A treadle can drive an off-centre crank pin on a disk through a connecting rod or pitman. This calculator uses an ideal slider-crank surrogate to explore selected length ratio and rod angle.
Treadle to Disk via Connecting Rod Interactive Calculator
Enter crank radius and selected pitman-length ratio. Outputs describe an ideal slider-crank geometry surrogate—not the full treadle linkage or any force, stress, wear or safety result.
Equation Used
- The geometry surrogate is an ideal in-line slider-crank with zero offset.
- Pitman length is defined by selected ratio N times crank radius r.
- The maximum surrogate angle is asin(r/L).
- The 15° tangent denominator is only a fixed mathematical reference, not a design limit.
- No input force, torque, inertia, friction, joint geometry, bearing area, material or allowable stress is modeled.
Treadle, Pitman and Crank Disk
A conventional treadle rocks about a pivot and connects through a pitman to an off-centre crank pin. U.S. Patent 682,355 describes this treadle, pitman and crank-or-flywheel arrangement and discusses moving away from dead centre.
The calculator does not solve that complete rocker linkage. It uses the simpler in-line slider-crank angle relation for comparison, without solving the treadle pivot geometry.
What This Calculator Represents
The tool calculates crank-pin orbit diameter, selects pitman length from L=Nr and reports the maximum ideal rod angle asin(1/N) for a zero-offset in-line slider-crank.
Its final output is tan(angle) divided by tan(15°), expressed as a percentage. Without an applied force it cannot be a side-force result.
Ideal Geometry Surrogate
crank-pin orbit diameter = 2r
maximum ideal rod angle = asin(1/N)
tangent index = 100 tan(angle)/tan(15°)
r and L are millimetres. N and the tangent index are dimensionless. The angle result assumes an ideal in-line slider-crank and does not include treadle pivot geometry.
Worked Geometry Example
For r=35 mm and N=4, selected pitman length is 140 mm and orbit diameter is 70 mm. The ideal maximum rod angle is about 14.48°. Its tangent is about 96.4% of tan(15°). This percentage is not force or allowable utilization.
Model Boundary
- Calculated: selected length, twice radius, one ideal angle and a normalized tangent.
- Not calculated: actual treadle-rocker motion, pivot locations, offsets, joint clearances, dead-centre starting, cadence, torque, side force, bearing load, stress, wear, flywheel energy, belt drive, power, ergonomics or safe machine design.
Frequently Asked Questions
Is the ideal rod angle the actual pitman angle?
Not necessarily; the real treadle is a rocker linkage with additional geometry.
Does the tangent index equal side load?
No. No force is entered.
Is 15° an allowable design limit?
No. It is only the fixed normalization reference used by this arithmetic.
Why does a larger length ratio reduce the angle?
Because asin(1/N) decreases as N increases.
Does crank radius affect the angle when N is fixed?
No; it scales both r and L while their ratio remains constant.
Can the calculator size a restoration or machine?
No.
References
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