The Workshop Trolley That Rolls Down the Ramp

Force down the ramp. Total mass = 60 + 18 = 78 kg, so weight W = 78 × 9.81 = 765 N. For a 1:12 slope, sin θ = 1 / √(1² + 12²) = 1 / 12.04 = 0.0830. Component along the slope = 765 × 0.0830 = 63.5 N. Add rolling resistance in the castors, roughly 1% of W = 7.7 N, so about 71 N must be held.

Brake force at the rim. Lever mechanical advantage = 220 / 60 = 3.67. Pad normal force = 30 × 3.67 = 110 N. Friction force at the rim = μN = 0.5 × 110 = 55 N. Brake torque = 55 × 0.05 m = 2.75 Nm. On a 100 mm wheel (radius 0.05 m) this is equivalent to 2.75 / 0.05 = 55 N retarding force at the ground.

Verdict. 55 N available against 71 N required. The brake is short by about 16 N, roughly 23%. It will hold an empty trolley but not the loaded worst case, and friction brakes lose effectiveness if the rim is wet or dusty. One braked wheel also allows the trolley to pivot about that wheel on the cross-slope.

If a second wheel were braked the available force would be 110 N, a margin of about 1.5 - acceptable, but it depends on the student always clamping both levers.

Recommendation: a spring-applied ratchet and pawl on the axle, with the friction brake as a parking supplement only.

Reasoning.

• Positive holding. A ratchet holds by geometry, so it cannot slip when the rim is wet, dusty or contaminated with timber resin. A friction brake's capacity is μN and μ is exactly the variable that degrades in a workshop.
• Fail-safe. A spring-loaded pawl engages when the handle is released, so the trolley is held even if the student lets go mid-slope. A lever friction brake requires continuous effort or a locking detent that students forget to set.
• Holding vs stopping. The trolley needs to be parked on the ramp, not braked from speed. The ratchet suits holding; the friction brake would glaze if used to hold for long periods.
• Behaviour on the 90° turn. A pawl on the axle locks the wheels against rolling backwards but still allows the castors to swivel, so the turn at the bottom is not fought by the brake.

Design points. Use a 12-tooth pawl with a spring, a release lever at handle height, and a guard so fingers cannot reach the teeth. Keep the two braked castors as a parking brake for level ground.

Rejection of (a) alone. Two friction brakes do meet the 71 N figure on paper (110 N), but the margin disappears in wet weather and depends on the student squeezing hard every time.

What is happening. The trolley is a rigid 1200 mm deck on four castors. When the front castors meet the 1:12 break at the top of the ramp, the front of the deck has to rise about 100 mm over 1200 mm. The deck cannot bend, so it pivots about the rear castors until the front wheels climb. In that instant the load's centre of gravity (roughly 300 mm up, near the middle of the deck) has its weight line behind the front contact, and the front castors unload.

The effect is worse because:

• swivelling castors have a trailing offset, so they can flip and skid rather than roll up the break;
• 100 mm castors are small relative to a 1:12 change of slope; a step-like break acts as an obstacle;
• a quick entry adds a pitching moment from the sudden change in direction of the load, and the momentum of 60 kg of timber is significant.

Design change. Use two large fixed rear wheels (200 mm) and one swivelling front castor, with the deck cut back so the fixed wheels sit close to the load centre of gravity. Large fixed wheels roll over the break instead of being stopped by it, the three-point layout keeps all wheels loaded on uneven ground, and the front castor still allows the 90° turn. Also chamfer or fillet the ramp break so it is not a sharp edge, and add a low kerb along the deck to stop timber sliding.