Brown movement 227 shows a chain passing over a toothed pulley. Alternating link planes leave openings for the wheel teeth. The animation follows that arrangement, showing the links entering and leaving engagement with the wheel. A separate force calculator compares a proposed lifting load and hand pull.
Motion design starts with geometry, not force alone. A chain wheel transmits torque because its pockets match the chain pitch — not because the operator pulls harder.
The chain-wheel drawing illustrates engagement. The force-ratio results describe a separate complete-system comparison.
Chain and Pulley Form 1 Interactive Calculator
Compare load force and hand force to find the required overall force ratio. The animation illustrates chain engagement only: a single fixed wheel does not provide the calculated lifting reduction.
Equation Used
- Gravity is 9.80665 m/s² for the force conversions.
- The animated six-tooth wheel is an engagement illustration, not the force multiplier.
- Rigid links retain constant pin-to-pin pitch with alternating link planes.
- No chain strength, brake, gearing, rated capacity or lifting procedure is calculated.
Historical chain-wheel engagement schematic, not a complete hoist. The calculator compares load force with entered hand force; it does not calculate the capacity or reduction of the pictured wheel. Chain pitch is kept constant in the animation. Tooth contours and link widths are illustrative.
Alternating links engage the wheel teeth
Brown’s movement 227 depicts a six-tooth wheel with a chain wrapped over its upper half. The accompanying text explains that links in different planes leave spaces for the pulley teeth.
Broad links alternate with narrow edge views in the diagram. Their pin positions remain connected, and the wheel teeth enter the intervening openings. Each link keeps a constant length as it joins the wrap and leaves on the opposite side.
The illustrated tooth outline is schematic. It is not a manufactured tooth profile, and the animation does not prescribe a chain specification or rated load.
A chain wheel is one part of a transmission
A chain wheel transfers motion by engagement with a matching chain. The historical illustration establishes that engagement principle, not the internal construction of a modern chain hoist.
A lifting system may also require reduction gearing, a brake, suitable load attachments and rated components. Those components are outside this drawing and calculator.
Force comparison versus transmission geometry
The calculator evaluates Fload = m g and Fhand = P g, where m is load mass in kilograms and P is hand pull in kilogram-force. Their ratio is m/P. The hand-force percentage is 100P/m.
This ratio is the overall force multiplication required of a complete lifting system. A single freely turning fixed wheel merely redirects a chain; it does not turn 30 kgf into 2,000 kgf.
For an ideal geared arrangement with input hand-wheel radius rh, output load-wheel radius rl, and speed reduction G, torque balance gives Fload/Fhand = G rh/rl. Actual losses reduce the available ratio. This wheel-radius relationship explains a geared system; the two-input calculator does not calculate wheel dimensions.
Reading the default comparison
A 2,000 kg load has weight 19.6133 kN. A 30 kgf hand pull is 294.1995 N. The required overall force ratio is therefore 66.67:1, and the hand force is 1.5% of the load force.
Those values state a requirement. They do not establish that a particular hoist can lift that load, nor that the illustrated wheel supplies the reduction. Increasing hand pull to 60 kgf halves the required ratio to 33.33:1 while leaving load force unchanged.
What the comparison can establish
The force ratio is useful for comparing proposed load and effort values. It does not establish efficiency, chain tension in a multi-part reeving system, lift speed, service life or component ratings.
Chain engagement also does not make a transmission immune to wear, poor alignment or unsuitable loading. Product-specific requirements belong to the applicable manufacturer documentation.
Geometry is not a condition assessment
This schematic cannot assess chain wear, tooth damage, twisting or brake condition. It supplies no universal wear percentage, machining tolerance or replacement interval.
Using the calculator
Enter the load mass and the hand-force value you want to compare. Read the resulting forces and overall ratio separately from the engagement animation. For equipment inspection, testing or lifting operations, use the instructions for the actual rated product.
Calculator questions
Does the pictured wheel multiply force?
A single fixed wheel does not provide the large ratio shown by the comparison. That ratio is a requirement for a complete system.
Why do alternating links look different?
They occupy different planes, leaving openings for the wheel teeth. The front view shows alternating broad and edge-on link shapes.
Why does changing the load not resize the chain?
The calculator does not size a chain. Load and hand pull update the force comparison, while the animation illustrates a fixed engagement geometry.
Is this a rated lifting calculator?
No. It computes force conversions and a ratio, without component strength, brake performance, gearing or a capacity rating.
References & Further Reading
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, Cornell digitized copy, printed pages 58–59, movement 227: alternating-plane chain and toothed pulley.
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