Topological design and positional closed-form solution research of 4 motion decoupled single-loop 2-DOF three-translation parallel mechanisms - SHE Junjie; LI Ju; KONG Xiangchao; SHEN Huiping (Jixie chuandong)
ObjectiveIn order to understand the influence of side chains with similar topological structures on the decoupling and derived motions of parallel mechanisms, parallel mechanisms with similar topological structures were designed, and their topological characteristics and position equations were analyzed.MethodsFirstly, based on the topology design method of parallel mechanisms using the position and orientation characteristic set theory, four novel single-loop spatial two-degree-of-freedom three-translation parallel mechanisms composed of similar branches were constructed. The design process was detailed, and the degrees of freedom were calculated. Secondly, kinematic models of these four mechanisms were established, and closed-form univariate octic （eighth-degree） equations for the forward kinematics were derived, with numerical methods employed to obtain numerical solutions. Symbolic inverse kinematic solutions were also derived analytically and verified. Finally, the intrinsic relation between the independently output motions and parasitic motions of the moving platform was analyzed.ResultsIt is found that these single-loop two-degree-of-freedom three-translation parallel mechanisms are motion-decoupled and exhibit parasitic motions, making them suitable as main structures for lightweight three-dimensional vibrating screens. The results lay the foundation for dimensional optimization, workspace analysis, and dynamic analysis of such mechanisms.