How to use it
- Pick the machine.
- Enter its two dimensions in the same unit (or the number of ropes, or the gear teeth).
- Enter the load and the efficiency, 100 % for an ideal machine.
- Read the IMA, the AMA and the effort you need.
Formulas
- Lever: IMA = effort arm ÷ load arm.
- Pulley system: IMA = number of supporting rope segments.
- Wheel and axle: IMA = wheel radius ÷ axle radius.
- Inclined plane: IMA = slope length ÷ height. Wedge: IMA = sloping length ÷ thickness.
- Screw: IMA = 2π × handle radius ÷ pitch.
- Gears: IMA = driven teeth ÷ driving teeth (torque gain).
- Actual: AMA = IMA × efficiency; effort = load ÷ AMA.
Worked example
A crowbar with 1.5 m from the fulcrum to your hand and 0.3 m to the rock: IMA = 1.5 ÷ 0.3 = 5. To lift 500 N you push with 500 ÷ 5 = 100 N, and you save 80 % of the force.
A block and tackle with 4 supporting ropes at 80 % efficiency: AMA = 4 × 0.8 = 3.2, so a 100 kgf load needs 100 ÷ 3.2 = 31.25 kgf of pull.
A screw jack with a 200 mm handle and a 2 mm pitch: IMA = 2π × 200 ÷ 2 = 628.3185, so 10,000 N needs only 15.9155 N in theory. Real screw jacks lose much of that to thread friction, often more than half, so set a realistic efficiency.
Tips
- Distance is the trade-off. Work in equals work out: with an IMA of 5 the effort moves 5 times as far as the load.
- An MA below 1 is not a mistake. A third-class lever like a pair of tweezers gives up force to gain speed and reach.
- Gears and speed. A gear pair with an MA of 3 turns the output three times slower than the input.