Machine Kinematics
solved, then drawn
Concept

Stephenson chain — where it appears

The six-link chain whose two ternary links do not share a pin. It has three orbits of links and therefore three distinct mechanisms, against Watt's two, and the difference between the two chains is the single fact of whether those ternary links touch.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Watt's chain. Six links and 7 pin joints, so Grübler counts 3(6 − 1) − 2(7) = 1 and the rank of the Jacobian measures 1. Two of the six links must carry three joints; they are shaded. Here they share a joint, which makes this a Watt chain. That adjacency is the entire classification, and it is read off the graph rather than off the picture.

Six bars, and what the extra dyad buys

Every linkage so far has had four bars, because four is the smallest closed chain that moves. The next one up is six, not five, and six is where the subject stops being one family and becomes a taxonomy — two chains, distinguished entirely by whether the two links carrying three joints happen to touch.

linkages · Synthesis A dwell is a measurement, not a stop. The Stephenson six-bar's output against a full turn of the crank, with the four-bar it is built on for comparison. Inside a band of ±1° the six-bar's output holds still for 145.8° of crank and the four-bar's for 41.9°. The dwell comes from a stretch of the coupler curve that fits a circle of radius 3.006 to within 2.96e-3, and the arm from the coupler point is that radius. Nothing here stops; it moves less than the band.

A dwell made from a curve

Parts of a coupler curve are very nearly circular arcs. Put a link of the arc's own radius on the coupler point and its far end stands almost still while the point runs along it, so the output dwells — 146° of crank inside a one-degree band, against 42° for the four-bar it is built on. A dwell linkage does not stop. It moves less than the tolerance, and how much less is a number.

linkages · Synthesis

Named alongside it

The objects these essays reach for when they reach for this one.

DwellSix-barCamCircular arcCoupler curveCurve fittingGrübler's criterionKinematic chainMobilityStructural errorTernary linkWatt chain

All concepts