Abstract: Based on the ordered single-opened-chain, a new method of direct displacement solution for spatial parallel mec- hanism is presented. According to the topological structure charact- eristics of the mechanism, the mechanism can be decomposed into some ordered single-opened-chains, which can further compose same basic kinematic chains. The mechanism coupling-degree is given, and following the principle of the mechanism coupling degree calculation method and the decomposition order of the single-opened-chains, the mechanism displacement analysis mathematics model that is uniform with its topological struc- ture characteristics is established. The direct displacement equations are derived, and the equations’ number of dimension is just equal to the mechanism coupling-degree and no skill to decrease the dimension is needed. As the mechanism coupling- degree is 1, all real number direct displacement solutions can be obtained by one-dimension search. The analysis processing is concise and universal, and its physicals meaning is clear. Com- pared with other general search methods, this method is of higher calculation efficiency and can gain all real number solutions. As an example, all real number direct displacement solutions of a 4-DOF parallel mechanism are obtained by one-dimension search.

Key words: Direct displacement solution Single-opened-chain, Parallel mechanism