Machine Kinematics
solved, then drawn
Concept

Mutilated gear — where it appears

A gear with its teeth cut away over part of its circumference, so its output turns while the teeth are in mesh and is held by a locking arc while they are not. It is the cheapest way to build a long dwell into a gear train, and what it costs is a locking arc that has to be concentric with the driven wheel's axis to a manufacturing tolerance.

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

30 teeth and two pallets. An escape wheel of 30 teeth and a pair of pallets spanning 4 tooth pitches. The heavier line at each pallet is the locking face, here an arc about the arbor; the lighter one is the impulse face the tooth slides along once it is let go. The wheel is drawn where the contact puts it, not where it looks well: at this pallet angle the tooth in play sits on the lock face and the wheel is -0.0323° from it. Dragging the pallet through its whole engagement moves the wheel by 0.107° of recoil. Of the 6.0° the wheel turns each beat, -37.3% is drop and does nothing.

The escapement that could not alternate

Four drawings of intermittent mechanisms that appear everywhere and would not work: pallets spanning a whole number of teeth, a pawl whose pivot is on the wrong side of the tooth face, a Geneva at the wrong centre distance, and an intermittent gear with no locking arc. Each one is put through the library that draws the working version, and each returns a number.

wrong · Misconception A quantity that is not there, refusing to converge. A second central difference of a function with a bounded second derivative settles as the step is halved; across a step in the first derivative it doubles, every time. The rising line is a mutilated gear at the instant its teeth engage, where the driven wheel goes from stopped to full pitch-line speed: its successive estimates grow by a factor of 2.000000, which is the signature and not an accident of the step. The flat line is a six-slot Geneva at the same point in its cycle, whose pin enters along the slot and whose acceleration is a number. This is the only way to report an acceleration that does not exist: not by quoting a large one, but by showing the measurement refuse.

The gear with its teeth cut away

Leave teeth on part of a gear's circumference and take the rest off, and the output turns for part of the input's revolution and stops for the rest. It is the cheapest intermittent drive there is and it engages at full speed, so its output's velocity has a step and its acceleration is not a large number — it is not a number, and the way to report that is to watch a difference quotient refuse to converge.

timing · Intermittent

Named alongside it

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

the Geneva mechanismIntermittent motionTangential entryAccelerationDropDwellEscapementFinite differenceIndexingJerkLocking faceMotion law

All concepts