With energy demands at an all time high, mechanical power systems are under great scrutiny. Substantial efforts are being made throughout the world to reduce energy use in common mechanical systems such as the internal combustion engine and transmission system. Eliminating or reducing efficiency losses in the transmission is a potential source of improving the efficiency of the system. To do so, various alternative types of transmissions are being investigated. At Brigham Young University, development of a Positively Engaged Continuously Variable Transmission (PECVT) is progressing. In addition to the efficiency increases that would occur as a result of operating the engine at a more constant speed, a PECVT type transmission may reduce efficiency losses that occur in a standard transmission by eliminating the disengagement of involute gear sets to change gear ratios of the transmission. For a PECVT, this is done by maintaining engagement of the input and output members of the transmission, while changing the gear ratio. Both of these types of losses are major contributing factors to the overall efficiency of the transmission and engine system, thus a PECVT is of great interest. The investigation for developing a feasible PECVT began with the identification of a behavioral issue identified in all known PECVT embodiments. This behavioral issue, known as the Non-Integer-Tooth-Problem (NITP), is due to the geometry of an involute gear and prevents specific gear ratios from being achieved. The research effort presented in this thesis returns to the conceptual design of a PECVT to address involutometry along with the NITP. A design tool entitled the Line-of-Action Model is developed which assists in quantifying how a conceptual solution can address the NITP using involutometry principles. As a result of the Line-of-Action Model, the Hybrid Involute Profile was discovered. Due to the simplicity of The Hybrid Involute Profile, it has proven to be an elegant solution to the NITP. Validation of the Hybrid Involute Profile concept was conducted to ensure that this concept satisfies the objectives and requirements of a PECVT and solves the NITP. The validation was completed using two case studies and a theoretical analysis. As a result of the validation, the Hybrid Involute Profile is declared a conceptual principal solution to the NITP. Fulfillment of the PECVT objectives, requirements list and elimination of the NITP by the Hybrid Involute Profile is also demonstrated. With the Hybrid Involute Profile as the conceptual principle solution, the development of a commercially viable PECVT is believed to be attainable.