A crossed belt connects parallel pulley shafts so that they rotate in opposite directions. Its two straight spans cross between the pulleys and meet their contact arcs tangentially. The calculator draws that geometry using the entered diameters and shaft spacing.
Crossed Belt Drive Interactive Calculator
Set pulley diameters, center distance and belt width. Inspect the tangent belt path, opposite rotation, exact ideal length and spacing ratio.
Equation Used
- Parallel shafts and circular pulley pitch lines.
- No slip; zero belt thickness, sag and twist-length correction.
- Strict center distance greater than the sum of radii.
- No belt tension, power, wear or service-life prediction.
- Side view to proportion; belt width shown separately.
C/width is a geometric ratio, not a wear probability. Length neglects belt thickness, sag and three-dimensional twist.
Follow the tangent path
The driver carries the belt around its outer contact arc, along a straight tangent span to the opposite side of the driven pulley, around that pulley and back on the second span. The pulley markings rotate in opposite directions with equal ideal belt speeds.
The drawing break at the crossing distinguishes the two spans. It does not establish belt-to-belt clearance. The supports hold both shaft centers fixed; the belt and pulley proportions follow the dimensions.
Reversing a parallel shaft drive
A crossed routing is a geometric means of reversing rotation between parallel shafts. This page evaluates the ideal path and speed ratio. Belt suitability, tracking, contact at the crossing and tension require separate design checks.
Exact zero-thickness path length
Let r1=D1/2, r2=D2/2 and S=r1+r2. A crossed tangent path requires center distance C greater than S. The tangent angle is α=asin(S/C), and each straight span has length q=√(C²−S²).
Both contact angles are β=π+2α radians. The two straight spans and two circular arcs therefore give L=2q+Sβ. This is the exact planar centerline length for the ideal geometry, neglecting belt thickness, sag and twist. The usual long-center approximation is 2C+πS+S²/C.
Without slip, driven speed divided by driver speed is −D1/D2. The card displays the positive magnitude with a reverse-direction label. Belt width w is separate from the side-view path; C/w is a dimensionless spacing ratio, not a wear probability.
Equal 200 mm pulleys
With D1=D2=200 mm and C=1000 mm, both pulleys have approximately 203.07 degrees of wrap. The exact ideal belt length is approximately 2668.45 mm, and the shafts rotate at equal speeds in opposite directions. A 50 mm belt width gives C/w=20.
Increasing belt width changes that ratio and the width-section illustration. It does not change the zero-thickness side-view centerline length. Increasing center distance changes the tangent spans, length and wrap.
Limits of a geometric calculator
A center-distance/width ratio cannot determine a percentage chance of wear. Material, thickness, surface condition, tension, speed and three-dimensional crossing behavior are not inputs. No efficiency, service-life or safe operating-speed claim is made.
At C=S the ideal pulley circles touch and tangent-span length vanishes. For C below S they overlap. The diagram shows the touching or overlapping circles and reports that the crossed belt path is unavailable.
Crossed-belt questions
Why does belt width not change the side-view line thickness?
Width runs along the pulley shaft direction. The side-view line represents the belt centerline; a separate section shows width.
Does center distance divided by belt width predict wear?
No. C/w describes spacing relative to belt width. Wear also depends on material, tension, speed, surface condition and contact at the crossing.
Does exact length mean a ready-to-order belt length?
No. It is an ideal centerline calculation. Thickness, tensioning allowance and construction details remain outside the model.
Why do pulleys remain visible without a belt?
The entered circles touch or overlap, so the crossed tangent construction is invalid.
Reference
IIT Kharagpur / NPTEL: Introduction to Belt Drives, module 13 lesson 1, figures 13.1.1–13.1.2, for crossed routing and opposite rotation. The reference illustrates the crossed routing. This calculator derives its exact centerline expression directly from internal tangents and circular arc lengths.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
