Cyclograph for describing circular arcs in drawings where the…
Cyclograph for describing circular arcs in drawings where the center is inaccessible. This is composed of three straight rules. The chord and versed sine being laid down, draw straight sloping lines from ends of former to top of latter, and to these lines lay two of the rules crossing at the apex. Fasten these rules together, and another rule across them to serve as a brace, and insert a pin or point at each end of chord to guide the apparatus, which, on being moved against these points, will describe the arc by means of pencil in the angle of the crossing edges of the sloping rules.
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
- Plan view (the apparatus lies flat on the drawing, so no gravity). Chord 30 and versed sine 9 are laid down; the two sloping rules, crossing at the apex, and the brace are one rigid frame, free to slide and turn on the paper. Needle points stand at the chord's ends. The hand (the one driven joint) moves the frame to and fro across the paper and presses it lightly against the needles (a soft spring); the needles alone set how high the frame lies and how it turns, and the pencil in the angle of the crossing edges describes the arc. A light readout from the inaccessible centre, pinned at the pencil, records its distance from the centre and carries nothing.
- Measured
- The pencil stays within 0.02 mm of the arc's radius while it sweeps about 15 degrees either side of the top; the rules turn exactly half as far as the pencil goes round the centre (slope 0.502, the angle in the segment); penetration stays under 0.02 mm.
- Notes
- The needles stand on the chord's ends and the rules' edges just clear them by the needles' radius, so the pencil runs on an arc 0.12 cm outside the laid-down one; the hand's press is a soft spring rather than a hand; the brace is set a little further from the needles than in the figure so that the sweep is longer.
Film (MP4) · Still (PNG) · Spec (YAML) · Model (MJCF)
