Study on Deformed Limacon Gear and Motion Optimization of Its Serial Mechanism

Abstract

In order to obtain the nonsinusoidal oscillation wave of continuous caster molds, a vibration generator comprised of an eccentric shaft and a new kind of noncircular gears called deformed limacon gear pair is proposed. The pitch curve equations of limacon gears are described based on the cosine rule. According to the closed property of noncircular pitch curves and residue theorem, the center distance between a limacon gear and its conjugate gear is deduced, as well as their transmission ratio and the pitch curve equations of the conjugate gear. Subsequently, the mathematical model of deformed limacon gears with dissymmetrical transmission ratio in one period is established and the kinematic formula of the serial mechanism is presented for optimization by a modified genetic algorithm. Here, a computer program is developed for optimizing the gear linkage mechanism to meet requirements in practice and results show that expected motion can be achieved by deformed gear linkage mechanism, which can provide a new choice for application.