# 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

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