Mathematical Modeling and Experimental Analysis of the Thread Take-up Function in Single-thread Chain Stitch Sewing Machines Type 101

Abstract

An analytical and experimental methodology for evaluating functional characteristics of the single-thread chain stitch formation process (type 101) is proposed. The evaluation is based on degree of correspondence between the required and actual thread take-up, which reflects the machine’s efficiency and the quality of stitch formation. A measuring system and an experimental procedure were developed to record thread take-up under different material thicknesses and stitch lengths. The obtained dependencies were approximated by sixth-degree polynomials with high accuracy (R² > 0.99), which made it possible to construct mathematical models of the thread take-up process. For GK-9 type machines, excessive thread take-up (20–64% above the required value) was set up, causing uneven thread tension and reduced stitch stability. The proposed methodology ensures quantitative evaluation, prediction, and regulation of thread take-up process, which improves functional efficiency of sewing machines and supports development of adaptive thread take-up control systems.