3.4 Gears, Belts, and Rotation Direction
Key Takeaways
- Each gear mesh reverses rotation; two meshing gears turn in opposite directions.
- An idler gear between driver and driven makes those two turn the same way and does not change their tooth-count speed ratio.
- A larger driven gear turns slower with more torque; a smaller driven gear turns faster with less torque.
- An open belt keeps the same rotation direction; a crossed belt reverses it.
- Gears mesh without slip on these figures; flat belts may slip unless the figure treats them as a positive drive.
The QFD candidate information pack names gears among Mechanical Reasoning topics. On the Online Cognitive Ability Test, that almost always means a diagram of toothed wheels, a belt loop, or both, plus a stem about direction, speed, or which shaft is harder to stop. You are not being asked to specify a pump gearbox for a Queensland appliance. You are being asked to apply a short list of cause-and-effect rules without a calculator or scratch paper.
Gears: each mesh reverses
When two gears mesh (teeth of one push teeth of the other), they rotate in opposite directions. Gear A clockwise forces Gear B counterclockwise. Add Gear C meshing with B, and C is clockwise — the same way as A. A compact memory: an odd number of gears in a simple end-to-end train means the first and last turn the same way; an even number means they turn opposite ways. Count the gears in the chain, not the empty spaces.
An idler is a gear in the middle that is not the output. Its job is usually to reverse the reverse so the driven gear matches the driver's direction, or to bridge a gap. In a three-gear row A (driver) — B (idler) — C (driven), A and C turn the same way. The idler's tooth count cancels in the overall speed ratio: RPM of C versus RPM of A still depends on teeth of A and teeth of C, not on B. A 12-tooth driver, a 20-tooth idler, and a 36-tooth driven still give C one-third the RPM of A, same as if A meshed C through a magic gap. The idler changed direction, not that ratio.
Size, RPM, and torque
If two gears mesh, the linear speed at the teeth is shared, so
RPM_A × teeth_A = RPM_B × teeth_B
A small driver turning a large driven gear: the driven gear is slower and, in the ideal case, has more torque. A large driver turning a small driven gear: the driven gear is faster with less torque. That is the same trade-off you already saw on levers and pulleys, now in rotation. A portable-pump flavour: a 20-tooth crank gear meshing with a 40-tooth pump gear. The pump shaft turns at half crank RPM and (ideally) twice the crank torque. The diagram may ask only "which shaft turns slower?" — pick the one with more teeth.
Same-size gears that mesh: same RPM, opposite direction, same ideal torque. Same-size gears connected by an idler: same RPM, same direction as each other.
Belts: open versus crossed, belt versus gear
A belt (or a chain drawn as a loop) connects two pulleys without teeth meshing. Direction depends on how the loop is drawn:
- Open belt: the loop is uncrossed, like two parallel sides. Both pulleys turn the same way.
- Crossed belt: the loop is a figure-8. The pulleys turn opposite ways.
Speed still follows size if the belt does not slip: RPM × diameter is the same on both pulleys (use diameter or radius consistently). A PPV-fan flavour: a small engine pulley of diameter 10 cm at 60 rpm, open-belted to a 20 cm fan pulley, gives the fan 30 rpm in the same direction as the engine. Cross the belt and the fan is still 30 rpm but opposite in direction.
Belt versus gear on these figures:
| Connection | Direction rule | Slip on aptitude figures | Size rule |
|---|---|---|---|
| Two gears meshing | Opposite at each mesh | No slip; teeth force the motion | RPM inverse to tooth count |
| Open belt | Same direction | Often treated as no slip unless the stem says the belt slips | RPM inverse to pulley diameter |
| Crossed belt | Opposite direction | Same as open belt for speed; more wear in real life, which the figure usually ignores | Same size rule as open belt |
| Idler gear in a train | Makes driver and driven match direction | No slip | Idler teeth drop out of the driver–driven ratio |
A toothed belt or a chain is closer to gears: treat it as a positive drive (no slip) unless the stem says otherwise. A shiny flat belt on a smooth pulley is the one that might slip if the stem mentions slip.
Worked trains
Worked gear train: Gear A (driver, 12 teeth, clockwise) meshes with Gear B (24 teeth). B is counterclockwise at half A's RPM and twice A's ideal torque. Gear B also meshes with Gear C (12 teeth). C is clockwise (same as A) at the same RPM as A, because 24/12 cancels the previous 12/24. If C is the winch drum, the drum turns with the crank, not against it.
Worked belt: a compartment extractor fan uses an open belt from a 15 cm motor pulley to a 15 cm fan pulley. Same RPM, same direction. If the figure redraws the belt as crossed, only the direction flips. If the fan pulley is redrawn at 45 cm, the fan drops to one-third motor RPM and the direction rule is unchanged (open = same, crossed = opposite).
Keep this list of gear and belt traps:
- Reversing only "the last gear" instead of reversing at every mesh
- Treating an idler as if it changed the driver–driven tooth ratio
- Mixing belts with gears: an open belt does not reverse; a mesh does
- Assuming a larger pulley must turn faster (it turns slower)
- Using a hydrant-key leftover rule ("clockwise from above") when the figure labels a different viewpoint
- Turning a gear diagram into a kinetic-energy or circuit item; spinning masses after a clutch opens, and lamps on a switch, are Chapter 4
If the stem asks which way a hanging mass moves after a gear-driven drum winds a rope, finish the gear direction first, then treat the drum as a winch: clockwise wind-on versus wind-off depends on which side of the drum the rope leaves. That last step is still simple-machine cause-and-effect, not kinetic energy, as long as the question is direction rather than "how hard does it hit the floor."
Gear A turns clockwise and meshes directly with Gear B. Which way does Gear B turn?
Driver Gear A meshes with idler Gear B, which meshes with driven Gear C. A is clockwise. Which way does C turn, and what sets C's RPM relative to A?
A PPV fan is driven from a motor by a crossed belt. The fan pulley is twice the motor pulley's diameter. If the motor turns clockwise, what happens at the fan?