The concept of spaces in the structural analysis and synthesis of mechanisms and machines

Abstract

Mobility analysis is the basic stage in structural synthesis of mechanisms, machines and other mechanical systems. Despite the development of the mechanism and machine theory, the discovery of new structural theories and formulas for determining mobility, many researchers continue to use the traditional Chebyshev formulas for flat mechanisms and Somov-Malyshev for spatial ones, which can lead to incorrect results. In the early 90s of the 20th century, Professor Smelyagin proposed to abandon the artificial division of mechanisms into “planar” (existing in a three-dimensional three-movable space) and “spatial” (existing in a three-dimensional six-movable space) in the structural analysis and synthesis of mechanisms and machines, and to use spaces of different dimensionality and mobility. In this paper, the proposed theory is revealed using practical examples of mechanisms and the spaces in which they exist. Using the concept of a M-movable space, there are derived equations to determine the mobility of simple and complex mechanisms. The examples of the formation of mechanisms in various spaces are given, and also the analysis of their mobility using the developed structural formulas is carried out.