This paper analyzes the basic forms of 4-DOF spatial motions through the introduction of logical propositions for the topological structural synthesis of multiloop hybrid spatial mechanisms. The proposed method for the topological structural synthesis is based on displacement group theory and consists of two elements. First, spatial multiloop detachment (SMD) is proposed for the analysis of the output motion relations in multiloop topological arrangements. Second, configuration cards for displacement subsets of subchains (CCDS) are developed for subchain design. To demonstrate the applicability of SMD and CCDS to the four basic forms of 4-DOF motions, 12 novel serial-parallel hybrid mechanisms are synthesized that include the nonspanning tree netted form of topological arrangements.

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