Mechanisms that incorporate internal cylindrical gears with a small difference between the numbers of teeth on the internal gear and the external gear offer several advantages, particularly when these mechanisms are used in cycloidal reducers, especially a high transmission ratio with a compact design. A special case of this type of mechanisms is when the difference between the numbers of teeth on the mentioned gears becomes zero. When the axes of the gears are fixed, the transmission ratio is equal to unity, and these gears can be used to transmit rotational motion in the same direction and with the same angular velocity between two shafts with a small distance between their axes. When the gear pair is part of a double-satellite cycloidal reducer, it can either cancel the satellite’s rotation around its own axis or allow motion to be extracted from the satellite and to be transmitted to the output shaft. In these cases, the transmission ratio of the cycloidal reducer is dictated by the difference in the numbers of teeth of the other pair of gears. When the difference in the numbers of teeth becomes zero, most of the mathematical equations used for classic internal-external gear pairs (where this difference is greater than zero) are no longer valid. This paper continues the presentation and discussion of some of the mathematical equations specific to these gear pairs. Some other part of these equations were presented and discussed in a previous paper.