if possible need solution without turtle

Spirograph was a popular toy when I was a child. It consists of two interlocking gears of different sizes; the larger wheel is pinned to the drawing board while the smaller one rotates around the outside (or inside of the larger. A pen, placed in a hole some distance from the center of the small wheel, traces out geometric patterns called epitrochoids (outside) and hypotrochoids the long lived (over 1500 years) Ptolemaic model was described by epitrochoids. The goal of this project is to program a Python script to draw epitrochoids and hypotrochoids using the matplotlib.pyplot module. The figures are defined by three parameters: the radii of the circles, R and r, and the distance of the pen from the center of the small circle, d. Illustrations can be found here and here. The curves can be traced out by incrementing the polar angle in the following expressions: x(0)=(R+r)cos8-d cos Epitrochoids y()=(R+r)sine-d sin x(O)=(R-1) cos 0+d cos o+d cos R-TO Hypotrochoids y(O)=(R-r)sin -d sin Write a python function to draw either an epitrochoid or an hypotrochoid for given values of the parameters R, r, and d.The selection of the figure (epitrochoid or hypotrochoid) should be an additional input argument to the function along with the number of circles. The script must not contain any numpy functions or other modules such as drawing modules, such as turtle. Plot 4 different figures (two epitrochoids and two hypotrochoids). Submit a python file that will plot all 4 figures you wish to have graded in a single frame using the module matplotlib.pyplot. subplot() Credit will be given for the quality and variety of the figures (30%). Plots should be customized as part of the script, using the functions described in tutorial 9. The remaining credit for the project (70%) will be for the program, which will be graded on accuracy (50%), simplicity (10%), and clarity (10%)