What is the formula for calculating the speed ratio of the planetary gearbox?

Planetary gear system, also known as planetary reduction system, is an important part of modern engineering. For speed changes, they can play a very large role. And, we can find it in the fields of automatic car transmission, industrial food mixer, operation table, solar panel and so on. It sounds very shocking to calculate the gear ratio of a planetary system by just using the four core components-the ring gear, the sun gear, and the planetary gear connected to the carrier-to calculate the gear ratio of the planetary system. However, the uniaxial nature of the system makes calculations easy. Just be sure to pay attention to the state of the gear system carrier.
Calculation:

　　 In order to make the calculation of gear ratio easier, then, we must pay attention to the number of teeth of the sun and ring gear. Second, add these two numbers together. The sum of the number of teeth of the two gears is equal to the number of teeth of the planetary gear connected to the carrier. For example, if the sun gear has 20 teeth and the ring gear has 60 teeth, then the planetary gear has 80 gears. The next step is to rely on the state of the planetary gears connected to the carrier. The method of calculating the transmission ratio is by dividing the number of teeth of the driving gear by the number of teeth of the driven gear.
　　 carrier as input:
　　 If the carrier plays the role of input in the planetary gear system, rotating the sun gear, and when the sun gear is stationary, the gears of the planetary gears are divided by the number of teeth of the ring gears. According to the previous example, 60 ÷ 80 = 0.75. Then, the reduction ratio is 3:4.
　　 carrier as output:
　　In the planetary reduction system, the carrier plays the role of output, and the sun gear rotates while the ring gear is at rest. Then, the calculation formula is, the gear of the sun gear divided by the number of teeth of the planetary gear. According to the first example, then the reduction ratio is: 80 ÷ 20 = 4, 4:1.
　　 The carrier is at rest:
　　In a planetary gear system, if the carrier is at a standstill and the ring gear rotates the sun gear. Then, the formula for calculating the speed ratio is: the number of teeth of the ring gear divided by the number of teeth of the sun gear. According to the previous example, 20 ÷ 60 = 3, 3:1.  CHINA HIGH PRECISION PLANETARY GEARBOX PL SERIES WITH LOW COST Item No.: PL01 planetary reducer used on robot arm cnc machine rotary table Output Torque: 48-160 Input Speed: 3000r/min Output Speed: planetary reducer The Allowed Radial Force F1: 3100N The Allowed Axial Force: 1550N Efficiency: 0.91-0.97 Life Time: 20000 Hours