Mechanisms, structures and mechanical systems
Mechanisms, structures and mechanical systems is examined through lever, gear, pulley and cam calculations, and through force analysis in frames.
Core rules
- Levers: class 1 (fulcrum between load and effort), class 2 (load between), class 3 (effort between). Moment = force x perpendicular distance.
- Gear ratio = teeth driven / teeth driver. Speed ratio is the inverse; torque increases with reduction. An idler changes direction but not ratio.
- Pulleys: velocity ratio = number of supporting rope sections; a movable pulley halves effort in an ideal system.
- Cams convert rotation to reciprocating motion; follower shape and cam profile set the motion.
- Structures: tension, compression, shear, torsion and bending. Triangulation stops a frame racking; ties take tension, struts take compression.
- Stability improves with a low centre of mass and a wide base.
Worked example
A motor turns at 600 rpm with a 12-tooth gear driving a 36-tooth gear. Ratio = 36 / 12 = 3:1 reduction, so output speed = 600 / 3 = 200 rpm, and torque is about three times higher, ignoring friction. Adding a 20-tooth idler between them reverses the output direction; the ratio stays 3:1 because the idler is both driven and driver.
Traps
Inverting the gear ratio; counting an idler in the ratio; using slant distance instead of perpendicular distance for a moment; confusing mass (kg) with weight (N); saying "triangles make it strong" without naming tension and compression.