A model of the loop formation process on knitting machines using finite automata theory

Abstract

Computer control systems, currently available for industrial knitting machines, have been developed by individual machine manufacturers. The result is that each system is applicable only to a particular machine type. This work is aimed toward the determination of a generic control system that could be applied to a wide range of knitting machine types. A model of a knitting needle operation is proposed. This takes the form of a multitape controlling automaton and an operational automaton functioning together. The conformity between the technological functions of the separate parts of knitting machines and the functions of an automaton is determined. Diagrams of states and alphabets of input, stack, and output symbols of an operational automaton are defined. The functioning of this automaton is reduced to the performance of nine operations, which are its system of instructions. This enables the processes of basic structural element formation, i.e., knitted loop, tuck loop, and float, on needles of different types and on knitting machines of various constructions to be modelled uniformly. The model proposed also describes the process of a loop transfer, the new knitted fabric commencing on empty needles and finished fabric press-off. Furthermore, consideration has been given to the operation of a multitape controlling automaton that would be integrated in the design of a knitting machine. An algorithm for output symbol determination has been developed that provides independent automaton control of the number of cam layers, the identification of cam track, and the number of needles in use. The software for minimization of the disjunctive normal form of Boolean functions, based on the methods of Quine and Gorbatov, has been developed. The possibility of modelling knitting machine malfunctions is described, enabling deviations from the correct process, such as hook or latch damage, to be studied.