Machine Kinematics
solved, then drawn
Concept

Apex — where it appears

A corner of a rotor where two branches of its generating envelope meet. On a rotary engine it is the only part of the rotor that touches the housing, which is why the sealing problem there is three lines rather than a ring.

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

A rotor that was not drawn, at 52° of shaft. The housing is an epitrochoid — the only shape here that was written down — and the rotor is the envelope of it, seen from a body that turns at a third of the shaft's rate about a centre orbiting at the eccentricity. Nothing about the rotor was chosen. Its three apexes come out at radius 100.000000, which is the generating radius R exactly, at 0° and ±120°; the middle of each flank comes closest to the centre at 72.0000, which is R − 2e. The apexes are the only part of the rotor that touches the housing, which is why a rotary engine's sealing problem is three lines rather than a ring. positioned by solving, not by drawing.

A rotor nobody drew

The rotor of a rotary engine has three corners, three flanks and one job: to stay in contact with a housing while turning at a third of the shaft's speed about a centre that orbits. Given the housing and that motion, the rotor is not designed. It is computed, corners and all, by the routine that cuts a gear tooth.

meshing · Meshing Three chambers, 15,257 mm² between them. Each chamber is bounded by one flank of the rotor and the arc of housing between the two apexes that seal it, so its area is a polygon integral over two curves that are both known exactly. At this shaft angle they are 6309, 1147, 7801 mm². They add to 15257, and the housing's area less the rotor's is 15258 — a number that cannot depend on where the rotor is, and does not, to 9.2e-6 of itself. The engine's displacement is that constant shared out differently, and the three chambers are one chamber counted at three phases of the same cycle. positioned by solving, not by drawing.

Three chambers and a constant

A rotor with three corners divides its housing into three chambers, and as the shaft turns they trade area: one grows exactly as fast as the other two shrink. The total does not move — and the fact that it does not is a measurement of whether the corners are actually touching the wall.

meshing · Meshing

Named alongside it

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

Conjugate-actionEccentricityEnvelopeEpitrochoidMeshing equationRotorCompression ratioCuspDimensionless ratioPitch pointSwept volumeTrochoid

All concepts