Mechanical systems application and selection practice questions.

A small stage hoist must give a 40:1 speed reduction in a single stage, turn the drive through 90 degrees, and hold the scenery in place if the power fails. Which arrangement meets all three requirements?

• A pair of spur gears
• A toothed belt drive
• A worm and wheel
• A bevel gear pair

Answer: A worm and wheel

A worm and wheel achieves a very large reduction in one mesh, drives at right angles, and its shallow helix angle makes the pair non-reversible so the load cannot back-drive it. Spur and bevel pairs would need several stages for 40:1 and neither holds the load when the motor stops.

A loaded cargo bicycle must be ridden up a steep hill by a rider who cannot push hard on the pedals. The 40-tooth chainring stays fitted. Which rear sprocket should be selected and why?

• 32 teeth, as the larger driven sprocket raises output torque
• 32 teeth, as the larger driven sprocket raises wheel speed
• 12 teeth, as the smaller driven sprocket raises output torque
• 12 teeth, as the smaller driven sprocket lowers the gear ratio

Answer: 32 teeth, as the larger driven sprocket raises output torque

Gear ratio is teeth on the driven gear divided by teeth on the driver, so moving from 12 to 32 teeth raises the ratio from 0.3 to 0.8 and multiplies the torque reaching the wheel by 32 / 12, about 2.7 times. The price is wheel speed, and the usual error is to assume that more teeth means faster.

A machine guard must lift about 200 mm each cycle, but the operator's foot can travel only about 100 mm. The pedal that lifts it pivots at its heel end. Where should the foot and the guard linkage be placed on the pedal?

• Guard linkage at the far end, foot midway along the pedal
• Foot at the far end, guard linkage midway along the pedal
• Pivot moved to the middle, foot and linkage at the two ends
• Foot and guard linkage together at the far end of the pedal

Answer: Guard linkage at the far end, foot midway along the pedal

Putting the effort between the fulcrum and the load makes the load end travel twice as far as the foot, which is exactly the 100 mm to 200 mm the guard needs. The price is force: an arrangement that multiplies travel has a mechanical advantage below one, so the foot must push harder than the guard weighs.

A packaging machine must convert the continuous rotation of a motor shaft into vertical reciprocation of a stamping head, and the head must pause briefly at the top of every stroke. Which mechanism should be selected?

• A crank and slider mechanism
• A rack and pinion
• A cam and follower
• A bevel gear pair

Answer: A cam and follower

Only a cam profile can be shaped to include a dwell, in which the follower stays still while the shaft keeps turning. A crank and slider reciprocates continuously and reverses immediately at the end of each stroke, so it cannot deliver the pause.

A 4 m sliding driveway gate is to be driven by a motor mounted on the gate post. The drive must be positive, must not slip when the track is wet, and has to move the gate in a straight line for its full travel. Which transmission meets these requirements?

• A friction roller pressed against the gate frame
• A cam and follower driven from the motor shaft
• A rack on the gate driven by a pinion on the motor
• A crank and slider linking the motor to the gate

Answer: A rack on the gate driven by a pinion on the motor

A rack and pinion converts rotary motion into linear motion through meshed teeth, so the drive cannot slip when wet and the travel is proportional to the rotation of the motor for the whole 4 m. A cam or a crank and slider gives only a short reciprocating stroke, and a friction roller is exactly the slipping drive the specification excludes.

A greenhouse roof vent is opened by a hand crank on the wall below it. The vent needs a straight push of about 150 mm, and the crank has to be releasable at any point with the vent staying exactly where it was left. Which arrangement should be selected?

• A lead screw and nut, because the thread will not be back-driven by the vent.
• A rack and pinion, because the pinion turns the crank's rotation into a push.
• A cam and follower, because the follower is pushed out once per turn of the cam.
• A crank and slider, because the slider gives a straight push from a turning crank.

Answer: A lead screw and nut, because the thread will not be back-driven by the vent.

All four give a straight-line output, so the deciding criterion is holding position: only the fine screw thread is self-locking, while a rack, a cam and a slider are all back-driven by the weight of the vent. A cam and a crank are also tied to a fixed stroke that repeats every revolution.