A differential movement
A differential movement. The screw, C, works in a nut secured to the hub of the wheel, E, the nut being free to turn in a bearing in the shorter standard, but prevented by the bearing from any lateral motion. The screw-shaft is secured in the wheel, D. The driving-shaft, A, carries two pinions, F and B. If these pinions were of such size as to turn the two wheels, D and E, with an equal velocity, the screw would remain at rest; but the said wheels being driven at unequal velocities, the screw travels according to the difference of velocity.
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
- Shafts level, gravity on. The driving shaft A (40 rpm, the one driven joint) carries two pinions: F (20 teeth, broad) gearing with D (30 teeth) on the screw shaft, and B (22) gearing with E (28), all of module 0.6 cm, so both pairs share the 15 cm centre distance. The screw C (pitch 1.6 cm, 8 turns, laid in 24 convex segments a turn) turns with D and slides freely along its axis in a carriage; its thread works in a 3-turn nut in the hub of E, which turns in its bearing but cannot move along it. D turns at 0.6667 of A and E at 0.7857, so the nut gains 0.119 of a turn on the screw each turn of A and the screw travels 0.19 cm a turn of A, by the difference alone. Only teeth and threads touch.
- Measured
- D follows A at -0.6667 and E at -0.7858 (ideal -0.6667 and -0.7857), r2 1.000. The screw travels -0.000303 m per radian of A (ideal -0.0003032 = the speed difference times the pitch over 2 pi), r2 0.998, over 1 to 9 s. The deepest contact is 4.2 mm, between gear teeth.
- Notes
- Brown gives no sizes. The wheels are straight-flanked teeth (20 degree flanks) with 0.12 cm backlash each, which clears them where involutes would mesh exactly; D and E carry a light damper so their teeth keep on one flank. The screw and D ride together in a carriage, F made broad so D keeps in mesh as it travels.
Film (MP4) · Still (PNG) · Spec (YAML) · Model (MJCF)
