Machine Kinematics
solved, then drawn
Concept

Ternary link — where it appears

A link carrying three pins rather than the two a binary link carries, which is what a chain needs before it can hold more than one loop. Where the two ternary links of a six-bar sit decides which chain it is: sharing a pin makes it Watt's, not sharing one makes it Stephenson's.

Named by 2 essays across 2 fields — 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 The same part, dimensioned two ways. Three holes at 0.00, 1.40, 3.50, each located to ±0.010 by the process. Dimensioned as a chain, each hole is placed from the last, so the two gaps are ±0.010 each and the errors accumulate over the whole span to ±0.0141. Dimensioned from a baseline, every hole is placed from H0, so the span is ±0.010 and the gap between H1 and H2 — which touches the datum at neither end — is ±0.0141. The two schemes are exactly √2 apart in opposite places. Nothing about the part decides this and nothing about the process does; the drawing does, and a tolerance analysis that starts from the lengths has already thrown the information away.

The same part, dimensioned twice

Three holes, one process, two drawings. Dimensioned as a chain the errors accumulate and the span is ±0.0141; dimensioned from a baseline the span is ±0.0100 and the gap between the second and third holes is ±0.0141. Exactly √2 apart, in opposite places, and nothing about the part or the process decides which — the drawing does.

metrology · Parameter

Named alongside it

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

Datum schemeDerived lengthDwellFeature toleranceGrübler's criterionKinematic chainMobilityRoot-sum-squareSetup errorSix-barStephenson chainTolerance

All concepts