Topological Design Methods Of Spatial Multi-loop Mechanisms With Serial-Parallel Hybrid Forms And Kinematotropic Properties

The spatial multi-loop mechanisms can be categorized into parallel and hybrid forms. However, as far as the design of hybrid non-spanning tree netted forms and variable mobility are concerned, there are no any developed method are available. Thus, to realize the systematic design of spatial hybrid mechanisms and kinematotropic analysis of mobility, this research presents a novel topological design method of spatial mutli-loop mechanisms with serial-parallel hybrid forms and kinematotropic properties.This research adopts12bits of binary string matrices to represent the spatial mechanisms based on mathematical logic method. Meanwhile, the three orders of six values non-classical logical matrices are developed to represent spatial topological motions, relations and determination of reference frames. The combinatorial logical sets are built and axiomatized for the design of topological structures. Thus, the motions and constraint relations can be defined in the structural operation of logical matrices, and the logical operation and reasoning can be developed in the design of topological structures.To realize the design of topological structures, the matrices of topological arrangements are presented in the connected forms of subchains and platforms. The topological arrangements can be generated by the linkage group mapping and fractal methods. The mapping relationships between the topological arrangement and geometry are developed which include the closed type and opened type of topological arrangements with single and multiple ending output manipulators respectively. Furthermore, the logical method of Spatial Multi-loop Detachment (SMD) is presented for the topological arrangements to analyze the relationships between the ending output motions and motions of subchains. Meanwhile, the Configuration Card of Displacement subsets of Subchains (CCDS) is developed for the structural configuration of subchains according to the results of SMD. The design of topological structure with non-spanning tree netted forms can be solved to build the novel systematic method of topological structural design. As far as the kinematotropic properties of multi-loop structures are concerned, the principles of kinematotropic mechanisms and topological structural sets are developed to design the spatial multi-loop mechanisms with kinematotropic properties.At last, various novel spatial multi-loop mechanisms are built as examples to illustrate the applications of the presented method. A novel kinematotropic hybrid parallel manipulator in dual axes KHPM-â…  is built in particular, and the kinematic properties are analyzed. Meanwhile, the corresponding prototype is manufactured and applied into the testing of the practical output motions.On the one hand, the presented method is helpful to the topological structural design of the complicate spatial multi-loop mechanisms, and on the other is that the mathematical logical representation and operations of structures are programmable, and it is somewhat to realize the automatic design of spatial multi-loop mechanisms easily.