Pulley Calculator
Calculate pulley system parameters including RPM, diameter, belt properties, and mechanical advantage
Pulley System Parameters
Diameter of the driving pulley (input pulley)
Rotational speed of the driving pulley
Diameter of the driven pulley (output pulley)
Power transmitted through the pulley system
Distance between the centers of both pulleys
Calculation Results
Key Formula: d₁ × n₁ = d₂ × n₂ (diameter × RPM constant)
Belt Velocity: v = π × d₁ × n₁ / 60 = 20.94 m/s
Driven Torque: 3.58 N·m
System Analysis
Example Calculation
Pulley System Setup
Driver Pulley: 0.4 m diameter, 1000 RPM
Driven Pulley: 0.1 m diameter
Power: 1500 W
Center Distance: 1 m
Step-by-step Calculation
1. Driven RPM: n₂ = (d₁ × n₁) / d₂ = (0.4 × 1000) / 0.1 = 4000 RPM
2. Belt Velocity: v = π × d₁ × n₁ / 60 = π × 0.4 × 1000 / 60 = 20.94 m/s
3. Belt Length: L = (0.4π/2) + (0.1π/2) + 2(1) + (0.4-0.1)²/(4×1) = 2.808 m
4. Belt Tension: F = P / v = 1500 / 20.94 = 71.6 N
5. Mechanical Advantage: 4000/1000 = 4x speed increase
Pulley System Types
Fixed Pulley
Changes direction of force
No mechanical advantage
Movable Pulley
Provides mechanical advantage
Reduces effort force
Compound Pulley
Multiple pulleys combined
Maximum mechanical advantage
Common Applications
Automotive
Engine belts, timing systems
Industrial
Conveyor systems, machinery
Construction
Cranes, elevators, hoists
Exercise
Weight machines, cable systems
Bicycles
Chain and gear systems
Understanding Pulley Systems
What is a Pulley System?
A pulley system consists of two or more pulleys connected by a belt or rope. It's a simple machine that can provide mechanical advantage by changing the direction of force or reducing the effort needed to move a load.
Key Principles
- •Conservation of energy: Power input equals power output
- •Trade-off between speed and force
- •Diameter ratio determines speed ratio
- •Belt connects pulleys and transmits motion
Essential Formulas
d₁ × n₁ = d₂ × n₂
v = π × d₁ × n₁ / 60
F = P / v
T = P / (2π × n / 60)
- d₁, d₂: Driver and driven pulley diameters
- n₁, n₂: Driver and driven pulley RPM
- v: Belt velocity (m/s)
- F: Belt tension (N)
- P: Transmitting power (W)
- T: Torque (N·m)
Remember: Smaller driven pulley = higher speed, lower torque. Larger driven pulley = lower speed, higher torque.
Mechanical Advantage in Pulley Systems
Mechanical advantage in belt-driven pulleys is determined by the diameter ratio. Unlike block and tackle systems, belt pulleys trade speed for torque (or vice versa) while maintaining constant power transmission.
Speed Advantage
Smaller driven pulley increases rotational speed but reduces torque
Torque Advantage
Larger driven pulley increases torque but reduces rotational speed
Power Conservation
Power remains constant: P = Torque × Angular velocity