Compound parallel ruler, composed of two simple rulers, A, A,…
Compound parallel ruler, composed of two simple rulers, A, A, connected by two crossed arms pivoted together at the middle of their length, each pivoted at one end to one of the rulers, and connected with the other one by a slot and sliding-pin, as shown at B. In this the ends as well as the edges are kept parallel. The principle of construction of the several rulers represented is taken advantage of in the formation of some parts of machinery.
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
- A plan of the drawing board, gravity off. Two rulers A, A, 26 by 2.4 cm. The lower one is held down on the paper. Two crossed arms, 20 cm long, are pivoted together at their middles. Arm E is pivoted to the lower ruler at its left end, and the pin at its far end slides in a slot in the upper ruler. Arm D is pivoted to the upper ruler at its left end, and its pin slides in a slot in the lower ruler (B in Brown's figure). The pins are 0.6 cm across, in 0.64 cm slots. The only input is the hand turning arm E on its pivot, ±11.5° about 37° at 0.25 Hz, which opens and closes the ruler between about 8.6 and 15 cm. The rest is held only by the pins bearing in the slots.
- Measured
- As E turns by θ, D turns the other way on it by 1.98θ (2 expected). The upper ruler turns back on D by 0.985θ (1 expected), so it ends where it started: its edges stay parallel to the lower ruler's within 0.15°, the pins' play in the slots. Both rulers' left ends are on the arms' fixed pivot line, so their ends stay square to each other too. The deepest contact is 0.006 mm.
- Notes
- Brown gives no sizes. The rulers, arms, angles and the pins' clearance are choices. The pivots carry light damping, which only matters in the negative control. Arms D and E are named here; Brown labels only the rulers A, A and the slot and pin B.
Film (MP4) · Still (PNG) · Spec (YAML) · Model (MJCF)
