are proposed, and the kinematic characters of mechanisms at singularity configurations are analyzed. Finally, the configuration examples of an isomorphic sub-chain parallel mechanism in the states of sub-chain singularity, platform singularity and actuator singularity are illustrated.

Key words: Force Jacobian, H4 parallel mechanism, Isomorphic sub-chain, Line geometry method, Singularity