Abstract: The analytical method of the motion composition for a moving point is discussed via the case of “wire + small ring”. The relative motion is described by an arc coordinate, and then the theorems of composition of velocities and accelerations are rigorously derived for a moving point. This analytical method highlights the intuitiveness of the theorems and the physical concept of the motion composition, which helps readers to have a deeper understanding of the transport points. The analytical method of solving motion composition by auxiliary geometric model is also practiced.