Continuous rotary → reversed continuous rotary

Crossed Belt Drive

Cross the belt between two parallel pulleys and the driven shaft reverses direction. In the ideal no-slip model, the pulley-size ratio is unchanged; only its sign changes.

Collection contextBrown 002
Mechanism Labanalytic · ideal crossed belt
Drag the mechanism or change a parameter.
180 mm
30 rpm
Output directionReversed
Speed ratio1.000
Output speed30.0 rpm
Belt speed0.141 m/s
Driver wrap
Ideal belt length

What changed from 001?

One routing change flips the output.

The two pulleys can keep the same diameters and spacing used by an open belt. The new ingredient is the crossing itself: each straight belt span switches sides between the pulleys, so the driven pulley must rotate opposite the driver to satisfy the no-slip contact condition.

ω₂ / ω₁ = −r₁ / r₂Ideal crossed belt: the magnitude of the speed ratio still comes from the pulley pitch radii. The minus sign records the reversed output direction.
|v| = r₁|ω₁| = r₂|ω₂|Crossing the belt changes direction, not the ideal belt-speed magnitude for the same driver radius and angular speed.

Why it matters

Direction becomes a design choice.

Movement 001 establishes that a belt can transmit rotation. Movement 002 shows that routing can control the direction of that transmission without changing the driver or adding a meshing gear pair. It is a compact lesson in mechanism design: geometry can change behavior even when the same components and ideal ratio are retained.

Compare it with the open belt

  • open belt: same-direction output;
  • crossed belt: opposite-direction output;
  • both: ideal speed-ratio magnitude set by pulley pitch radii;
  • crossed routing: a stricter minimum center distance is required for real tangent geometry.

Engineering tradeoff

The crossing is useful—and physically consequential.

In a real flat-belt transmission, the two spans must pass one another at the crossover. That can introduce belt rubbing, extra flexing, heat, and wear if the installation does not provide enough separation or guidance. The ideal Atlas model computes planar tangent geometry and kinematics; it does not yet model belt thickness, self-contact, frictional losses, tension, or lateral tracking.

Notice the geometry limit in the lab as well: for a crossed belt, the center distance must exceed the sum of the two pitch radii. Drag the center-distance handle too close and Atlas keeps the last valid physical state while showing the invalid proposal.

Collection 001 · Henry T. Brown

Brown turns reversal into a control system.

Brown explicitly presents movement 2 as a modification of movement 1: substitute a crossed belt and the pulley directions reverse. He then extends the idea to a driven shaft carrying one fast pulley and two loose pulleys. With both an open and a crossed belt available, shifting which belt runs on the fast pulley selects the shaft direction while the driver continues rotating.

“Differs from 1 in the substitution of a crossed belt for the open one.”Henry T. Brown, movement 2 · online transcription reference

The live model above isolates the two-pulley crossed-belt principle. Brown's larger fast/loose-pulley reversing arrangement is application context, not something this simple model claims to simulate.

View the current 507movements.com reference ↗

Learning progression

Transmission → direction → engagement.

The first two movements answer two different questions: can rotation be transmitted? andwhich way should the output turn? The next belt-drive step in this learning path adds another kind of control: engaging or disengaging the transmission with a tightening pulley.

001
Open Belt Drive

Review the baseline · same components · same-direction output.