Machine Kinematics
solved, then drawn
Concept

Datum scheme — where it appears

The choice of which features a part's dimensions are measured from. Chain dimensioning accumulates error along the chain and baseline dimensioning does not, so the same part made by the same process has two different tolerance analyses and only the drawing says which.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Where a length comes from. A coupler 3.5 units long is a part with two holes in it, and neither hole's position is the length. Each carries an error of 0.010, of which 60% is common to both because they were bored in one setup — the whole pattern shifts by that much and the distance between the holes does not change. What survives is the independent part, 0.0063 at each hole, combining to 0.0089 on the length. A drawing that tolerances the length at ±0.010 is describing a part nobody makes, and it is out by a factor of 0.894 — optimistic below a shared fraction of one half and pessimistic above it.

Where a length comes from

A coupler 3.5 units long is a part with two holes in it, and neither hole's position is the length. What reaches the length is only the part of each hole's error the two do not share — so a drawing that tolerances the length is describing a part nobody makes, and is out by a factor of √2 in one direction or by everything in the other.

metrology · Parameter 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 Which feature to hold tight. A budget of 0.020 divided between the four lengths in inverse proportion to their sensitivities, and the same budget divided between the features those lengths are derived from — a frame jig-bored in one setup at 0.90 shared, a crank drilled twice at 0.10, a coupler at 0.60 and a rocker at 0.30. The tightest tolerance moves from b to a. And the null result matters as much: with one process for the whole machine the two allocations are identical to the last digit, because the transmission factor is then common and divides out. Feature-based tolerancing changes the answer when the parts are made differently and not merely when they are made.

Which feature to hold tight

A budget divided between four lengths in inverse proportion to their sensitivities gives one answer. The same budget divided between the features those lengths are derived from gives the same answer exactly — unless the parts are made differently, in which case the tightest tolerance moves from the rocker to the crank and the frame's loosens by a factor of two.

metrology · Parameter

Named alongside it

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

Derived lengthFeature toleranceSetup errorToleranceWorst caseCalibrationClearancePrecision positionRoot-sum-squareSensitivityTernary link

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