Mechanical Movement 9 — Continuous Cone Pulleys

01:26

How do two cones give a smoothly variable speed?

Mechanism No. 9 from 507 Mechanical Movements: two plain cones mounted the opposite way round, with a belt that can be slid along them by a fork. Wherever the belt sits, it runs on a driving diameter D₁ and a driven diameter D₂, and the speed ratio is n₂/n₁ = D₁/D₂. Sliding the belt changes the ratio continuously, with no steps: an early continuously variable transmission, used for example in spinning machinery to slow a bobbin gradually as it fills. Simulation: cones 80 → 200 mm, 400 mm apart.

How it works, step by step

1. Middle: 1 : 1

With the belt in the middle both diameters are 140 mm, so the output turns at the driver’s speed.

2. Slide toward slow

The fork moves the belt to the small driving end: 113 mm driving 167 mm, ×0.68.

3. No steps

Sliding the belt across sweeps every ratio from 0.42 to 2.38 smoothly. Now ×0.80, 477 rpm.

4. The hidden snag

An open belt needs 1.1 mm more length here than in the middle: straight cones leave it tight at the ends, slack in the centre.

The key idea

i = D₁ / D₂ — Sliding the belt along two opposite cones changes the ratio smoothly, with no steps.

Opposed cones give a continuously variable ratio n₂/n₁ = D₁/D₂ simply by sliding the belt.

Model and assumptions

Straight cones keep D₁ + D₂ constant, which keeps a crossed belt exactly the right length. An open belt also needs (D₁−D₂)²/(4C) of extra length, so it is slack in the middle and tight at the ends (up to about 7 mm over the range used here); No. 10 shows the curved cones that fix this.

Frequently asked questions

How is the speed changed?

A fork slides the belt along the cones, changing both working diameters at once.

Is the ratio stepless?

Yes. Any position along the cones gives a different ratio, with no steps.

What is the problem with straight cones?

An open belt needs slightly different lengths at different positions, so tension changes; Movement 10 fixes this with curved cones.

Part of the 507 Mechanical Movements series

This is Movement No. 9 from Henry T. Brown’s 507 Mechanical Movements (1868), redrawn and simulated by BCRUZ.