A new viewpoint on structural composition of mechanism is proposed in this paper: any mechanism can be decomposed into a group of ordered single-open-chains (SOC). Based on the ordered SOC and its constraint property, the following concepts or principles are proposed or established: (1) the criteria for determination of basic kinematic chain (BKC). (2) the coupling degree of BKC, (3) the criteria for determination of types of degree-of-freedom, (4) the formula for calculation of number of mechanism configurations, and (5) a new unified modular method for structural, kinematic and dynamic analysis of mechanism.

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