A cord or belt connecting two pulleys shares tangential travel between their rims. With ideal no-slip contact, pulley rotational-speed ratio is the inverse of their diameter ratio.
Considering a separate actuator-driven linkage
The pulley-diameter comparison below cannot establish whether an actuator can drive a treadle arrangement. A separate actuator-driven linkage needs a complete geometry and load calculation, including the return motion and end positions.
When comparing a cylinder to an electric actuator, convert the discussion into stroke, force, speed, duty cycle, and installed length. Matching one specification is not enough.
The clean way to review it is to sketch the linkage at the start, middle, and end of travel. At each position, check the line of action, required force, available clearance, and whether the actuator rod remains close to axial loading.
- Map actuator stroke to the actual output travel before choosing a model.
- Check for binding, changing leverage, and peak load near the ends of travel.
- Decide whether timed motion is acceptable or position feedback is required.
For a FIRGELLI design review, calculate the load case with the FIRGELLI actuator force calculator and plan the switching or controller arrangement with the linear actuator wiring diagram generator. If an actuator or cylinder is already installed, the linear actuator replacement finder helps keep the comparison tied to real dimensions.
Treadle With Cord And Pulley Interactive Calculator
Enter driver and driven pulley diameters. Outputs are ideal diameter geometry only—not actual shaft speed, cord travel per treadle stroke, power, torque or machine performance.
Equation Used
- Pulley diameters are effective pitch diameters for an ideal comparison.
- Cord or belt motion is assumed to have no slip for the ratio interpretation.
- Both pulleys share the same ideal tangential cord speed.
- Circumference is pi times entered diameter.
- No cadence, rpm, wrap angle, tension, traction, elasticity, groove geometry, torque, power, efficiency, inertia or load is modeled.
Cord-Coupled Pulley Geometry
A cord or belt transmits motion between pulley rims. In an ideal no-slip comparison the tangential speed at both pitch circles is equal, so rotational-speed ratio is inversely proportional to pulley diameter.
U.S. Patent 872,848 describes a treadle and flywheel arrangement whose motion is transmitted by a belt or cord to a driven pulley. The calculator isolates only the two-pulley diameter geometry.
What This Calculator Represents
The tool divides entered driver diameter by entered driven diameter, calculates each circumference and subtracts the driven diameter from the driver diameter.
Because it has no cadence or shaft-speed input, it cannot predict rpm. Because it has no force or loss inputs, it cannot predict torque, power or efficiency.
Ideal Pulley Diameter Comparison
driver circumference = pi D
driven circumference = pi d
signed diameter difference = D-d
D and d are entered effective diameters in millimetres. The ratio is dimensionless. Positive difference means D is larger; negative means it is smaller.
Worked Geometry Example
For D=250 mm and d=60 mm, the ideal driven/driver speed ratio is 4.17:1. Circumferences are about 785 mm and 188 mm, and the signed diameter difference is +190 mm. Actual speeds require at least one shaft speed and real transmission behavior.
Model Boundary
- Calculated: diameter quotient, two circumferences and one signed diameter difference.
- Not calculated: treadle travel, cord travel per stroke, shaft rpm, direction, wrap angle, slip, tension, traction, belt or cord selection, torque, power, efficiency, inertia, bearing load, fatigue, cutting rate or safe operation.
Frequently Asked Questions
Does the ratio output equal actual spindle rpm?
No. It is dimensionless; no input rpm is provided.
Why is the ratio D/d?
Under the ideal no-slip assumption, equal tangential cord speed makes angular speed inversely proportional to diameter.
Can the signed difference be negative?
Yes. That simply means the entered driver diameter is smaller.
Are groove and cord diameters included?
No; the entered values are treated as effective diameters.
Does the calculator predict torque or power?
No.
Can it select a cord, belt or safe machine speed?
No.
References
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