A reciprocating feed ratchet turns repeated back-and-forth input strokes into one-way indexed rotation. A driving pawl advances the toothed wheel, and a holding member prevents reverse motion while the driver returns. Use the calculator to compare the angular step produced by different tooth counts and selected teeth per stroke.
Reciprocating Feed Ratchet Interactive Calculator
Vary ratchet tooth count and teeth advanced per stroke to see the indexed output angle and wheel motion.
Equation Used
- Each effective drive stroke advances exactly the selected integer number of teeth.
- A separate holding dog prevents reverse motion during pawl return.
- No missed engagement, backlash, friction, tooth stress, impact, feed force or speed limit is predicted.
The animation shows one drive-and-return stroke, then rewinds the drawing for replay. The rewind is not working motion: a feed ratchet normally retains its advance while the driving pawl returns.
How the feed stroke works
The driving pawl is carried by an oscillating arm. During the working stroke it engages a tooth and turns the ratchet wheel. A separate holding member takes over before the driver returns, retaining the advance while the driving pawl moves back to its starting position.
The calculator assumes every effective stroke advances exactly k teeth on a wheel containing N equally spaced teeth. It does not derive the number of teeth from rocker throw, spring motion or engagement clearance. In a physical mechanism, those details must allow the selected whole-tooth step to occur reliably.
Parts shown in the diagram
- Ratchet wheel: supplies the repeated tooth positions around the output shaft.
- Pawl carrier: carries the driving pawl through its outward and return motion.
- Driving pawl: engages the wheel during the advance and clears it during return.
- Guided holding dog: seats against a tooth to retain the completed index.
- Fixed support: holds the guide relative to the wheel.
The display is a single-stroke illustration. Its final rewind makes the example repeat; it does not represent how a continuously operating feed accumulates rotation. The tooth shape and drawn pawl motion are illustrative, not manufacturing dimensions or a spring-dynamics calculation.
Using intermittent rotation for feed
A small angular step can turn a feed screw or roller between working strokes of a machine. The useful output then depends on the screw lead or roller circumference and any gearing between it and the ratchet shaft.
One documented example is William F. Zimmermann’s 1930 shaper feed patent, US1764092A. It describes an oscillating lever, pawl and ratchet arrangement that produces intermittent feed-shaft rotation, with gearing connecting the shaft to the table feed screw. The patent’s full arrangement includes parts beyond this illustration.
Here the two controls isolate the indexing relationship. They can compare coarse and fine angular steps, but do not select a commercial feeder, qualify a press installation or establish feed accuracy under load.
Tooth count and feed equations
For N equally spaced teeth and an effective advance of k teeth per stroke:
These four values are the calculator outputs. N and k are whole tooth counts. A fractional Strokes / Rev value describes an average ratio, not a command to perform part of a stroke.
Optional conversion to linear travel
If a roller of diameter D is directly coupled to the ratchet wheel and the material does not slip, travel per stroke is pi × D × k/N. Multiplying by an assumed effective stroke rate f gives the average linear feed rate:
With D in millimetres and f in strokes/min, these results are millimetres/stroke and millimetres/min. Diameter and stroke rate are not controls in this calculator. For a directly coupled screw, replace πD with the screw lead. Any intervening gearing must also be included.
Worked example: two teeth per stroke
Set Ratchet Teeth to 24 and Teeth / Stroke to 2. Tooth Pitch is 360°/24 = 15°. Index Angle is 2 × 15° = 30°. The wheel takes 24/2 = 12 strokes per revolution, advancing 8.33% of a revolution each stroke.
For an additional illustrative calculation, suppose a directly coupled roller is 50 mm in diameter and has no slip. Its travel is π × 50 × 2/24 = 13.09 mm per stroke. At an assumed 180 effective strokes/min, average feed is about 2,356 mm/min. These assumed roller and speed values are not ratings or additional calculator inputs.
Two pinch rollers on opposite sides of the same strip do not double this distance. If both contacts have the same surface travel without slip, the strip travels that distance once.
When the ratio is not a whole number
With N = 10 and k = 3, Index Angle is 108° and Strokes / Rev is 3.33. Three complete strokes accumulate 324°; four accumulate 432°. After ten strokes the wheel returns to its starting tooth position after three complete revolutions.
What the two controls change
| Change | Calculated effect |
|---|---|
| Increase N at fixed k | Smaller tooth pitch and index angle; more strokes per revolution. |
| Increase k at fixed N | Larger index angle; fewer strokes per revolution. |
| Keep k/N constant | Same ideal angle per stroke, although tooth spacing differs. |
None of these comparisons predicts tooth strength, spring preload, wear or maximum operating speed. Those depend on the actual parts and loads. Choosing a feeder also requires the required travel, holding behaviour, accuracy and timing of the complete machine.
Feed-ratchet questions
What does changing the tooth count do?
For the same teeth advanced per stroke, more teeth reduce the angular step. With k = 1, a 12-tooth wheel gives 30 degrees per stroke and a 48-tooth wheel gives 7.5 degrees. Tooth count alone does not determine torque capacity or engagement reliability.
Why can Strokes / Rev be fractional?
It is N/k, an average ratio. With 10 teeth and 3 teeth per stroke, the ratio is 3.33 strokes per revolution. After three complete strokes the wheel has advanced 324 degrees; after four it has advanced 432 degrees. It does not stop exactly at one revolution at the end of either stroke.
Why does the wheel move backwards at the end of the animation?
The final segment rewinds the drawing so the same single stroke can be replayed. That rewind is not part of the feed mechanism’s working cycle. During the illustrated return stroke, the holding dog keeps the indexed wheel still.
Does the calculator predict linear feed length?
It calculates rotation from tooth counts. Linear travel also needs a roller diameter or screw lead and any transmission ratio. For a directly coupled roller of diameter D with no slip, travel per effective stroke is pi × D × k/N.
Does a second pinch roller double the feed length?
No. Two rollers gripping the same strip do not add their surface travel. The strip follows the common contact speed if it does not slip. A different feed ratio must come from an actual transmission or geometry, not from counting both rollers.
Can this tool choose spring preload or diagnose missed teeth?
No. Spring dynamics, contact geometry, wear, load and backlash are outside its inputs. Missed indexing requires inspection of the actual equipment against its operating and service instructions; the tooth-count calculation cannot identify a single cause.
Is chord travel the same as travel along a roller circumference?
No. For an angle alpha in degrees, arc length is pi × D × alpha/360, whereas chord length is D × sin(alpha/2). Use the measurement that matches the geometry; inserting a chord into the arc-length formula gives the wrong angle.
Primary mechanism references
- US726819A, Feeding mechanism (1903) — a reciprocating pawl carrier drives a fine-toothed ratchet on its working motion and passes freely on return.
- US1764092A, Shaper feed mechanism (1930) — an oscillating lever and pawl index a ratchet wheel to operate a feed screw once per stroke.
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