Vibrations of a crank‐shaft in a sewing machine induced by a zigzag mechanism

Torsional vibrations of a shaft induced by a zigzag mechanism in a sewing machine with an oscillatory hook are studied in this paper. The dynamic equations of the motion are derived using the principle of virtual work. The discrete forms of the functions relating the motion of machine elements are found using Newton‐Brent method. They are replaced locally by the continuous ones using Lagrange formula. The limit cycle trajectory is found by direct numerical integration and it is illustrated graphically. The presented mathematical model of the zigzag sewing machine makes it possible to choose the proper parameters of the machine at the preliminary state of design.