Mechanisms & linkages

An engine can really do only one thing: spin. Yet the needle of a sewing machine runs up and down, the windscreen wiper swings back and forth and the pliers grip. Between the plain rotation and the useful motion sit mechanisms: chains of rigid links and joints that translate one form of movement into another. If you can read them, you understand the inner life of almost every machine.

The crank: rotation becomes back and forth

The most important translator is the crank drive. A pin sits at distance $r$ from the axis and traces a circle, a connecting rod links it to a slider that can only move straight. The result: the slider shuttles between two end points, its stroke is exactly $2r$. In a sewing machine such a crank drives the needle bar. A car engine uses the same mechanism in reverse: there the piston pushes the connecting rod and forces the crankshaft to turn.

Eccentric and cam

Sometimes no joint is needed at all, an offset centre is enough. An eccentric is a round disc whose shaft deliberately misses the centre by an offset $e$: with every revolution its rim raises and lowers whatever rests on it by $2e$, twice the offset. Cams take this further, their rim is a freely shaped curve that stamps a precise motion schedule onto a follower. That is how the camshaft in an engine opens every valve at exactly the right moment.

Lever chains in everyday life

Link several levers together and you get a linkage. The windscreen wiper is the textbook case: a small motor turns a crank, a linkage turns that into the swinging of the wiper arms, and both arms move neatly in step. Pliers too are a lever chain, two levers sharing one pivot, and bolt cutters put two lever pairs in series. Their advantages multiply, turning hand force into thousands of newtons at the blade.

The golden rule reigns here too

However intricate a mechanism is, the golden rule of mechanics holds at every joint: force times distance is preserved, minus friction. If the pliers' jaw moves only a fifth as far as your hand, it squeezes five times as hard. How big that advantage turns out follows from the distances to the pivot, the joint of the pliers: if your hand grips 20 cm from the joint but the wire sits only 4 cm from it, your hand travels five times as far, because 20 divided by 4 is 5. Engineers therefore trace the motion link by link through the chain and know precisely how fast, how far and how forcefully the last link works.