# Kinematic analysis of Spur Planetary Gear

In order to carry out dynamic analysis of the system, this section first analyzes 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 fixed with the planetary carrier, but in the analysis, the acceleration of the mass center of the components used should be absolute acceleration, so it is necessary to express the displacement, displacement and displacement of each component in the generalized coordinate system through coordinate transformation Speed and acceleration.

As shown in Fig. 1, the schematic diagram of coordinate transformation is shown. Let the components of vector r in the planetary carrier moving coordinate system oxcyc are CX and CY; 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: