Polygon-head Chebyshev N3 Wheel
cf. N=2 case: Chebyshev N=2 Polygon Wheel (2016/07/10)
I found N=3 almost exact line model, after 2 years.
■ Straight line drawing linkage
Ordinary Chebyshev linkage is 4, 5, 5, 2 length bars frame, 180° span angle.
Above picture linkage is 4, 8.5, 8.5, √3 length bars frame, 120° span angle.
having long legs, and triangle head. ---- almost exact straight line. Ex. value y(E) ≒ 7.5 constant.
Regular-Triangle head △ center E ・ becomes pedal axis.
■ N=n Polygon Wheel
n Regular-Polygon head Chebyshev. Add (n-1) semi line-symmetrization coordinator bars.
Mechanism is simple, but n increaser, leg longer. So, N=3 is affordable?!.
cf. Polygon-head Chebyshev N4 Wheel
(4, 12.6, 12.6, √2 length bars)
■ N, is even-number or odd-number?
If N = 2n (n ≧ 2) case, you can use point-symmetrization coordination for n pairs.
(Center point E symmetry figure ---- parallelization mechanism. )
Ex. N= 4 case: 2 parallelization mechanism bars, and, 1 semi line-symmetrization bar.
(or, 3 all are semi line-symmetrization bars, that's OK, too. )
■ Exact length a
Theoretical value is below.
E(x,y)=E(x,y(x))
x=0 : y(0) = a-1
x=2 : y(2) = √(a2-(2+√3/2)2) -0.5
so, y(0) = y(2)
--- then, a = 5+2√3 = 8.464101616...