# Pulleys of the third system, three pulleys (7 : 1)

> How does the third system of pulleys work?

- Category: Mechanisms › Pulleys and tackle
- Kind: Hardware
- Basis: Xem Studio design following Brown No. 21 (1868)
- Page: https://xemstudio.com/objects/third-system-pulleys-7-to-1-mechanism/ · JSON: https://xemstudio.com/api/geometry?object=third-system-pulleys-7-to-1-mechanism · Plain text: https://xemstudio.com/objects/third-system-pulleys-7-to-1-mechanism/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); files Xem Studio Design License (free to use and sell from, not to redistribute as files: https://xemstudio.com/license/)
- Use in every chat: add https://xemstudio.com/mcp as a connector (https://xemstudio.com/use-with-ai/)

**Exact dimensions.** True size, with no printing tolerance added.

## Notes

- Every rope ends on the load: rope 1 runs from the load over the fixed pulley to the first runner, rope 2 from the load over that runner to the second, rope 3 from the load over the second runner to the hand. Tensions double up the chain — P, 2P, 4P — and the load gets all three: W = 7P (2ⁿ − 1 with n = 3).
- Pitch-Ø80 fixed block, pitch-Ø40 and pitch-Ø20 runners; rope ends on a load bar at x = −40, 20 and 50, whose weight stem sits on the resultant (x = −10).
- Brown's No. 21 (a combination following the doubling rule; the single Spanish burton, No. 16, is the same system with two pulleys).
- Parts (each has its own page): tackle-beam-240-sockets, tackle-block-40-top-stem, tackle-block-20-top-socket, tackle-block-10-top-socket, rope-sheave-3mm-pitch-80, rope-sheave-3mm-pitch-40, rope-sheave-3mm-pitch-20, ropes-3mm-third-system-pulleys-7-to-1, tackle-weight-d40x40-socket, load-bar-100-sockets-m40-20-50, dowel-pins-metric.
- Brown's movement No. 21 (1868) shows it; this model is a Xem Studio design following his figure, every part at true size.

## Sizes

| parameter | value |
|---|---|
| fixed block | pitch Ø80 |
| runners | pitch Ø40 and Ø20 |
| rope tensions | 4P, 2P, P |
| mechanical advantage | 7 |

## Where the files are

- Henry T. Brown (1868, public domain): [Five Hundred and Seven Mechanical Movements — scan on archive.org](https://archive.org/details/fivehundredseven00browiala) — web — Publisher's page; dimensions are facts
- 507movements.com: [Brown's movement No. 21: figure, his text and an animation](https://507movements.com/mm_021.html) — web — Publisher's page; dimensions are facts

## Free STEP/STL (1 parts, Xem Studio Design License, Xem Studio)

Index: https://xemstudio.com/files/hardware/third-system-pulleys-7-to-1-mechanism/index.json · license: https://xemstudio.com/files/hardware/third-system-pulleys-7-to-1-mechanism/LICENSE.md

- third-system-pulleys-7-to-1-mechanism-assembly: [STEP](https://xemstudio.com/files/hardware/third-system-pulleys-7-to-1-mechanism/third-system-pulleys-7-to-1-mechanism-assembly.step) · [STL](https://xemstudio.com/files/hardware/third-system-pulleys-7-to-1-mechanism/third-system-pulleys-7-to-1-mechanism-assembly.stl) — Assembled mechanism, all parts placed at one pose (STEP keeps each part separate)

## Questions

**How does the third system of pulleys work?**

Every rope ends on the load: rope 1 runs from the load over the fixed pulley to the first runner, rope 2 from the load over that runner to the second, rope 3 from the load over the second runner to the hand. Tensions double up the chain — P, 2P, 4P — and the load gets all three: W = 7P (2ⁿ − 1 with n = 3).

## Fits with

- [Tackle beam 240 × 20 × 12 with Ø3 sockets every 5 mm](https://xemstudio.com/objects/tackle-beam-240-sockets/)
- [Single block for a pitch-Ø80 sheave, stem up (fixed block)](https://xemstudio.com/objects/tackle-block-40-top-stem/)
- [Single runner block for a pitch-Ø40 sheave, rope socket on top](https://xemstudio.com/objects/tackle-block-20-top-socket/)
- [Single runner block for a pitch-Ø20 sheave, rope socket on top](https://xemstudio.com/objects/tackle-block-10-top-socket/)
- [Rope sheave for Ø3 rope, pitch Ø80 (rope centre), Ø84.4 rim, Ø4 bore](https://xemstudio.com/objects/rope-sheave-3mm-pitch-80/)
- [Rope sheave for Ø3 rope, pitch Ø40 (rope centre), Ø44.4 rim, Ø4 bore](https://xemstudio.com/objects/rope-sheave-3mm-pitch-40/)
- [Rope sheave for Ø3 rope, pitch Ø20 (rope centre), Ø24.4 rim, Ø4 bore](https://xemstudio.com/objects/rope-sheave-3mm-pitch-20/)
- [Ø3 ropes for the pulleys of the third system, three pulleys (drawn in place)](https://xemstudio.com/objects/ropes-3mm-third-system-pulleys-7-to-1/)
- [Weight Ø40 × 40 with a Ø3 top socket (394.58 g in steel)](https://xemstudio.com/objects/tackle-weight-d40x40-socket/)
- [Load bar 100 × 10 × 8 with 3 rope sockets and a weight stem](https://xemstudio.com/objects/load-bar-100-sockets-m40-20-50/)
- [Dowel pins, 2–6 mm (ISO 2338 / DIN 6325)](https://xemstudio.com/objects/dowel-pins-metric/)