# Kinematic analysis of components in Spur Planetary Gear System

In order to analyze the dynamics of the system, firstly analyze the acceleration of each component in the planetary gear transmission system. As mentioned above, the coordinate system used for dynamic analysis is the coordinate system connected with the planetary carrier. However, the acceleration of the mass center of the component used in the analysis should be absolute acceleration. Therefore, the displacement and velocity of each component in the generalized coordinate system should be expressed by coordinate transformation And acceleration.

As shown in the figure is the diagram of coordinate transformation. Let the components of vector r in the planetary carrier moving coordinate system oxcyc be XC and YC; in the fixed coordinate system oxy, the components are x, Y:

According to the geometric relationship, it can be seen that:

Where:

ω C, T — angular velocity and time of planet carrier respectively.

After calculating the first derivative of the formula for time, the expression of velocity relation in generalized coordinates can be obtained

After calculating the second derivative of time, the expression of acceleration relation in generalized coordinates can be obtained

It can be seen that the central acceleration of each component is: 