Animations for "Meditations on Breguet and Mathematics"
The following animations are used in the article "Meditations on Breguet and Mathematics". Some are new animations and some are links to animations listed elsewhere.
The purpose of these animations is to show that the dimensions of the stop-work can be varied to create different, but equally satisfactory designs.
Figure 1 below, based on Breguet's designs, explains the angles and measurements used. It shows (not to scale) two positions of the finger (green) during winding. The finger starts by leaving the leading edge of a slot (blue) in the barrel wheel (at the top of the diagram). The arbor wheel then rotates anti-clockwise until the finger starts entering the next slot (blue) at the bottom.
Ra is the radius of the arbor wheel; Rb is the radius of the barrel wheel; and C is the distance between the centers of these wheels.
Ω is the angular width of the slots, and φ is the angular width of a section, a segment and a slot; the width of the segment is φ - Ω .
δ is the angle (as the finger enters a slot) between the leading edge of the slot and the trailing edge of the finger. The minimum value depends on the size of the finger and the maximum value is Ω .
All slots are identical and four sections are the same size. So the angular width of the fifth section is 360° - 4φ.
Figure 2 is an example taken from an animation below where Ra = 1.75, Rb = 1.86, C = 2.68, Ω = 15°, φ = 74°, and δ = 7°. The fifth section is 64° wide.
Figure 1 is almost completely defined by Ra, Rb and C and from these dimensions we can calculate φ + δ. However, Ω , φ and δ can vary within sensible limits. Alternatively we can choose particular angles and calculate C from them.
The animations below show some of the possible variations: