Fusee chain and spring-box, being the prime mover in some watches,…

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

Brown's figure seen from a little in front and above: the spring-box (barrel, 8 cm across) on the left and the fusee on the right, both on upright arbors in a plate. The fusee is a cone (6.8 cm across at the foot, 3 cm at the top) with a helical groove (a colliding rib between the turns). A chain (120 links) is made fast near the fusee's foot, lies 3 turns up its groove, leaves it at the top (the small diameter: the watch wound up) and runs across to the barrel, where its other end is made fast. The one driven joint is the barrel, turned by its mainspring: 0.4 N m fully wound, less 0.015 N m for each radian it uncoils (driver torque and the barrel's spring rate). It winds the chain onto itself and draws it off the fusee, which turns the train (a viscous load, 0.1 N m s). gen046.py.

Measured

Started at rest, the barrel uncoils 10.8 rad in 10 s and the fusee turns 17.4 rad the same way. Barrel to fusee speed rises from 0.51 to 0.73 across the run as the chain leaves the fusee lower down (ratio_range 0.4 to 0.9), while the spring's torque falls by about 40 percent; the fusee's speed against its load stays near even (1.77 to 1.87 rad/s after the first second; turning check, 95 percent of samples above 0.7 of the mean). Penetration under 1 mm. With the chain's ends cast off, the spring runs the barrel round and the fusee stands.

Notes

The fusee is a smooth cone with a groove rather than Brown's stepped one; the chain is a pinned cord of links (drawn round), not a watch chain's plates; the spring is the driver's torque less a joint stiffness, not a coiled spring in the box; a 10 s run uses 3.3 of the fusee's turns.

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