Machine Kinematics
solved, then drawn
Concept

Operating point — where it appears

The position of a mechanism at which a varying quantity was measured, and without which a quoted value of it means nothing. A ratio, a rocker ratio, a pressure angle and a roll centre are all functions of position, so a number quoted without one is a number that cannot be checked.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

What each machine is sold with. Every mechanism in this field arrives with a number. The middle column is that number; the right-hand column is what the mechanism was measured to have, by the library named under the row. The coloured bar and the word under each machine are the verdict: exact means the mechanism has the number at every position, mean that it is the average of something that varies within every cycle, bounded that it is false by a stated and negligible amount, point that it is the value at one position, and quoted that the mechanism has no such quantity at all. Of the 14 rows, 6 are quoted and 3 are exact.

The number on the box

Fourteen machines, fourteen quoted numbers, and five different things a quoted number can be. Six of the fourteen name a quantity the mechanism does not have at all; three are exactly right, and all three of them are counts. The field is built on the difference.

applied · Misconception What the valve does, against what the ratio promises. The solved valve lift, and the cam's lift multiplied by the nominal ratio. They are the same curve to the eye and they are not the same curve: the peak is 12.777 mm against a promised 12.842 mm, short by 0.51%. The shortfall is not an error in either number. It is what happens when a ratio measured at one position is applied across a movement, and it is why cam cards and rocker ratios are quoted together.

The cam is not the valve

A rocker arm's ratio is the ratio of two moment arms measured at one position, and the rocker swings twelve degrees while the valve opens. The instantaneous ratio runs 1.588 to 1.605, so the peak valve lift is 12.78 mm where the number on the box promises 12.84 — and the shortfall depends on how the rocker was set up, not on the cam.

applied · Cam Where the pad touches, and the rule that fixes it. The contact point's travel across the valve tip through one cam event, for a rocker squared up with the valve shut and for the same rocker squared up at mid-lift. The first wipes 1.35 mm and the second 0.34 mm — a factor of 4.0 for a shim under a stud. The rule an engine builder is taught is that the geometry is symmetric about wherever it is set square, so setting it square at rest puts the entire lift on one side of the symmetry. It is folklore that turns out to be geometry, and the same shim brings the peak lift back to 12.84 mm against 12.78.

Where the pad touches

A rocker's pad slides 1.35 mm across the valve tip through one cam event when the geometry is squared up with the valve shut, and 0.34 mm when it is squared up at mid-lift. The engine builder's rule about shimming a rocker stud is folklore that turns out to be geometry, and the same shim brings the peak lift back to what the ratio promised.

applied · Cam What each machine is sold with. Every mechanism in this field arrives with a number. The middle column is that number; the right-hand column is what the mechanism was measured to have, by the library named under the row. The coloured bar and the word under each machine are the verdict: exact means the mechanism has the number at every position, mean that it is the average of something that varies within every cycle, bounded that it is false by a stated and negligible amount, point that it is the value at one position, and quoted that the mechanism has no such quantity at all. The lit row is the one this essay is about. Of the 14 rows, 6 are quoted and 3 are exact.

Which numbers survived

Fourteen machines were measured against the numbers they are sold with. Three survived exactly, and all three are counts. One is false by a stated bound, two are exact means of things that vary, three are honest values at a stated position, and six name quantities their mechanisms do not have. The pattern is not about honesty; it is about what kind of thing a number is.

applied · Misconception

Named alongside it

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

Rocker ratioVelocity ratioCamCatalogue numberConstraintDerivativeFollowerLiftMobilityRatioToleranceApproximation

All concepts