Cycloid

t = -6.203185307179586 (slider from (-2 * π) to (π * 3), step 0.01)
A: ((2 * t), 2)
B: (x(A), 0)
c = Circle(A, B)
B' = Rotate(B, (-t), A)
α = Angle(B', A, B)
B'' = Sequence(Rotate[B', (π / 6 * t), A], t, 1, 12)
seg = Sequence(Segment[Element[B'', t], A], t, 1, 12)