Program to simulate the forward kinematics of a 2R Robotic Arm

Objective:

1. To write a program to simulate the forward kinematics of a 2R Robotic Arm
2. To create an animation file of the plot

Program:

'''Program for 2R Robotic arm simulator.
there are two links of length, l1 and l2 respectively.
theta_1 and theta_2 are the angles made by these links with the horizontal at different instances.
the base point of link_1 is [x0, y0], link_2 is [x1, y1] and the position of the manipulator is [x2, y2]
x1 = l1 * cos(theta_1)
y1 = l1 * sin(theta_1)
similarly,
x2 = x1 + l2 * cos(theta_2)
y2 = y1 + l2 * sin(theta_2)
we need to create a program to animate the positions of the two arms when theta_1 and theta_2 value lies between 0 to 90 degree.
'''
import math
import matplotlib.pyplot as plt
import numpy as np

l1 = 1
l2 = 1
x0 = 0
y0 = 0
theta_start = 0
theta_end = math.pi/2
n_theta = 10
theta_1 = []
theta_2 = []

for i in range(0,n_theta):
    theta_tmp = theta_start + (i * (theta_end - theta_start)/(n_theta - 1))
    theta_1.append(theta_tmp)
    theta_2 = theta_1

print(theta_1)
print(theta_2)
count = 1
for t1 in theta_1:
    for t2 in theta_2:
        x1 = l1 * math.cos(t1)
        y1 = l1 * math.sin(t1)
        x2 = x1 + l2 * math.cos(t2)
        y2 = y1 + l2 * math.sin(t2)

        filename = '%05d.png' % count # %05d is used so that the images are arranged in the same order when called in cmd
        count = count +1

        plt.figure()
        plt.plot([x0,x1],[y0,y1])
        plt.plot([x1,x2],[y1,y2])
        plt.xlim([-1,3])
        plt.ylim([-1,3])
        plt.savefig(filename)

#for converting to gif, go to the folder in which the images are saved using cmd and then use 'magick *.png name.gif' command to combine all the images in the folder and create a gif.

Explanation:

1. Imported the necessary modules
2. Defined the variables.
3. Used a for loop for creating the list of theta values ranging from 0 to 90 degrees (theta_1 and theta_2 both)
4. Used a for loop to get the values of (x1,y1) and (x2,y2) for every theta_1 and theta_2 in the range(0 to 90 degrees)
5. Used the values of x1, x2, and y1, y2 to plot the robotic arm position at different instances.
6. Saved all the plots in a folder and combined them together in the correct sequence using ImageMagick for creating a gif file showing the motion of the two links of the robotic arm.

Output:

1. The output is the animation of the motion of the robotic arm for theta varying from 0 to 90 degrees.