Cicloid

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation

R = 3

def circle(a, b, r):
    T = 100
    x, y = [0]*T, [0]*T
    for i,theta in enumerate(np.linspace(0,2*np.pi,T)):
        x[i] = a + r*np.cos(theta)
        y[i] = b + r*np.sin(theta)
    return x, y


def gen():
    for theta in np.linspace(0, 20*np.pi, 150):
        yield R*(theta-np.sin(theta)), R*(1-np.cos(theta)), R*theta

fig = plt.figure(figsize=(6, 3))
ax = fig.add_subplot(111)
ax.set_ylim(0, 20)
ax.set_xlim(0, 70)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_aspect('equal')
#ax.grid()
#time_text = ax.text(0.05, 0.8, '', transform=ax.transAxes)

cycloid, = ax.plot([], [], 'r-', lw=2)
line, = ax.plot([], [], 'y-', lw=2)
circle_line, = ax.plot([], [], 'g', lw=2)
point, = ax.plot([], [], 'bo', ms=4)

xx, yy = [], []

def func(data):
    x, y, Rt = data
    #time_text.set_text(r'$\theta$ = %.2f $\pi$' % (Rt / np.pi))
    xx.append(x)
    yy.append(y)
    cx, cy = circle(Rt, R, R)

    cycloid.set_data(xx, yy)
    line.set_data((x, Rt), (y, R))
    circle_line.set_data(cx, cy)
    point.set_data(x, y)

ani = animation.FuncAnimation(fig, func, gen, blit=False, interval=50)
plt.show()