This page now isolates the exact ideal no-slip pitch-line speed relation for two separate quarter-turn belt branches driven by pulleys on one horizontal shaft. It does not predict tracking, tension, power, efficiency, life or safe dimensions.
Two-Branch Quarter-Turn Belt Speed Explorer
Enter driver speed, common driver pitch diameter and the two driven pitch diameters. The connected animation applies the same ideal belt speed to each separate branch without inventing slip or performance factors.
Equation Used
- Two separate endless quarter-turn belt loops run from two driver pulleys fixed to one horizontal shaft.
- All diameters are declared pitch diameters.
- Each belt is inextensible and has no slip, creep or thickness correction.
- Animation phase represents one driver revolution; driven angular phase follows the exact diameter ratio.
- Pulley alignment, belt routing details, wrap, crown, idlers, tension, friction, centrifugal effects, power, torque, efficiency, tracking, edge strain, material, joint, vibration, wear, service life, guards, installation and safe operation are excluded.
Replaces unsupported tracking, power and maintenance claims with exact ideal no-slip pitch-line speed identities for two explicit belt branches.
One horizontal shaft drives two independent quarter-turn belt branches
Two driver pulleys are fixed to one horizontal shaft. Each has its own endless flat-belt loop to a pulley on a vertical shaft, so each loop changes the shaft direction by 90 degrees.
The animation keeps both loops connected and gives each driven pulley the angular phase required by its entered pitch diameter.
Use this page to audit ideal branch speeds
The worksheet checks the no-slip pitch-line speed shared by the driver and driven pulley in each branch. It can compare the two ideal driven speeds when their pitch diameters differ.
It cannot select belts, pulleys, idlers, bearings or guards, and it cannot predict whether a physical quarter-turn belt will track or transmit a load.
Apply equal ideal pitch-line speed to each branch
Diameters are in metres for v in metres per second; the diameter ratio is unitless.
A transparent two-branch example
At 240 rpm with a 350 mm driver, ideal belt speed is 4.398 m/s. A 250 mm left pulley turns at 336.0 rpm and a 300 mm right pulley at 280.0 rpm, so right speed divided by left speed is 0.833.
No actual slip, load or efficiency is inferred.
Ideal speed identity is not a belt-drive design
A real quarter-turn drive depends on belt material and construction, pulley crown and face, routing, alignment, center distance, idlers, wrap, initial and operating tension, friction, speed, load, edge strain, environment, joints, guards and manufacturer ratings.
The former universal center-distance rule, fleet-angle limits, horsepower, efficiencies, service intervals, material strengths, failure diagnosis and named-site claims are removed because they were not established for one documented arrangement.
Quarter-turn belt ledger questions
Does the 90-degree shaft change alter the ideal speed ratio?
No. In the no-slip scalar ledger, rim speed remains pi D n/60; real routing and tracking still require a detailed design.
Are the two driven speeds always equal?
Only when their entered pitch diameters are equal.
Does the animation prove the belts will track?
No.
Does ideal belt speed establish power capacity?
No.
Quarter-turn belt references
- Textile Mathematics II: equal belt and pulley surface speed gives D_h n_h=D_v n_v when slip is neglected.
- US Patent 1,075,280: a horizontal driving shaft, vertical driven shaft, quarter-turn belt and adjustable idlers.
- US Patent 1,148,677: horizontal countershaft, vertical spindle and quarter-turn belt with tracking idlers.
- US Patent 4,990,125: turned flat-belt paths and edge strain in quarter-turn drives.
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