Dynamic analysis of a geared infinitely variable transmission (IVT) that can generate a continuous output-to-input speed ratio from zero to a certain value is studied for vehicle and wind turbine applications. With the IVT considered as a multirigid-body system, the Lagrangian approach is used to analyze its speeds and accelerations, and the Newtonian approach is used to conduct force analysis of each part of the IVT. Instantaneous input and output speeds and accelerations of the IVT have variations in one rotation of its input shaft. This work shows that the instantaneous input speed has less variation than the instantaneous output speed when the inertia on the input side is larger than that on the output side and vice versa. The maximum torque on the output shaft that is a critical part of the IVT increases with the input speed.