# The principle of speed change of planetary gear mechanism

Because the single row planetary gear mechanism has two degrees of freedom, it has no fixed transmission ratio and can not be directly used in variable speed transmission. In order to form a transmission mechanism with a certain transmission ratio, one of the three basic elements, the sun wheel, the ring gear and the planet carrier, must be fixed (even if its speed is 0, also known as braking), or its movement must be constrained (that is, the component can rotate at a fixed speed), or the two basic elements must be connected with each other (that is, they have the same speed), The planetary array is transformed into a mechanism with only one degree of freedom, and definite transmission is obtained.

Set the number of teeth of the sun gear as Z1, the number of teeth of the ring gear as Z2, the rotation speed of the sun gear, the ring gear and the planet carrier as N1, N2 and N3 respectively, and set the ratio of the number of teeth of the ring gear and the sun gear as α, that is

Alpha =Z2/Z1

The general motion law of planetary gear mechanism can be expressed as follows:

n1+αn2-（1+α）n3=0

It can be seen from the above formula that in the three basic elements of the sun gear, ring gear and planet carrier, two can be selected as the driving and driven parts respectively, and the other element can be fixed (making the element rotate at zero speed) or its movement subject to certain constraints (making the element rotate at a certain value), then the whole gear system transmits the power with a certain transmission ratio. Different connection and fixing schemes can get different transmission ratios. Different combinations of three basic elements can have six different combinations. In addition, there are eight combinations of direct gear transmission and neutral gear. Accordingly, five different transmission ratios can be obtained. 