Machine Kinematics
solved, then drawn
Concept

Efficiency — where it appears

The share of the power put into a machine that comes out of it where it is wanted, the rest lost to friction, slip or heat in its elements. In a split drive it depends on which branch carries the power, because a branch that circulates power carries it through its lossy element more than once.

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

What each branch carries, against what the engine delivers. The power in the variator's branch and in the straight path, as multiples of the engine's own, for a planetary of K = 1.40. Both are ratios of powers, so the load cancels and nothing here is a force: the split comes from requiring the gearset to be lossless at every admissible set of speeds, which fixes the torques at 1 : K : −(1+K). The variator carries v/(K − v) and the straight path K/(K − v), and both run away at the pole. The variator first carries the engine's whole power at v = 0.700, which is exactly half the way to the pole — and the straight path is already carrying more than the engine everywhere past nought, flowing the other way through the planetary. That excess is the circulation.

The power that goes round twice

Sliding a power split's travel towards its pole buys ratio span for nothing, on the kinematics. It is not for nothing. The variator's own branch carries v/(K−v) of the engine's power and overtakes it at exactly half the way to the pole, and the tolerance trim the span was computed from is not reached until the variator is rated for six times the engine — which no machine is.

transmission · Transmission Every power split, on one curve. 1,994 power splits: all six ways of putting an engine, a variator and an output on a simple planetary's three shafts, with the variator coupled at the input or at the output, turning either way, on nine gearsets, with its travel placed at eleven positions. Every variator spans 3.333, as the variator of the previous essay does. Each dot is one split: the largest share of the engine's power its variator carries anywhere on the travel, and the span its output covers. They fall on three curves and nowhere else, to 7e-16: with no circulation, span R/(R(1 − S) + S), never more than the variator's own; with the variator's branch running backwards, 1 + S(1 − 1/R); with the variator carrying more than the engine, 1 + S(R − 1). 1188, 394 and 412 splits lie on the three. Which curve a split is on is decided by where its travel sits, not by which shafts it uses: every one of the twelve attachments appears on all three.

Every power split is on one curve

There are twelve ways to attach an engine, a variator and an output to a planetary's three shafts, and asking which is best turns out to be the wrong question. On 1,994 splits across all twelve and nine gearsets, the output's span is (1 + R·a)/(1 + a) to 5 × 10⁻¹⁵, where R is the variator's own span and a is the power the variator carries over the power the gears carry. Every split lies on one of three curves of span against the variator's largest share. The previous essay's 1.70 is 2 − 1/R on the worst of them, and a split beats its variator's own span only by making the variator carry more than the engine.

transmission · Transmission

Named alongside it

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

Continuously variableDesign ruleEpicyclicGear trainRatioVariatorSensitivityTolerance

All concepts