Analysis and Synthesis Procedures for Geneva Mechanism Design

This paper contains general analytical results which can be applied to high-speed Geneva design. The results are derived from classical mechanics theory and provide explicit relationships between the performance parameters (those parameters such as contact stress, maximum load, etc., which can have a significant effect on the mechanism performance) and the design variables which specify a Geneva mechanism (number of slots, wheel diameter, pin diameter, etc.). In the past, the complexity of the mathematical formulation of this problem has precluded synthesis of the Geneva wheel proportions. Using these results, however, it is now possible to synthesize the wheel configuration directly, instead of by a repeated trial and error analysis. Two examples are given demonstrating the analysis and synthesis techniques. Introduction Geneva mechanisms have long been popular as a means of producing positive incremental motion. This popularity stems in part from the simplicity of the mechanism, both in design and construction, which makes it a relatively low-cost indexing device. In addition, the mechanism inherently produces a precise positioning motion that is necessary for many applications. In the applications where this mechanism is presently utilized, it has proven to be extremely trouble-free and dependable. In the future it is expected that this device may find many applications requiring higher speeds. As the higher speeds become necessary, the mechanism becomes less attractive as an incremental device because of its kinematic limitations.’ For instance, a severe limitation under these conditions may result from the high maximum wheel acceleration relative to its average acceleration.’ This characteristic may cause excessive dynamic loads which in turn can cause severe drive pin and slot wear and/or wheel breakage. Therefore the analytical design problem in the case of high-speed Geneva mechanisms, where inertial loads are dominant, is one where the best combination of the design variables is sought to reduce the inherent kinematic limitations of the mechanism. The primary objective of this paper is to present explicit graphical relationships between the limiting stresses (both wear and breakage) and the available design variables so that their quantitative influence may be readily evaluated 186 by the designer to produce an optimum Geneva design. These relationships will not only allow one to analyze an existing design but also, more importantly, will allow the designer to synthesize the wheel configuration from maximum stress and/or load criteria. Design approach Many factors contribute to a successful Geneva mechanism design, such as materials used, surface finish, tolerances, loads, stress levels, lubricant, etc. Unsuccessful experimental applications of this mechanism usually result in two modes of failure: pin wear and wheel breakage. Of these two modes, wear is the hardest to control. The present design approach will be to reduce wear by altering the geometry of the Geneva wheel to reduce the contact stress while maintaining acceptable stress levels in other regions of the wheel. R. C. Johnson3 showed that an optimum wheel diameter exists for minimum wear stress. In this paper, consideration is given to two additional dimensions (pin diameter and tip thickness) on the wear stress and certain internal beam stresses. This paper will begin by defining the wheel geometry and then developing the relationships between this geometry and the wheel inertia, the maximum pin load, the contact stress, and the internal wheel stresses. These performance parameters will be normalized to the corresponding parameters of a set of predefined “standard” Genevas for convenience in interpreting results. For the “standard” set chosen, curves will show the stress and load parameters as a function of inertia and speed. The normalized curves IBM JOURNAL MAY 1966