A reciprocating pawl-and-ratchet mechanism turns a back-and-forth input into stepped rotation. One pawl advances the wheel; a separate locking pawl holds the indexed position during return. Use the calculator to find the angle per tooth, the corresponding pitch-circle arc, and the ideal accumulated rotation after a selected number of successful one-tooth strokes.
Driving the pawl lever with an actuator
An actuator attached to the lever must complete the working stroke and allow the drive pawl to return while the locking pawl holds. The pitch-circle arc shown by this calculator is not the actuator stroke: mounting positions and lever pivots determine that travel.
Establish the actual load and linkage dimensions before selecting a drive. The indexing calculator does not calculate actuator force or prove that the pawls will engage under load. Use appropriate stroke limits and a control sequence for the complete mechanism.
Related FIRGELLI tools include the actuator force calculator, linear actuator wiring diagram generator and linear actuator replacement finder. Check each tool’s geometry and assumptions against your installation.
Reciprocating to Intermittent Circular via Pawl Interactive Calculator
Watch one drive stroke advance a ratchet wheel by one tooth while a separate locking pawl holds its position during return. Calculate tooth spacing and accumulated rotation for successful one-tooth strokes.
Equation Used
- One successful forward stroke advances exactly one tooth.
- A distinct locking pawl holds the wheel during drive-pawl return.
- Pitch radius is a geometric reference for arc pitch only.
- No incomplete stroke, overshoot, backlash, spring dynamics, inertia, friction, tooth profile, load, wear, strength, or safe-speed prediction.
The drive pawl advances one tooth, the locking pawl seats, and the drive pawl returns while the wheel stays indexed. The drawing repeats this single-step sequence; the Total ideal index and Total ideal turns cards show the result for the entered stroke count.
One pawl advances; another holds
The drive pawl is carried by a reciprocating lever. On its working stroke, the pawl pushes a tooth and turns the ratchet wheel. A separately pivoted locking pawl retains the wheel’s indexed position as the drive pawl returns.
US3237467A describes a spring-biased actuating pawl arranged to advance a wheel one tooth at each reciprocation. Its locking pawl holds the wheel during backward movement and assists in preventing overtravel. US3049338A illustrates a feed pawl and holding pawl in a ratchet hoist. The patents describe particular mechanisms; this drawing illustrates their general drive-and-hold sequence.
Parts shown
- Ratchet wheel: divides a revolution into N equal angular pitches.
- Drive pawl and carrier: supply the working stroke.
- Locking pawl and frame pivot: retain the wheel during return.
Pawl lift and seating follow a prescribed sequence in the drawing. The mechanism is not being simulated under load. Each animation loop resets the illustration to the starting tooth so that the same step can be watched again; the calculated totals remain based on the entered number of strokes.
Where drive-and-hold pawls are used
The referenced patents show this principle in a stepping mechanism and a ratchet hoist. A reciprocating drive provides the working movement, while a separate holding element retains the result during return.
The calculator is useful for comparing ideal indexing increments and counting completed steps. It does not give a load rating, a tooth profile or a complete design for a counter, feeder or hoist. Actual mechanisms may include stops, release controls, reversing features or additional pawls.
Ideal tooth-pitch arithmetic
For N equally spaced teeth, one angular pitch is 360°/N. At pitch radius r, the corresponding pitch-circle arc is 2πr/N. If s completed strokes each advance exactly one tooth, the ideal accumulated index is s·360°/N, or s/N revolutions.
The pitch-circle arc is not automatically equal to handle travel or pawl-tip travel. Those depend on the actual lever pivots, contact geometry, clearances, and stroke limits.
Worked ideal example
A 24-tooth ratchet has a 15° angular pitch. At a 60 mm pitch radius, one pitch spans 15.71 mm along the pitch circle. Six completed one-tooth drive strokes produce an ideal 90° total index, or 0.25 revolution. This arithmetic assumes every stroke engages and completes one tooth.
What this model includes—and omits
More teeth reduce the angular and arc pitch at a fixed radius, giving finer ideal indexing. The same change also leaves less physical space per tooth, but this calculator does not infer a manufacturable tooth profile or reliable pawl size. Real performance depends on flank geometry, spring response, clearances, inertia, friction, load, material, lubrication, and positive stroke stops.
Reciprocating pawl questions
Does every back-and-forth stroke advance one tooth?
That is the assumption here: each counted drive stroke engages and completes one tooth. Incomplete travel, overshoot, bounce or a different mechanism can give a different result.
Why is a locking pawl shown?
It retains the indexed wheel position while the drive pawl returns. In the stepping mechanism described in US3237467A, it also assists in preventing overtravel at the end of a step.
Is pitch-circle arc the required lever stroke?
No. It is the pitch-circle circumference divided by tooth count. Lever stroke depends on the pivots, contact geometry, clearances and stroke limits of the actual mechanism.
Does the calculator determine tooth angles or spring force?
No. Its inputs specify tooth count, pitch radius and completed strokes. They are sufficient for angular pitch and accumulated index, but not for tooth strength, spring force, wear or operating speed.
Why does changing Completed drive strokes not run more animation cycles?
The input changes the total calculated angle and turns. The drawing repeats one drive-and-return sequence and resets to its starting tooth at the end. It does not animate the entire entered stroke count or represent a physical reverse step.
Why does Pitch radius change the arc result without enlarging the wheel?
The drawing keeps the wheel at a fixed display size. Pitch radius sets the physical arc length in the calculation. It does not set handle length, pawl length or the proportions of the drawing.
Primary mechanism references
- US3237467A, Stepping mechanisms (1966) — reciprocating spring-biased actuating pawl advances one tooth; a separate locking pawl holds during backward movement and assists in preventing overtravel.
- US3049338A, Ratchet hoist (1962) — feed pawl advances on one yoke direction while the holding pawl ratchets; on return the holding pawl locks while the feed pawl passes over the stationary teeth.
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