An escapement with a lantern wheel

Only the input is driven; every other part of this model moves by physics (MuJoCo), and its ratios are measured. Run it live, change its parameters, or switch the friction off to see the output stop.

Modelled as

An elevation (gravity on). The lantern wheel has 8 staves between two plates. It turns counter-clockwise, as Brown's arrow shows. The arm A hangs from a pivot above and right of the wheel, behind it (dashed in Brown's figure), and goes on down to a bob, so the arm is the pendulum. It carries two flat pallets across the staves' path. B is outside the staves' circle and crosses it 40° up the right side. C is inside and crosses it 17.5° up. When the arm swings right, C goes out into the staves' path and B comes out of it. When it swings left, B goes in and C comes out. A rising stave meets the underside of the pallet in its way. The underside slopes, so the stave pushes the pallet out of its way and the arm along with it (the impulse). The stave then slips off the tip. By then the arm has swung over and put the other pallet in the way, 22.5° (half a pitch) further on. The only input is a constant torque on the wheel (the weight). The arm starts hanging at rest, and the staves set it going.

Measured

The wheel goes 0.3927 rad per beat (half a stave's pitch; 0.3927 expected) over 16 beats. The swing builds to a steady 4.5° either side. As in any recoil escapement, the pallets push the wheel back a little after each catch, by up to 0.04 rad. The period is 0.742 s against 0.787 s for the arm swinging freely. It runs a little quick because the pallets push the pendulum back toward the middle. The deepest contact is 0.21 mm.

Notes

Brown gives no sizes. The stave count matches the figure. The pivot's place, the pallets' slopes and the bob are choices. In the figure, B and C are drawn at a slant that does not fit the arrow's direction. Here their undersides are sloped so that each stave pushes its pallet out of the way.

Film (MP4) · Still (PNG) · Spec (YAML) · Model (MJCF)