For an ideal open rope drive with no slip or creep, equal pitch-line speed gives N₁D₁ = N₂D₂. Selected driver speed and pulley pitch diameters therefore determine driven speed and rope pitch-line speed, but not power capacity or a permissible rope diameter.
Linear actuator checks for Rope Transmission Mechanism
An actuator-driven version of rope transmission mechanism should be reviewed for stroke, linkage angle, and peak force. The mechanism may feel light through most of the travel and still bind or spike in force at one position.
For structural members, the actuator load should be applied through brackets that do not introduce unintended bending. Check both static load and the extra load created when the mechanism starts, stops, or binds.
If the application needs synchronized motion, feedback should be treated as a requirement rather than an accessory. Two open-loop actuators wired together can drift apart when friction, load, or mounting geometry differs between sides.
- 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.
Selected Ideal Rope-Transmission Kinematics
Explore ideal no-slip speed and pitch-line relationships for two selected grooved pulleys joined by an open rope.
Equation Used
- D₁ and D₂ are compatible effective pitch diameters.
- The open rope has equal pitch-line speed at both pulleys with no slip or creep.
- The torque factor assumes ideal power conservation and is not an actual torque output.
- Rope construction, tension, friction, wrap, losses, power, loads, fatigue and ratings are excluded.
The secondary figure uses the same selected pitch diameters and driver speed as the calculator.
Selected open-rope topology
Two grooved pulleys on parallel shafts are joined by an uncrossed rope. In the selected ideal model the rope has one common pitch-line speed at both pulleys, so the shafts rotate in the same direction and angular speed varies inversely with pitch diameter.
Real rope drives transmit force through tension difference and groove contact. Slip, creep, elastic stretch and effective pitch diameter can change actual speed.
What this calculator demonstrates
Select driver pitch diameter, driven pitch diameter and driver speed. The calculator returns ideal speed factor, driven speed, lossless torque factor and pitch-line speed.
It does not select rope material or diameter, groove form, pulley size, centre distance, tension, wrap, number of ropes, power, bearing load, efficiency, life or safe operating limits.
Ideal no-slip kinematics
Common pitch-line speed gives v = πD₁N₁/60 = πD₂N₂/60, so N₂ = N₁D₁/D₂. The ideal speed factor is D₁/D₂. If power were conserved with no loss, the corresponding torque factor would be T₂/T₁ = D₂/D₁.
The torque factor is a ratio only. Without input torque, tension, friction and losses it is not an actual output torque or power rating.
Default selected example
For D₁ = 1.50 m, D₂ = 0.50 m and N₁ = 160 rpm, ideal driven speed is 480 rpm, speed factor is 3.00 and pitch-line speed is 12.57 m/s. The lossless torque factor is 0.333.
Scope and correction boundary
The removed calculator hard-coded 100 rpm and asserted maximum fibre-rope diameter as one-thirtieth of the smaller pulley. That rule cannot select a rope without construction, manufacturer data, duty, tension, groove and fatigue criteria.
The former article also supplied universal angles, speeds, slip limits, tensions, efficiencies, life predictions and failure diagnoses plus a fabricated mill example. Those claims and the unrelated video are removed.
Questions
Does diameter ratio set ideal speed?
Yes, when both diameters are compatible pitch diameters and slip and creep are neglected.
Is the torque factor an actual output torque?
No. It is the inverse kinematic ratio under an ideal no-loss power assumption.
Can pulley diameter determine maximum rope diameter?
No. Rope selection requires product-specific construction, bending, tension, groove and duty information.
Does the calculator predict transmitted power?
No. It has no rope tension, friction, wrap, number-of-ropes or loss inputs.
Primary technical and historical references
- J. J. Flather, Rope-driving — historical treatise on fibrous-rope power transmission, pulleys, tension and design.
- MIT FUNdaMENTALs, Topic 7 — pulley radius, rotational speed and linear-speed relationships for friction and belt drives.
- OpenStax University Physics, Work and Power for Rotational Motion — angular speed, torque and rotational power relationships.
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