A concave-grooved pulley supports a round belt in a curved groove around its rim. This calculator explores groove radius and depth relative to cord diameter. The animation pairs a moving belt drive with an enlarged section so the belt path and groove shape can be understood separately.
Concave-grooved Pulley for Round Band Interactive Calculator
Explore a trial round-belt groove using cord diameter, groove-radius factor and depth factor. The enlarged section shows the actual circular bottom and straight entry walls. The moving belt travels along its length around the upper pulleys.
Equation Used
- Round cord and circular-bottom groove; no elastic flattening is modelled.
- Straight entry walls extend the circular bottom to the selected depth.
- The cord is seated tangent to the bottom; larger groove radius does not imply uniform clearance.
- Two equal schematic pulleys illustrate continuous belt travel with no slip. Pulley diameter and speed are not sizing outputs.
The enlarged groove is an undeformed geometry comparison. Select belt and pulley dimensions using the chosen manufacturer’s data. Animation speed and pulley spacing are illustrative.
How the round belt sits in the groove
The belt travels along its length around the pulley. The cord follows the pulley groove without twisting about its own cross-section in this model. The upper side view exposes the cord path through transparent near rims; the enlarged lower view cuts across that path.
The section has a circular bottom of radius Rg and straight entry walls. The walls are needed because the chosen depth h is greater than the bottom radius throughout this calculator’s ranges. A circular profile continued above its widest point would create an undercut, which is not the open groove represented here.
The undeformed round cord touches the bottom. If Rg exceeds the cord radius r, the two circle centres differ, and clearance varies around the profile. Real cord deformation and contact pressure depend on material and belt loading and are not calculated.
Where the groove comparison is useful
Round-belt pulleys and idlers are used to guide or transmit motion through round-section belts. Manufacturer catalogues specify the supported belt size, groove dimensions, pulley diameter and mounting details.
Use this tool to see the consequences of a selected profile. It does not prescribe a common power limit or prove that the belt can tolerate the illustrated bend radius. Those decisions require the selected belt and pulley data.
Groove geometry equations
For cord diameter d, the cord radius is r = d/2. The selected radius factor k gives Rg = kr. The selected depth factor q gives h = qd. The radius difference is Rg − r.
In the illustrated U-shaped section, the straight-wall length is h − Rg, the open width is 2Rg, and the cord centre lies h − r below the rim surface. Cord protrusion above that surface is d − h. These are geometric relationships, not traction or load-capacity equations.
The example factors 1.05 and 0.7 are adjustable assumptions. They are not presented as universal optimal values. The manufacturer reference provides actual product dimensions that should be checked for a chosen installation.
Example: 4 mm round cord
With d = 4 mm, k = 1.05 and q = 0.7, the cord radius is 2 mm, the groove radius is 2.1 mm and the depth is 2.8 mm. The radius difference is 0.1 mm.
The straight entry walls are 2.8 − 2.1 = 0.7 mm long. The groove opening is 4.2 mm wide. The seated cord centre is 0.8 mm below the rim surface, leaving 1.2 mm of cord above the rim in this undeformed section.
Changing k changes the groove width and bottom curvature; changing q changes its depth and wall length. Changing d scales all these dimensions at the chosen ratios. The enlarged view adjusts its display scale to keep small cord sizes readable.
Geometry does not establish drive performance
A closer-fitting groove and a deeper groove change how the cord is supported, but neither is automatically preferable. Avoid treating the radius difference as a uniform clearance or using the diagram to infer a contact-pressure distribution.
Belt material, tension, wrap, pulley diameter, alignment and surface condition affect actual operation. No universal limits for power, speed, noise, service life or shaft misalignment are provided by this geometry calculator.
Round-belt groove questions
Why are the sides straight above the curved bottom?
The selected groove is deeper than its bottom radius. Straight entry walls keep the opening accessible instead of continuing the circle into an undercut.
Is the radius difference a constant gap?
No. The cord rests on the bottom, so the gap varies around its surface when the two radii differ.
Does the animated cord spin within the groove?
No. Markers travel along the belt. The cross-section remains stationary because it represents an undeformed section at the pulley.
Are the default ratios a standard?
No. They are trial values. Check the selected belt and pulley manufacturer’s dimensions and recommendations.
Can this calculate transmitted torque?
No. The available inputs determine groove geometry only.
Manufacturer geometry reference
Fenner PowerMax round-belt idlers provides photographs, a section drawing and product-specific belt-size, radius, bore and outside-diameter dimensions. Those references establish the recognizable pulley and open groove form; the adjustable section on this page is an original simplified geometry illustration.
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