Stepper Motor Driven Four-Bar: Dynamic Modeling and Synthesis

Abstract

Abstract This paper presents the dynamic modeling and synthesis of a four-bar mechanism that is driven by a four-phase, variable-reluctance stepper motor. Dynamic models of both the mechanism and the motor are derived and subsequently combined in order to numerically determine the system dynamic response. In the stepper motor model, full circuit equations are derived for each of 8 stator poles, with full expressions for armature self- and mutual-inductances, as well as developed motor torque. The stepper motor model admits arbitrary input pulse trains, and includes both coil resistance and inductance. A set of five, simultaneous, nonlinear, second-order ordinary differential equations is analytically derived and numerically solved to determine stepper response. In the four-bar mechanism model, three dynamical properties (primary effective inertia, secondary effective inertia, and gravitational disturbance torque) are derived using a Lagrangian approach, and utilized to determine the dynamic suitability of candidate four-bars for three-position, rigid body guidance. Three candidate four-bar mechanisms are synthesized, and their dynamic response (when coupled to the variable-reluctance stepper motor) is compared. It is shown that an engineering trade-off exists between parallelogram and crank-rocker four-bars, in which the former may possess lower primary effective inertia, but the latter may possess lower gravitational disturbance torque.