Mechanical Movement 18 — Two Fixed, One Movable
Why do two fixed pulleys and one movable give three to one?
Mechanism No. 18 from 507 Mechanical Movements: “a combination of two fixed pulleys and one movable pulley.” The rope runs from your hand over the upper fixed pulley, down under the movable pulley that carries the load, up over the second fixed pulley and back down, where its end is tied to the axle of the movable pulley. Three parts of the rope hold the movable pulley up, so the pull is a third of the load and the rope moves three times as far.
How it works, step by step
1. Two fixed, one movable
From your hand: over the top pulley, under the movable one, over the second fixed pulley, tied to the axle.
2. Three strands
Three parts of the rope hold the movable pulley up, each with the same tension: 198 N ideal.
3. A third of the load
Pull 224 N for 589 N: mechanical advantage 2.97.
4. Three times the rope
Your hand has moved 44 cm for 15 cm of lift.
The key idea
F ≈ W / 3 — Tying the rope end to the movable pulley gives it three supporting strands.
Tying the rope end to the movable pulley adds a third supporting strand: 3 : 1 with only one moving pulley.
Model and assumptions
Ideal mechanical advantage 3 (three supporting strands). Friction: each of the three pulleys passes on a fraction η of the power, so lifting needs about W / (3 η³).
Frequently asked questions
Why three strands?
Tying the rope end to the movable pulley adds a third strand holding it up.
Would it be 2 : 1 without that?
Yes; with the end tied to the beam only two strands would support the movable pulley.
How much rope is pulled?
Three times the lift.
Part of the 507 Mechanical Movements series
This is Movement No. 18 from Henry T. Brown’s 507 Mechanical Movements (1868), redrawn and simulated by BCRUZ.
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