---
# System prepended metadata

title: Gear Train
tags: [Mechanical Principle, gear]

---

# Gear Train
## Type of mechanical transmission element
![type of mechanical transmission element_S](https://hackmd.io/_uploads/B1IOdn3Llg.png)

## Speed Ratio
**Simple Gear Train**
<div style="text-align: center;">
<img src="https://d2t1xqejof9utc.cloudfront.net/screenshots/pics/320e0794001dd3e388f78c7d58f500e9/large.png
" alt="image"width="300">
</div>

>https://grabcad.com/library/simple-gear-train-3

$$T_AN_A = T_BN_B$$

$$\frac{T_A}{T_B} = \frac{N_B}{N_A}$$

* Increase speed : $\frac{N_{out}}{N_{in}}>1$
* Constant speed : $\frac{N_{out}}{N_{in}}>1$
* Reduce speed : $\frac{N_{out}}{N_{in}}>1$

$$\tau = r\times F$$

$$F_A = F_B$$

$$\frac{T_A}{T_B} = \frac{\tau_A}{\tau_B} = \frac{N_B}{N_A}$$

**Compound Gear Train**
<div style="text-align: center;">
<img src="https://woodgears.ca/gear/7-21-9-30.png" alt="image"width="300">
</div>

>https://woodgears.ca/gear/ratio.html

$$T_AN_A = T_BN_B$$

$$T_CN_C = T_DN_D$$

$$N_B = N_C$$

$$\frac{T_A}{T_B} = \frac{N_B}{N_A}$$

$$\frac{T_C}{T_D} = \frac{N_D}{N_C}$$

$$\frac{T_A}{T_B}\frac{T_C}{T_D} = \frac{N_B}{N_A}\frac{N_D}{N_C} = \frac{N_D}{N_A}$$

* Worm : Number of Threads >> $T$

**Epicyclic Gear Train**
<div style="text-align: center;">
<img src="https://ww2.mathworks.cn/help/sdl/ref/planetary.gif" alt="image"width="300">
</div>

>https://ww2.mathworks.cn/help/sdl/ref/planetarygear.html

$$\frac{N_A-N_m}{N_B-N_m} = \frac{T_B}{T_A}$$

**Compound Epicyclic Gear Train**
<div style="text-align: center;">
<img src="https://www.mathworks.com/help/sdl/ref/compound_planetary.gif" alt="image"width="300">
</div>

>https://ww2.mathworks.cn/help/sdl/ref/compoundplanetarygear.html


$$\frac{N_A-N_m}{N_Z-N_m} = \frac{T_BT_DT_F...T_Z}{T_AT_CT_E...T_Y}$$