Brown movement 229 shows projections on the inner edges of the chain links engaging recesses in a wheel. The animation keeps the links connected as they enter, wrap and leave. It distinguishes this mechanism from a pocketed load-chain sheave or differential hoist.
Chain and Pulley Form 3 Interactive Calculator
Compare a static reference force with an assumed number of sharing contacts, and compare a measured pitch difference with a user-entered limit. Blue links identify the assumed contacts; their actual forces are not solved by the animation.
Equation Used
- Static reference load; no acceleration or shock model.
- Equal scalar sharing is a comparison assumption, not a prediction of actual tooth loads.
- Connected rigid links in an illustrative inward-tooth geometry.
- The tolerance limit is user supplied and is not validated as a manufacturing requirement.
- No chain strength, lifting capacity, brake behavior or allowable wear is calculated.
The animation follows Brown movement 229, an inward-toothed chain engaging a notched wheel. It is not a differential hoist. The load/contact division is an explicit equal-share arithmetic reference, not the tension carried by each chain link or a solved contact model. The tolerance limit is entered by the user.
Teeth on the links, recesses in the wheel
Brown movement 229 illustrates chain links with inward projections and a matching notched wheel. The links are joined by pins; their projections enter the wheel recesses as the chain wraps around it.
The animation follows that visible arrangement. Each link keeps its length, adjacent pins stay connected, and the tooth pattern rotates with the wheel. Sixteen engagement positions are used for the illustrative reconstruction; the source supplies no production dimensions.
The blue links identify the selected number of assumed sharing contacts. That highlight is a calculator aid, not a measurement of where contact forces actually act.
A positive chain transmission
This example explains one way a chain can engage a wheel through shaped links. It should not be read as a drawing of a complete lifting appliance.
A differential hoist uses different wheel diameters and a specific chain routing. Neither that routing nor a brake, reduction gearbox or lifting hook appears in the selected mechanism.
Keep chain tension separate from contact sharing
A static mass m produces reference force F = mg. The calculator converts that force to kilonewtons and displays F/N as an explicitly assumed equal-share comparison.
A chain’s links form a series load path. Several links touching a wheel do not mean every chain link carries only F/N. Actual wheel-contact forces depend on geometry, stiffness, tension on both spans and the sequence of engagement. Those forces are not solved here.
The pitch comparison is separate: tolerance use = 100|e|/T, and remaining entered tolerance = T−|e|. The chosen T is an input, not a tolerance recommended by this page. The calculation does not establish a required contact count or an acceptable engagement margin.
Reading the reference values
For a 680 kg static reference mass, F = 6.6685 kN. Dividing by three assumed contacts gives an arithmetic value of 2.2228 kN. This does not mean the loaded chain span carries only 2.2228 kN.
A measured pitch difference of 0.10 mm compared with an entered limit of 0.30 mm uses 33.33% of that limit and leaves 0.20 mm. If the measured difference becomes 0.40 mm, the result is 133.33% and −0.10 mm remaining.
Changing the assumed contact count updates the reference division and the blue highlights. Changing a tolerance input updates the dimensional comparison; the animation continues to show the same illustrative link engagement.
What remains outside the model
Tooth profiles, clearance and connector thickness are schematic. They are not a conjugate profile design or a model of elastic contact and wear.
The calculator does not establish component strength, working load, service life, inspection intervals or allowable pitch error. Product-specific limits require the actual chain and wheel documentation.
Calculator questions
Does force divided by contacts give tension in a link?
No. It is an equal-share arithmetic reference. A chain’s series tension and the wheel’s individual contact forces require a different analysis.
Is this a differential chain hoist?
No. The selected historical drawing is an inward-toothed chain and a notched wheel.
Do the blue links show measured force?
No. They identify the assumed number of sharing contacts selected for the comparison.
Does within-limit mean the chain is suitable?
It means only that the measured difference is no greater than the entered tolerance. The calculator does not validate that tolerance or the equipment.
References & Further Reading
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, Cornell digitized copy, printed pages 58–59, movement 229: inward-toothed chain and notched wheel.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
