Velocity Ratio Calculations
Definition
Velocity Ratio
A measure of how fast one part of a mechanical system moves compared to another, helping designers control speed, torque, and efficiency.
Key formula:
$$\text{Velocity Ratio (VR)} = \frac{\text{Input Speed}}{\text{Output Speed}}$$
NoteVelocity ratio is a dimensionless quantity, meaning it has no units. It simply expresses a relationship between two speeds.
Velocity Ratios in Gear Systems
- Gears are used to transmit torque and rotational motion between shafts.
- The velocity ratio in a gear system is determined by the number of teeth on the gears.
- A large output gear = slower speed, more torque
Formula:
$$\text{VR} = \frac{\text{Number of teeth on output gear}}{\text{Number of teeth on input gear}}$$
ExampleInput gear = 20 teeth, Output gear = 40 teeth → VR = 40 / 20 = 2
Tip- When calculating velocity ratios, always identify which gear is driving and which is driven.
- This ensures accurate calculations and understanding of the system's behavior.
Velocity Ratios in Pulley Systems
- Pulleys are used to change the direction of force and provide mechanical advantage.
- The velocity ratio in a pulley system depends on the diameter of the pulleys.
Formula:
$$\text{VR} = \frac{\text{Diameter of driven pulley}}{\text{Diameter of driver pulley}}$$
ExampleDriver pulley = 50 mm, Driven pulley = 100 mm → VR = 100 / 50 = 2
