OPTIMAL DESIGN OF A STEPPER-DRIVEN PLANAR LINKAGE USING ENTROPY METHODS

Abstract

Stepper motors can be used to provide open-loop motion control in mechanisms. Unlike servo controlled mechanisms, however, the rotational drive input error cannot be resolved below the step error in the motor. Therefore, there is a fixed level of rotational position error that must be accepted in stepper driven mechanisms, and this rotational position error will inevitably propagate to kinematic position error in the mechanism. In this paper, the direct linearization method will be used to derive a model for kinematic position error based on uncertainty in the rotational input angle of a mechanism. Using this model, a method of constrained optimization to design a mechanism to minimize the effect of uncertain input conditions on kinematic position will be presented. The method is based on entropy minimization techniques that have been applied in a variety of robotic system applications. The method will be demonstrated in a case study, and will be shown to optimize the positioning reliability of a mechanism under input angle errors. The method will be shown to accurately predict drive error propagation, through comparison to Monte Carlo simulation. When coupled with entropy-based system reliability optimization methods, optimal mechansims can be synthesized in response to various positioning constraints.