Structural Synthesis of Serial-Parallel Hybrid Mechanisms Based on Representation and Operation of Logical Matrix

Abstract

This paper presents a systematic approach on structural synthesis of serial-parallel hybrid mechanisms from the point of displacement group theory and mathematical logic. The hybrid mechanisms can be represented by binary 12 bit string matrix, where the lower 4 bits represents the universal set of spatial displacement subsets, while the higher 8 bits represents the two-order adjacent relations of spatial displacement subsets. Meanwhile, the concept of an arrangement matrix and three types of fractal operations can be developed. Utilizing the novel representational approach of mechanisms, the displacement subsets and spatial adjacent relations can be operated in logical matrices based on the given mapping of logical matrix operation. The binary logical mirror coordinate system of mechanisms is developed by logical representations. Finally, an example of structural synthesis of hybrid mechanism (two-order hybrid mechanism) is introduced using the proposed approach. The approach is helpful for the processing of serial-parallel hybrid mechanism designs.