Four-Bar Mechanisms and Inversions

Three links pinned in a plane form a rigid triangle. Four gives one degree of freedom: drive one link and every other position follows deterministically. One actuator controls an entire motion, which is why the four-bar appears in wipers, suspension, pliers and landing gear.

Points on the coupler trace curves that are neither circles nor straight lines. Watt used one to guide a piston rod along an approximate straight line when no machine tool could cut a true cylinder.

If s + l ≤ p + q — shortest plus longest against the other two — at least one link can rotate fully, so a continuously turning motor can drive it. If not, every link merely oscillates: a triple rocker.

It is the first thing checked in any linkage design, because it decides whether the mechanism can be motor-driven at all.

Inversion means grounding a different link of the same chain. The relative motion between links is unchanged; the absolute motion is completely different. The slider-crank is a four-bar with one pin at infinity, and its inversions give the Whitworth quick-return and the shaper.

The angle between coupler and output link decides how much transmitted force becomes useful output torque. Below about 40° the bearing loads climb steeply; at 0° or 180° the mechanism reaches a toggle position and locks.

A toggle is a fault in a mechanism expected to keep moving and a feature in a clamp or crimping tool — enormous mechanical advantage at zero output speed, and it self-locks because the load cannot push it back through.

A servo produces any motion you program; a linkage produces one motion permanently, with the timing encoded in its geometry rather than in software. It needs no controller, cannot lose synchronisation, and pin joints carry enormous loads cheaply.

That is why aircraft landing gear and heavy press mechanisms remain linkages — the trade is flexibility against reliability, and safety-critical machinery still chooses the second.