Code for parallel version (Use Linux)

# -*- coding: utf-8 -*-
\"\"\"
Simulate 2R Robotic arm

Created on Mon Jun 18 09:56:21 2018

@author: Vishwesh Ravi Shrimali
\"\"\"
import matplotlib.pyplot as plt
from math import pi, cos, sin
from numpy import linspace
import multiprocessing as mp
import os
def getNumberOfProcessors():
    return int(input(\"Enter number of processors to use: \"))

def mainPlot(subDataIndex):
    i = subDataIndex
    #for i in subDataIndex:
    data = DATA[i]
    plotRoboticArmPosition(data[0],data[1],data[2],data[3],data[4],data[5],data[6],data[7])
    plt.ylim([-(l1+l2)*1.1,(l1+l2)*1.1])
    plt.xlim([-(l1+l2)*1.1,(l1+l2)*1.1])
    fileName = folderName+\'plot_{0:06d}.png\'.format(i)
    plt.savefig(fileName)
        

def plotRoboticArmPosition(x0,y0,x1,y1,x2,y2,theta1,theta2):
    # Clear figure
    plt.clf()
    plt.cla()
    plt.close()
    plt.plot(x0,y0,\'o\',markersize=10)
    plt.plot(x1,y1,\'o\',markersize=10)
    plt.plot(x2,y2,\'o\',markersize=10)
    # Plot link 1
    plt.plot([x0,x1],[y0,y1],\'-\',c=\'k\',label=\'Link 1\')
    # Plot link 2
    plt.plot([x1,x2],[y1,y2],\'-\',c=\'r\', label = \'Link 2\')
    # Turn axis off
    title = \"2R Robotic arm for theta1 = {:.2f}, theta2 = {:.2f}\".format(theta1,theta2)
    plt.title(title)
    plt.legend(loc=\'upper left\')

def main():
    # Define lengths
    #l1 = 1
    #l2 = 0.5
    # Base of robot
    x0 = 0
    y0 = 0

    # Number of theta values
    n_theta = 100
    
    theta1 = linspace(-pi/2,pi/2,n_theta)
    theta2 = linspace(-pi/2,pi/2,n_theta)
    
    imgCount = 0

    for i in range(n_theta):
        imgCount = i*n_theta
        for j in range(n_theta):
            DATA_INDEX.append(imgCount+j)

    for i in theta1:
        for j in theta2:
            # Link1 - link2 connector
            x1 = x0+l1*cos(i)
            y1 = x0+l1*sin(i)
            # Link 2 end
            x2 = x1 + l2*cos(j)
            y2 = y1 + l2*sin(j)
            # Append to DATA
            DATA.append([x0,y0,x1,y1,x2,y2,i,j])
            # Plot position
            #plotRoboticArmPosition(x0,y0,x1,y1,x2,y2,i,j,imgCount)
            #plt.xlim([-(l1+l2)*1.1,(l1+l2)*1.1])
            #plt.ylim([-(l1+l2)*1.1,(l1+l2)*1.1])
            #fileName = folderName+\'plot_{0:06d}.png\'.format(imgCount)
            #plt.savefig(fileName)
            #imgCount+=1
        theta2 = theta2[::-1]

if __name__ == \"__main__\":
    # Make folder
    folderName = \'robotic2RPlots/\'
    try:
        os.mkdir(folderName)
    except:
        print(\"%s already exists. Continuing...\"%(folderName))
    DATA = []
    DATA_INDEX = []
    l1 = 1
    l2 = 0.5
    main()
    numProcs = getNumberOfProcessors()
    p = mp.Pool(numProcs)
    p.map(mainPlot,DATA_INDEX)

Code for Single Processor (Serial version - Can work on any OS)

# -*- coding: utf-8 -*-
\"\"\"
Simulate 2R Robotic arm

Created on Mon Jun 18 09:56:21 2018

@author: Vishwesh Ravi Shrimali
\"\"\"
import matplotlib.pyplot as plt
from math import pi, cos, sin
from numpy import linspace
from os import mkdir
# x0 = 0, y0 = 0
# l1 = 1
# l2 = 0.5

folderName = \'robotic2RPlots/\'
try:
    os.mkdir(folderName)
except:
    print(\"%s exists. Continuing...\"%(folderName))
def plotRoboticArmPosition(x0,y0,x1,y1,x2,y2,theta1,theta2,imgCount):
    # Clear figure
    plt.clf()
    plt.cla()
    plt.close()
    plt.plot(x0,y0,\'o\',markersize=10)
    plt.plot(x1,y1,\'o\',markersize=10)
    plt.plot(x2,y2,\'o\',markersize=10)
    # Plot link 1
    plt.plot([x0,x1],[y0,y1],\'-\',c=\'k\',label=\'Link 1\')
    # Plot link 2
    plt.plot([x1,x2],[y1,y2],\'-\',c=\'r\', label = \'Link 2\')
    # Turn axis off
    title = \"2R Robotic arm for theta1 = {:.2f}, theta2 = {:.2f}\".format(theta1,theta2)
    plt.title(title)
    plt.legend(loc=\'upper left\')

def main():
    # Define lengths
    l1 = 1
    l2 = 0.5
    # Base of robot
    x0 = 0
    y0 = 0

    # Number of theta values
    n_theta = 100
    
    theta1 = linspace(-pi/2,pi/2,n_theta)
    theta2 = linspace(-pi/2,pi/2,n_theta)
    
    imgCount = 0
    
    for i in theta1:
        for j in theta2:
            # Link1 - link2 connector
            x1 = x0+l1*cos(i)
            y1 = x0+l1*sin(i)
            # Link 2 end
            x2 = x1 + l2*cos(j)
            y2 = y1 + l2*sin(j)
            # Plot position
            plotRoboticArmPosition(x0,y0,x1,y1,x2,y2,i,j,imgCount)
            plt.xlim([-(l1+l2)*1.1,(l1+l2)*1.1])
            plt.ylim([-(l1+l2)*1.1,(l1+l2)*1.1])
            fileName = folderName+\'plot_{0:06d}.png\'.format(imgCount)
            plt.savefig(fileName)
            imgCount+=1
        theta2 = theta2[::-1]

if __name__ == \"__main__\":
    main()

Result

Sample Output

Animation (for n_theta = 20)

Explanation:

An animation has been created to display a 2R robotic arm simulation. A parallel version of the code has also been created since the graph can be evaluated at any time step using the formula, the process can be parallelized.