Gear and Belt-Driven Systems in Motion
- Gear and belt systems aren’t just about motion: they also control Input Work or Power.
- Designers use them to:
- Increase or decrease speed
- Increase torque (rotational force)
- Reverse the direction of rotation
- Transfer motion between different axes
Understanding the System
$$\text{Gear ratio} = \frac{\text{Drive gear teeth}}{\text{Driven gear teeth}}$$
- A high gear ratio → more torque, less speed
- A low gear ratio → more speed, less torque
Belt Drives work similarly to gears, but:
- Allow flexible distance between components
- Can slip, which may be desirable in safety systems
- Can reverse motion depending on belt twist
Gear and Belt-Driven System Applications
| Product | Function of Gears or Belts |
|---|---|
| Bicycle gear system | Alters pedaling resistance and speed. Large front gear + small rear gear = fast, low-torque ride. |
| Cordless drill gearbox | Low gear for high torque when driving screws; high gear for speed when drilling. |
| Lathe belt system | Switches between belt positions to vary spindle speed for different materials. |
| Robotic arm | Gear trains reduce speed and increase precision torque for movement control. |
Direction Change Example
- Two meshed gears rotate in opposite directions.
- Add a third (idler) gear between them to maintain original rotation direction while adjusting spacing.
Calculating Speed of Rotation in Gear Systems
- To calculate the speed of rotation at different points in a gear system:
- Identify the Input Speed: The speed of the drive gear.
- Apply the Gear Ratio: Multiply the input speed by the gear ratio to find the output speed.
- Formula: $$\text{Speed of driven gear} = \frac{\text{Speed of driver gear}}{\text{Gear ratio}}$$
Example question
Calculate the output speed of a gear system with a drive gear rotating at 100 RPM and a gear ratio of 2:1. What is the speed of the driven gear?
Solution
$$\text{Speed of driven gear} = \frac{\text{Speed of driver gear}}{\text{Gear ratio}}$$
$$ = \frac{100}{2} = 50 \text{ RPM}$$
