A continuous-motion ratchet drives its output in the same direction during both halves of a reciprocating input cycle. The historical three-bevel-gear arrangement uses alternating ratchet engagement. This page illustrates a documented ratchet-drill version and calculates an ideal one-tooth-per-half-cycle output, with a separate screw-feed comparison.
Continuous Motion Ratchet Interactive Calculator
Explore a double-acting ratchet drive and compare ideal screw-feed rates. A cycle means one forward stroke plus one return stroke. The diagram uses a three-bevel-gear arrangement with alternating ratchet couplings.
Equation Used
- Exactly one output tooth is advanced per half-cycle, with no lost motion or slip.
- All three entered rates are complete forward-and-return cycles per minute, not individual strokes. Comparison rates A and C need not be smaller or larger than nominal.
- Illustrative 2:1 bevel ratio: handle swing per half-cycle is 180/Z degrees and pinion swing is 360/Z degrees.
- Single-start screw, ideal 1:1 output connection; pitch equals lead.
- Four-times-slower animation, ideal sinusoidal handle motion. Tooth clearance, spring dynamics, flywheel inertia, torque and service life are not calculated.
One output tooth per half-cycle and a 1:1 connection to a single-start screw are assumed. The screw is a separate application of the output; it is not a reconstruction of the drill-feed mechanism.
Three bevel gears and alternating ratchet couplings
Hiscox figure 1022 identifies three bevel gears and opposed ratchet action. For the cutaway here, Richards’s 1880 ratchet-drill drawing supplies the construction reference: a rocking main wheel drives two opposed pinions. Sprung ratchet couplings connect them alternately to one vertical spindle. The flywheel, fixed support and tool socket complete the visible assembly. The protective sleeves are cut away to expose the couplings.
The drawing illustrates that operating arrangement with schematic dimensions. It omits the optional take-off gear and does not model the flywheel’s smoothing effect. The simple angular model instead reaches zero speed at handle reversal. “Continuous” here describes drive on both strokes; it does not promise perfectly uniform rotation.
Using the calculator
The illustrated machine is a historical hand-driven ratchet drill. The feed calculation is a separate example: connect the output ideally, at 1:1, to a single-start screw. Its lead in millimetres per revolution then converts output speed into linear travel per minute.
Enter three cycle rates to compare them. Rate A, nominal and rate C are independent values; each rate keeps the value you enter. Only nominal controls playback speed. Screw pitch changes the feed results, while ratchet tooth count changes both angular increments and feed.
From teeth per cycle to screw feed
Let Z be the ratchet tooth count and f the number of complete forward-and-return cycles per minute. This worksheet assumes one output tooth on the forward stroke and one on the return stroke. Thus there are 2f tooth advances per minute and the output speed is N=2f/Z revolutions per minute.
For a single-start screw with pitch p millimetres per revolution, ideal linear feed is v=Np=2fp/Z millimetres per minute. The average angular speed is N×360/60=12f/Z degrees per second.
The input label is cycles/min because one cycle contains two strokes. If counting individual strokes, divide that count by two before entering it. This distinction prevents a factor-of-two error.
The illustrative large bevel wheel has twice the pitch radius of either pinion. Its required one-way swing is therefore half a ratchet tooth angle: 180/Z degrees. That geometric ratio does not add another multiplier to the feed equation, which already starts from output tooth advances.
Example at the initial settings
With 60 ratchet teeth and 50 complete handle cycles per minute, the output advances 100 teeth/min. Dividing by 60 gives 1.6667 rpm, or 10 degrees per second on average.
A 10 mm/rev single-start screw would consequently travel at 16.6667 mm/min. At comparison rates of 20 and 90 cycles/min, the corresponding ideal feeds are 6.6667 and 30 mm/min.
Each full handle cycle advances 2/60 revolution and 0.3333 mm of screw travel. Doubling the cycle rate doubles average speed and feed. Doubling the screw pitch doubles feed without changing spindle speed. Doubling the tooth count halves the output increment and feed under this one-tooth-per-half-cycle assumption.
Limits of this model
The one-tooth assumption defines the illustrative handle travel; it is not a prediction that every hand stroke on a real tool advances exactly one tooth. A wider handle swing, another bevel ratio, backlash or missed engagement would require a different model.
The calculation estimates motion only. No torque, spring preload, tooth stress, wear allowance, load capacity, safe operating speed or fatigue life can be inferred from these five inputs. The animation also excludes flywheel dynamics, so it should not be used to size that component.
The tooth and coupling profiles are simplified to keep the cutaway readable. Their dimensions are not manufacturing specifications. The feed bars share a common zero and scale so their relative lengths can be compared directly.
Questions about the ratchet model
What is one cycle?
One complete forward stroke and return stroke of the handle. It contains two output advances in this model.
Why do the upper and lower pinions turn opposite ways?
They mesh on opposite sides of the rocking bevel wheel. Their ratchet couplings alternately pass the useful direction to the common spindle.
Is output speed constant?
No. The model slows to zero at each reversal. The reported speed is the average over a complete cycle.
Why does screw pitch not change the gears?
Pitch converts output rotation into hypothetical linear feed in a separate 1:1 screw application. It does not set the ratchet motion.
Why is handle movement small at high tooth counts?
The model assumes one output tooth advances per half-cycle. More teeth mean a smaller tooth angle and therefore a smaller handle swing for the same bevel ratio.
Mechanism references
- W.H. Richards, US231361, Ratchet Drill (1880): drawing sheet and construction description.
- G.D. Hiscox, Mechanical Movements, Powers, Devices and Appliances: figures 1022 and 1022a, printed page 258 (PDF 268).
The motion and screw-feed equations are derived above from the stated tooth-per-cycle assumptions.
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