Mechanical Movement 15 — White’s Pulleys
Why do White’s pulleys use grooves of 1 to 6?
Mechanism No. 15 from 507 Mechanical Movements: White’s pulleys. Instead of three loose sheaves in each block, each block is one solid wheel with three concentric grooves: diameters 2, 4 and 6 in the upper block, 1, 3 and 5 in the lower. In a tackle with six strands the rope runs at 1, 2, 3, 4, 5 and 6 times the speed of the load in successive grooves, so grooves sized in the same proportion let each wheel turn as one piece. No sheave rubs against its neighbour and each block has a single bearing, so less effort is lost to friction. Six strands carry the load: the ideal pull is one sixth of the weight.
How it works, step by step
1. One wheel, three grooves
Each block is a single wheel with three grooves: Ø 2, 4, 6 above and Ø 1, 3, 5 below. Six strands hold the load.
2. Rope speeds 1 to 6
Lifting at 8 cm/s, the rope runs 1, 2, 3 … 6 times as fast in successive grooves, exactly as the diameters grow.
3. No rubbing
So every groove on a wheel needs the same turning speed. Pull 253 N, against 282 N with six loose sheaves.
4. Six for one
302 cm of rope has passed through your hand for 50 cm of lift: six times as far.
The key idea
Ø groove ∝ rope speed — Rope runs 1 … 6 times the load speed in successive grooves, so each wheel turns as one piece with one bearing.
Grooves in the ratio 1 to 6 follow the rope speeds, so one wheel per block replaces six rubbing sheaves.
Model and assumptions
Rope speed in each groove = groove diameter × the same angular speed, so both wheels turn at ω = v / u. Brown’s caption gives the power as 1 to 7; in the arrangement drawn, with the dead end on the upper block, six strands carry the load, so the ideal advantage is 6 : 1. The model compares one bearing per block (η = 0.985 each) with an ordinary tackle of six separate sheaves (η = 0.96 each).
Frequently asked questions
Why are the grooves different sizes?
In a six-strand tackle the rope runs 1 to 6 times the load speed in successive grooves; diameters in the same ratio let the whole wheel turn together.
What is the advantage over ordinary blocks?
One bearing per block and no sheaves rubbing against each other, so less friction.
Brown says 1 to 7: why does the model show 6?
In the arrangement drawn, with the dead end on the upper block, six strands hold the load, so the ideal advantage is 6 : 1. A seventh share would need a third groove pair or the dead end on the lower block.
Part of the 507 Mechanical Movements series
This is Movement No. 15 from Henry T. Brown’s 507 Mechanical Movements (1868), redrawn and simulated by BCRUZ.
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