A cone-pulley shifter moves a belt axially to select a different opposing pulley pair. For one selected driver/driven pitch-diameter pair, ideal no-slip speed ratio is D₁/D₂. The calculator also converts a selected input-shaft revolution interval into time; it does not predict an actual shifting time.
Cone-Pulley Selected Belt Pair and Shift Interval
Explore exact ideal kinematics for one selected cone-pulley pair and a connected illustrative shifting fork.
Equation Used
- The selected driver and driven diameters are pitch diameters for one open-belt pair.
- The belt has no slip in the ideal speed calculation.
- Both shafts rotate at constant selected speeds.
- Complete cone profiles, belt length, tension, loads, ratings, guards and actual shifting behavior are excluded.
The opposed cone stack and fork travel are illustrative because the inputs specify only one pitch-diameter pair.
Selected open-belt pair and connected shifter
The main view draws the selected pitch circles and their exact common external tangents. Both pulleys rotate in the same direction at the ideal diameter ratio. The lower side view shows a finite fork translating a belt band along an illustrative opposed cone stack through a pivoted handle and connecting link.
The step stack is illustrative: the entered diameters define only the selected pair, not every available cone step.
What the calculator determines
Select input speed N₁, driver pitch diameter D₁, driven pitch diameter D₂ and a selected interval n in input-shaft revolutions. The calculator reports ideal output speed, speed ratio, driver pitch-line speed and the time occupied by n input revolutions.
Ideal selected-pair identities
N₂ = N₁D₁/D₂; ratio = D₁/D₂; belt pitch-line speed = π(D₁/1000)N₁; and selected rotation interval t = 60n/N₁.
Selected-input arithmetic
At 800 rpm with D₁ = D₂ = 100 mm, ideal output is 800 rpm, ratio is 1.00, pitch-line speed is about 251.3 m/min and 2.5 input revolutions occupy 0.1875 s.
Intentionally partial mechanism
The time output is not a measured shift time; it is only the duration of the selected number of input revolutions. Real cone-pulley design requires the complete paired profile, center distance, belt length and section, tensioning, permissible shift state, fork clearances, axial travel, speed/power ratings, guards and operating procedure.
Primary and authoritative references
- Mechanical Movements, Powers, Devices and Appliances, item 91 — historical description of the divided belts, guiding webs, tighteners, carrier nut, and screw-shaft shifting arrangement.
Questions
Does the calculator predict how long a shift takes?
No.
Does the drawing prove the belt fits every cone position?
No.
Why do both pulleys rotate the same way?
An open belt gives the same rotation direction.
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