A treadle and chain can rock an arm carrying a driving pawl while a holding pawl resists reverse rotation. This calculator compares an entered angular sweep with uniform ratchet tooth pitch.
Treadles and Chain to Ratchet Wheel Interactive Calculator
Enter illustrative rocker sweep and ratchet tooth count. Outputs are angular pitch arithmetic only—not guaranteed teeth engaged, wheel advance under load or machine performance.
Equation Used
- Ratchet teeth are represented by uniform angular pitch 360°/N.
- Entered sweep is an angular magnitude available for comparison.
- Complete pitches are counted with a floor operation.
- Unused sweep is the nonnegative angular remainder below one pitch.
- Pawl geometry, starting phase, chain travel, backlash, force, load, friction, spring behavior, wear and structural strength are omitted.
Treadle, Chain, Rocker and Ratchet
A treadle can pull a chain or cable that rocks a driving member. A pawl can engage a ratchet during the working motion, while a separate holding pawl can resist reverse rotation during return.
U.S. Patent 2,630,333 describes foot-operated treadles pulling cable and chain to sprocket elements with ratchet teeth and spring-urged pawls. The calculator does not reproduce that patent geometry; it isolates uniform angular pitch.
What This Calculator Represents
The tool divides 360° by entered tooth count, divides entered sweep by that pitch, floors the quotient and reports the remaining angle.
The whole number is a count of complete pitch intervals. Actual indexed teeth depend on pawl position, tooth profile, engagement phase, clearances and loading.
Uniform Pitch Arithmetic
sweep/pitch quotient = theta N/360°
complete pitches = floor(quotient)
unused sweep = theta - complete pitches × pitch
N is an integer tooth count and theta is the entered sweep in degrees. The remainder is at least zero and less than one pitch.
Worked Angular Example
For N=24, pitch is 15°. A 30° sweep spans exactly 2.00 pitches, so the complete-pitch count is 2 and the unused sweep remainder is 0°. This arithmetic alone does not guarantee two teeth of physical advance.
Model Boundary
- Calculated: uniform tooth pitch, sweep quotient, floor count and angular remainder.
- Not calculated: pawl engagement, starting phase, tooth and pawl profile, chain displacement, rocker radius, backlash, missed engagement, reverse holding, force, torque, load, spring rate, friction, wear, fatigue, output travel or safe operation.
Frequently Asked Questions
Does complete-pitch count equal teeth actually advanced?
No. It is only a geometric floor count.
Why is the remainder always less than one pitch?
Because the complete-pitch count is the floor of sweep divided by pitch.
Can the count be zero?
Yes, when entered sweep is smaller than one pitch.
Are pawl clearances and starting phase included?
No.
Does a zero remainder prove reliable indexing?
No.
Can this calculator size a loaded ratchet mechanism?
No.
References
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
