Epicicloid

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

R1 = 8
R2 = 8

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(0,15*np.pi,500):
        k = R1/R2
        a = R2 * (k + 1)*(np.cos(theta) - np.cos((k + 1) * theta )/ (k + 1))
        b = R2 * (k + 1)*(np.sin(theta) - np.sin((k + 1) * theta )/ (k + 1))
        yield a, b, (R1+R2) * np.cos(theta), (R1+R2) * np.sin(theta)

fig = plt.figure(figsize=(6, 3))
ax = fig.add_subplot(111)
ax.set_ylim(-20, 20)
ax.set_xlim(-20, 20)
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)

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

xx, yy = [], []

def func(data):
    x, y, Rx, Ry = data
    xx.append(x)
    yy.append(y)
    cx, cy = circle(Rx, Ry, R2)
    c1_x, c1_y = circle(0, 0, R1)

    cardiod.set_data(xx, yy)
    line.set_data((x, Rx), (y, Ry))
    circle_line.set_data(cx, cy)
    circle_static.set_data(c1_x, c1_y)
    point.set_data(x, y)

ani = animation.FuncAnimation(fig, func, gen, blit=False, interval=50)
plt.show()
# fn = 'cacloid_FuncAnimation'
# #ani.save('%s.mp4'%(fn), writer='ffmpeg', fps=1000/50)
# xx, yy = [], []
# ani.save('%s.gif'%(fn), writer='imagemagick', fps=1000/50)