Research in developing a Positively Engaged Continuously Variable Transmission (PECVT) has been underway at Brigham Young University for some time. The inherent problems associated with embodiments of this type of transmission, namely the Non-Integer Tooth Problem (NITP), have been identified. This research is focused on the development of a Positively Engaged Piecewise Continuous Transmission (PEPCT), which is a subset of the PECVT. This document describes the hypothesis and analysis of using non-circular gearsets to overcome the NITP. This proposed solution enables a varying angular output from a constant angular input. In this research two analytical methods were evaluated based on their theory, mathematics and simulated results. Haupt's concept is shown to have discrepancies between the theorized and mathematical results which produce a gearset that has velocity spikes in its output. The second method, proposed by Danieli, describes the behavior on an infinitesimal level and the theorized results match up with the mathematical result. As a result of the analysis, Danieli's method is declared to produce a varying output from a constant input. The method requires only the definition of an input function that defines the shape of the pitch line similar to the pitch circle for circular gears. Using this function an infinitesimal approach is used to describe the interaction of consecutive contact points on the tooth profiles. This interaction takes into consideration adapted principles that are derived from the Fundamental Law of Gearing and the Law of Conjugate Action. With these principles defined it is possible to design gearsets that are capable of producing a varying angular output from a constant angular input. With the validation of the second method, and the principles defined by which it is governed, the proposed gearset is achievable allowing a PEPCT to be conceived. The proposed transmission utilizes the non-circular gearset to accelerate a secondary shaft to the next desired ratio while maintaining constant engagement. This concept is then analyzed and recommendations are made for the development of a Positively Engaged Continuously Variable Transmission.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





continuously variable transmission, gear, non-circular, gearset