Mechanical Advantage Simulator Back
Simple Machines

Mechanical Advantage Simulator

Calculate and animate mechanical advantage for levers, pulleys, inclined planes, and screw jacks. Adjust friction and input force to see real force amplification and efficiency.

Select Machine Type

Parameters

Results
Ideal MA (VR)
-
Actual MA
-
Efficiency η
-
%
Output force
-
N
Machine Diagram
Required Input Force vs Load
Theory & Key Formulas
MA = F_out / F_in

What is Mechanical Advantage?

Mechanical advantage is the ratio of output force to input force. A large MA lets a small input force lift a larger load, but the input point must move farther. The simulator shows that trade-off directly through the diagram and force chart.

$$MA=\frac{F_{out}}{F_{in}}$$

Practical Notes

Friction lowers actual mechanical advantage. Real machines should be checked over the full operating range, because the weakest point is often not the default setting but the high-load or high-friction case.

Applications And Limits

Levers, pulleys, screw jacks, inclined planes, and wheel-and-axle mechanisms all trade force for travel distance. Use the chart to compare concepts, then verify stress, deflection, bearing load, and operator ergonomics before treating a mechanism as practical.

How to Use

  1. Enter the coefficient of friction (mu) between 0.05 and 0.8; typical values are 0.15 for steel-on-steel lubricated, 0.5 for wood-on-wood dry
  2. Specify the input force (finNum) in Newtons; for example, 50 N applied by hand on a lever handle
  3. Select mechanical system type and input the mechanical advantage numerator (muNum) representing lever arm ratios or pulley count; click Simulate to animate force distribution and calculate output force accounting for friction losses

Worked Example

A steel pry bar with 6:1 lever ratio (muNum=6) and friction coefficient mu=0.20 receives finNum=100 N input force. Ideal mechanical advantage yields 600 N output. With friction losses: efficiency = (1 - 0.20) = 0.80, actual output force = 600 × 0.80 = 480 N. The simulator displays real-time load path and calculates work input (100 J per 1 m displacement) versus work output (480 J per 0.167 m displacement).

Practical Notes

  1. Pulley systems with four rope segments (muNum=4) on marine hoists typically operate at 85-90% efficiency with mu=0.10 for sealed bearings; add 5-10% safety margin to calculated load
  2. Inclined plane efficiency degrades sharply above 30° angles or mu above 0.6; recalculate before using on steep ramps with high friction coatings
  3. Animate multiple scenarios to verify force amplification never exceeds theoretical limit; friction always reduces output proportionally