Scroll(Res, 1, 10, 1, 5)
Scroll(\theta, 0, 2\pi, \pi/30, 7\pi/4)
Scroll(twists, 0, 5, .01, 1/2)
Scroll(r, 0, 5, .01, 3)
v1=10[cos(u), sin(u), 0]
T1=[D(v1(1), u), D(v1(2), u), D(v1(3), u)]/(D(v1(1), u)^2+D(v1(2), u)^2+D(v1(3), u)^2)^(1/2)
N1=[D(T1(1), u), D(T1(2), u), D(T1(3), u)]/(D(T1(1), u)^2+D(T1(2), u)^2+D(T1(3), u)^2)^(1/2)
B1=Cross(T1, N1)
RB1=[[1, 0, 0], [0, 1, 0], [0, 0, 1]]*cos(twists*u+T)+[[0, -T1(3), T1(2)], [T1(3), 0, -T1(1)], [-T1(2), T1(1), 0]]*sin(twists*u+T)+(1-cos(twists*u+T))*([[T1(1)^2, T1(1)T1(2), T1(1)T1(3)], [T1(1)T1(2), T1(2)^2, T1(2)T1(3)], [T1(1)T1(3), T1(2)T1(3), T1(3)^2]])
V=(RB1*Transpose(B1))*r*sin(2v)+(RB1*Transpose(N1))*r*sin(v)+v1
ParametricPlot3D(V(1, 1), V(2, 1), V(3, 1), [u, 0, \theta, Res*15+50], [v, 0, 2\pi, Res*10+25])