An analytical framework of the kinematic geometry for general point-contact gears from contact path

Abstract

Based on the idea that the relative curvature relationships along total contact path will better reflect the contact characteristics of gears, this study attempts to develop an analytical framework for the kinematic geometry of point-contact gears from the contact paths. First, a general method for obtaining the contact path of a gear from a pinion is proposed. Second, a normal curvature and geodesic torsion calculation method in the contact path direction is developed. Then, based on the linearly dependent condition of the tangent vectors of the two contact paths, two relative normal curvature analysis methods are proposed by applying the fundamental form theory. Finally, a sample case is presented to show the application and complete the verification of the kinematic geometry methods. The sample case agrees with the analytical model.