A spatial gear-mechanism with double curvature tooth surfaces is discussed. The following results are obtained: a) the relationship between the principal curvatures of the surfaces, b) the conditions under which the path of the contact point on the surface is a geodetic line in the local sense. A method of synthesis of mismatched gearing proposed here permits determination of optimal conditions of meshing in the vicinity of the main contact point.

Kinematic and kinetic performance are important issues in designing multi-degree-of-freedom mechanisms such as robotic manipulators. In the engineering design stage, it is especially important that the designer can grasp the characteristics of the mechanism. The aim of this study is to develop a means of representing the kinematic and kinetic performance of the mechanism in such a way that the performance characteristics are quantified analytically and visible graphically to the designer in their entirety at the conceptual design stage. Various performance indices are derived from the Jacobian matrix and its quadratic form. These performance indices are the local kinematic cross-coupling index (angle of intersection between column vectors of the Jacobian), the local directional mobility index (ratio of Jacobian’s eigenvalues), and the local efficiency index (product of Jacobian’s eigenvalues). Graphical images of these performance characteristics using eigen-ellipsoid and workspace trajectory contours are introduced. Critical performance points in mechanism workspace are identified and elaborated for design considerations. Based on the graphical representation of these performance characteristics, design rules for achieving different performance objectives can easily be implemented. This method is applicable to computer-aided design of a mechanism and predetermination of its kinematic and kinetic performance.

Methods for synthesis and analysis Hypoid gears generated by Helixform and Formabe methods are suggested. The article is a three-part one divided according to the considered stages of synthesis and analysis: (a) the determination of machine settings for the member-gear manufacture (after that tooth surface of the member-gear can be obtained); (b) machine setting calculations for the pinion on the base of the local synthesis for gears with approximate meshing; (c) methods for analysis (in the whole area of meshing) and optional synthesis for the mismatch gearing and its application for Hypoid gears.

No abstract

In this third and final part are proposed: (a) methods for analysis and optimal synthesis of mismatch gearing, (b) application of those methods for the analysis and synthesis of hypoid gear-drives generated by “Formate” and “Helixform” methods. In the previous parts, machine settings for the member-gear and the pinion of the Hypoid gear-drive were obtained. Use of these settings guarantee: (a) that the gear surfaces will be in tangency at a previously chosen point M, (b) that the conditions of meshing will be favorable at the point M and in its vicinity. But it is necessary to provide favorable conditions of meshing in the whole area of meshing. Methods proposed in this part permits achievement of those mentioned aims: (a) the analysis of gearing permits collection of the necessary information of meshing conditions in the whole area of meshing, (b) the optimal synthesis permits improvment of the conditions of meshing by variation of some parameters of pinion machine settings.