A generalized approach for topological design of parallel mechanisms featuring symbolic forward kinematics and motion decoupling using motion-decoupling branches

Designing parallel mechanism (PM) with symbolic forward kinematics (SFK) and motion decoupling (MD) is highly beneficial for subsequent tasks such as real-time control, motion trajectory planning, dimensional synthesis, error analysis, and dynamic analysis. Inspired by first principles, using directly from motion-decoupling branch (MDB) as design units that enables PM to simultaneously achieve SFK and MD, this paper proposes a generalized topological design approach for PMs based on degrees of freedom (DOF) and position and orientation characteristics (POC) as fundamental functions, with SFK and MD as performance indicators. First, nine simple and ten hybrid MDBs are introduced. Second, a general approach for PM topological design using MDBs is proposed. This approach can covers two types of PMs: Type I—designing a PM consisting of MDB with the number of actuated pairs DOF₀ (DOF₀ < DOF) and end-effector POC, along with (DOF - DOF₀) unconstrained branches, followed by topological verification. Type II—first designing at least one MDB and one or more constrained branches, then assembling them into various PMs, and finally obtaining the DOF and POC of the series of PMs through topological analysis for classification and application. Third, five examples, with total eleven novel designed 3-DOF PMs with different type of POCs, are provided to illustrate the design process of general over-constrained PMs using the approach. Finally, guided by the approach, three conditions achieving AI-based topology design for PMs using MDBs are suggested, and the preliminary results for AI-based topology design of 2-DOF 1T1R novel PMs are also discussed.