Reuleaux triangle wheel W
How to make Reuleaux triangle wheel Bicycle ?
This is one hint.
This is a Two-wheel drive (wikipedia). Silent tank (or Continuous track ) can be made from this N-wheels (?).
■ width of 凹凸 (in Cyan trace curve)
Always 凹 width < 凸 width
Proof:
BC = d, DD'= e, [ e > 0, this is general case. cf. See Reuleaux triangle-Omusubi ]
凹 = (π/3)(d+e) - d/√3
凸 = (π/3) e + d/√3
So, 凸-凹 = 2d/√3 - (π/3)d =(2/√3 - 1/3)d =(2√3 - π)(d/3)
Then, 2√3=2*1.732..=3.464.. π=3.14..
So, (2√3 - π) > 0
So, 凸 > 凹
[ Above figure, e = 0 case. 凹 = (π/3 -1/√3)d , 凸 = (1/√3)d, ratio 凸/凹 ≒ 1.23 , 凹+凸 = (π/3)d ]
[ Velocity of E = 0.5 ( velocity of A) ]
■ How to get/ keep horizontal or vertical ?
① Add vertical suspender to the wheel axis. It supports the weight from the saddle. (2 wheels)
[ width (from axis to axis): ▶◀ shortest, ◀▶ longest , saddle (90°) is horizontal. ]
or
② Add one more wheel. (3 wheels)
3 wheels 1--E--2--E'--3 (i.e. 3-wheel drive), E and E' are mean, so y(E)=y(E'), so E-E' segment is horizontal.
( E-E' width is constant. ∵ 1-3 width is constant. 1 // 3, 1 ≡ 3. ---- i.e. 2 is an intermediate. )
ex. roller skate type of
━┳━┳━ ← board
▲┻▼┻▲
cf. new caster : N=3 2R-Virtual Wheel (Reuleaux triangle-Omusubi)
■ Node B/ C/ D propety
Node traces 3 types of curve. i.e. 1. cycloid, 2. arc, 3. straight