Adjust lever dimensions above.
Understanding Compound Levers
Overview
A compound lever links two or more levers so that the output force of one becomes the input of the next. The total mechanical advantage equals the product of each individual lever’s MA, enabling very large force amplification from compact mechanisms.
How Compound Levers Multiply Force
Each lever amplifies force based on the ratio of its effort arm to its load arm. In this calculator, the effort arm (L1) is the distance from the input load (W) to the fulcrum, and the load arm (L2) is the distance from the fulcrum to the output point. The closer the output point is to the fulcrum, the greater the force amplification:
The total compound output is:
MA₁ = L1a ÷ L1b (Lever 1 mechanical advantage)
MA₂ = L2a ÷ L2b (Lever 2 mechanical advantage)
F₂ = final compound output force
The Displacement Trade-Off
Force amplification comes at the cost of displacement. A system with 40:1 compound MA requires 40 times the input stroke to achieve a given output movement:
This is critical when sizing a linear actuator to drive the system. If you need 2 inches of output movement with a 44:1 compound lever, the actuator must provide 88 inches of stroke.
Efficiency and Friction
Each pivot point introduces friction losses. With standard bronze bushings, a single pivot operates at roughly 80–95% efficiency. Using sealed ball bearings can push each pivot above 95%, giving 90%+ system efficiency.
Common Applications
Industrial presses and clamping — Small actuators generate tonnage-level forces for stamping, forming, and assembly.
Heavy hatches and covers — Boat hatches and vault lids operated with modest actuators through compound linkages.
Brake systems — Bicycle and industrial brakes amplify hand force into high clamping pressure.
Robotic grippers — Compound lever linkages generate high grip force from compact actuators.
Platform scales — Traditional scales reduce large loads to measurable forces on the balance beam.
Design Tips
Move L2 closer to the fulcrum for more force — The smaller L2 is relative to L1, the greater the mechanical advantage. Even small changes in L2 position create large force differences.
Account for stroke multiplication — High compound MA requires proportionally longer actuator strokes.
Use bearings at all pivots — Friction losses multiply in a compound system. Sealed bearings can reduce required input by 10–15%.
Make the linkage rigid — The connection between levers must withstand intermediate forces without deflection.
Apply a safety factor of 1.5× minimum — Dynamic loading and wear increase real-world requirements.
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