N=4 2R-Virtual Wheel

This is a typical a kind of Square Wheel.
2R-circle Wheel with R-circle outline. (Outer appearance is like a r=1R circle, but real foot has r=2R circle.) This is Virtual tire technique. Red bullet A ● is axis, 4 cheese shaped rigid foot team works. ■ Reuleaux triangle (wikipedia) Above apparatus is related the polygon of Reuleaux a bit. ■ Linkage techniques This apparatus is very educational, I think so. This apparatus use many basic linkage tools. ① Line symmetry 1-1: To keep ∠BAO = ∠B'AO, I use Antiparallelogram. cf. Line Symmetry Linkage (Alias: Imai's Butterfly) (GeoGebra) In above figure case, on x(A) =3.14 point, red Antiparallelogram shrinks in a line, point P and R is out of wheel, so, we must reduce the Antiparallelogram size to half or mor small. 1-2: To keep Point black D and blue D' are symmetry with C''C' line. I used "MA + AG = constant", is the same "MA + AW = constant" ---- Black and Blue are connected by this relation. Tip: In real world: Axis A ● is swinging between M---G arc curve. So, MA + AG = constant (2π/4=3.14/2=1.57, [r=2, angle=45°=π/4 case] ) 1.57 is 凸 curve length value, liner approximation was adjusted to 1.53 But, MA and AW is bent, so we cannot use MW ≒ constant. so, I rotated MA by 90° clockwise, get point I'. I'A and AW are loosed bent. So I'A + AW ≒ I'W is true. So, "I'W = constant" is good approximation. ( Here, At least, ∠EBH angle is 0° and 45° points must be satisfied the symmetry condition. At other angle case, rough is OK. ) IA rotate by 90° into I'A, is supported by Pink colored tool. --- From comparing above Blue B'D' and Purple B'K', this approximation is considerable exact. (From observation, value 90° digs the ground a bit, so 110° tuning had better result than 90° case. ---- this is interesting result.) ② Point symmetry To keep BD (black)// D'1H (orange), I used/ added Cyan 3 bars (GL, LL', L'N). ■ 1-2 Another method/ solution Most orthodox method. N=4 2R-Virtual Wheel (Vers.-B) (exact line symmetry.).