Effect of belt extensibility on variation of the relative position of a needle and a hook in a sewing machine

Considers the mathematical modelling of sewing machines. The machine with a rotary hook and with a feed mechanism driven by two triangle cams is studied. The behaviour of the system is described by a set of non‐linear autonomous ordinary differential equations. It is shown that, due to the timing belt extensibility, the actual relative position of the needle and the hook is different from that expected. This difference is a result of the conflict between the almost constant speed of the hook shaft and the fluctuating speed of the crank‐shaft caused by the reciprocating motion of working elements. The vibration of the belt increases with speed. Resonance increase of vibrations takes place when the shaft speed is equal to natural frequency or its fraction 1/n for n = 1, 2, 3, 4, 5.