Determining the accelerations of points of a planar eight-link third-class mechanism using graph-analytical method

Abstract

A characteristic feature of technological machines used in the fashion industry is the complexity of motion of the working links, both in terms of geometry and motion laws. Such technological motions are provided by complex mechanisms, the basis of which consists of structural groups of third-class and higher-class links. In multi-link structural groups of higher classes, complex motions of certain points along trajectories resembling planar linkage curves of various geometric shapes are observed. If the centers of external kinematic pairs of another structural group, which is attached to the previous group of links, are placed at such points, theoretically, any trajectory of the working point of the machine with the necessary motion laws required for performing a technological operation can be obtained. In practical application, the use of higher-class structural groups within the kinematic scheme of a planar mechanism leads to complexities in its further investigation. This is explained by the necessity of conducting studies using specially developed methods for their implementation. In cases where these methods cannot be applied, there arises the need for individual development of a sequence for conducting such studies in each specific case of such complex mechanisms, taking into account their structural characteristics. A sequence of actions has been developed and a kinematic analysis of an eight-link third-class mechanism has been conducted using a graph-analytical method. Acceleration plan has been graphically constructed, and the magnitudes and directions of angular accelerations of the mechanism’s links have been calculated. The selection of a conditionally different possible initial mechanism allowed transforming the eight-link third-class mechanism with two sequentially attached structural groups of links into a mechanism with sequentially-parallel attachment of second-order second-class link groups and performing the analysis of the third-class mechanism in a manner characteristic of the analysis of second-class mechanisms. The proposed method of analyzing higher-class mechanisms may be useful for conducting similar studies.