This page now identifies the mechanism as a Weston differential pulley block, not an automotive differential gear. Two unequal upper chain sheaves are rigidly coupled on one axle, and one endless chain passes around the load-carrying movable block.
Weston Differential Pulley Ideal Ledger
Enter the larger and smaller upper sheave pitch diameters and a declared hand-chain effort. The connected view reports exact ideal travel ratio, hook rise per upper revolution, hand-chain travel and ideal supported load.
Equation Used
- D and d are declared pitch diameters of rigidly coupled upper chain sheaves, with D>d.
- One upper revolution takes up pi D on the larger sheave and pays out pi d on the smaller sheave.
- The movable lower block is supported by two chain legs, so hook rise is half the net chain take-up.
- Declared effort acts through ideal hand-chain travel pi D.
- Chain and sheaves are inextensible, massless and lossless in the ledger.
- Pocket geometry, chain pitch and wear, friction, efficiency, braking, self-locking, dynamics, ratings, inspection, maintenance and safe operation are excluded.
Corrects the subject from a fabricated pulley-plus-bevel-differential hybrid to a Weston differential pulley block and isolates exact ideal travel/work identities from real hoist performance.
Unequal coupled sheaves create a small net chain take-up
Weston's historical differential pulley uses two unequal chain sheaves rigidly coupled on one upper axle, an endless chain and a lower movable block. In one upper revolution, the larger sheave takes up pi D while the smaller pays out pi d.
The two lower supporting legs share the net shortening, so the hook rises by pi(D-d)/2. This is a differential pulley block; no bevel-gear differential or twin output shafts are present.
Use this page only for the ideal Weston travel ledger
The worksheet reports ideal travel ratio, hook rise, hand-chain travel and lossless supported load for declared pitch diameters and effort.
It cannot select, rate, inspect, maintain or authorize a hoist or lifting operation.
Derive the ratio from one upper-sheave revolution
Ideal mechanical advantage equals velocity ratio only in the stated lossless work ledger. Real machines require measured efficiency and rated equipment data.
A transparent ideal differential-pulley example
For D=120 mm, d=114 mm and P=250 N, hook rise is 9.425 mm per upper revolution and hand-chain travel is 376.99 mm. The ideal velocity ratio is 40.000 and ideal supported load is 10000.00 N.
No actual capacity, holding behavior or safe load follows.
High ideal ratio comes with small hook travel
Reducing D-d increases the ideal velocity ratio while reducing hook rise per upper revolution. Actual behavior also depends on chain-pocket geometry, friction, wear, alignment and device-specific braking or holding provisions.
The former automotive differential, torque-splitting, exact efficiency, capacity, tolerance, deployment, maintenance and troubleshooting claims are removed, along with the unrelated pin-gear video.
Weston differential-pulley questions
Is there a bevel-gear differential?
No; differential refers to the difference between the two rigidly coupled upper sheave pitch diameters.
Why is hook rise half the circumference difference?
Two chain legs support the movable lower block and share the net shortening.
Does ideal supported load equal a rated capacity?
No.
Does the calculator prove self-locking?
No.
Weston differential-pulley references
- T. A. Weston, US Patent 134,337, Improvement in Differential Pulleys: historical differential sheave, chain, guide and lower-block topology.
- Maharashtra State Board of Technical Education, Engineering Mechanics 312312: Weston differential pulley block diagram and VR=2D/(D-d).
- UK Maritime and Coastguard Agency, General Engineering Science I syllabus: Weston differential pulley block, efficiency, mechanical advantage and velocity ratio are distinct quantities.
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