Instrument for describing pointed arches
Instrument for describing pointed arches. Horizontal bar is slotted and fitted with a slide having pin for loop of cord. Arch bar of elastic wood is fixed in horizontal at right angles. Horizontal bar is placed with upper edge on springing line, and back of arch bar ranging with jamb of opening, and the latter bar is bent till the upper side meets apex of arch, fulcrum-piece at its base insuring its retaining tangential relation to jamb; the pencil is secured to arched bar at its connection with cord.
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 elevation, the instrument lying on the drawing (no gravity): the horizontal bar with its upper edge on the springing line and its slot, the jamb of the opening drawn upright, and the arch bar of elastic wood fixed upright at the jamb with the fulcrum-piece at its base. The arch bar is fifteen 2 cm pieces hinged end to end, each joint a spring of 2.5 N m/rad that leaves the bar straight when free. A cord (a chain of 25 links) is looped on the slide's pin in the slot and tied to the bar's end, where the pencil is; it alone holds the bar bent into the arch (1.6 N with the cord upright). The hand moving the slide along the slot (6 cm either way) is the one driven joint.
- Measured
- As the slide moves, the cord leans with it and draws the bar's end out or lets it in, and the bar bends more or less at its foot: the bend at the foot follows the slide's place with slope 0.189 rad/m (r² 0.988), against 0.191 rad/m (r² 0.989) solved quasi-statically for this bar and cord by the generator (least bending energy, followed along the slide's travel); the check holds the model to that within 10%. The response is slight and not quite linear because the bar is far stiffer sideways than the cord's lean.
- Notes
- The bar's foot stands upright at the jamb (tangential to it, as Brown says), so the arch starts upright; the bar is drawn thinner than Brown's; the slide is a brass plate so the hand's drive stays steady.
Film (MP4) · Still (PNG) · Spec (YAML) · Model (MJCF)
