Simulation of forward kinematics of a 2R Robotic Arm using Python

Aim: To write a program in python to simulate the forward kinematics of a 2R Robotic Arm.

Theory:

• The robotic arm consists of two links with lengths L1 & L2
• Xo, Yo is the starting point of link 1 which is attached to the base with an angle theta1
• Link2 starts from the ending point of link1 at a point X1, Y1 therefore

X1 = L1*cos(theta1)

Y1 = L2*sin(theta1)

• X2, Y2 is the endpoint of link2 which is at an angle theta2 with link1

X2 = X1+L1*cos(theta2)

Y2 =Y1+ L2*sin(theta2)

The flow of the project:

1.Code to simulate the forward kinematics of a 2R Robotic Arm.

2.Code explanation

3.Results

1.Code to simulate the forward kinematics of a 2R Robotic Arm.

import matplotlib.pyplot as plt

import numpy as np

import math

#inputs

L1 = 5

L2 = 3

x0 = 0

y0 = 0

A = np.linspace(0,math.pi/2,10)

B= np.linspace(0,math.pi/2,10)

ct = 1

for theta_1 in A:

x1 = L1*math.cos(theta_1)

y1 = L1*math.sin(theta_1)

for theta_2 in B:

x2 = x1+L2*math.cos(theta_2)

y2 = y1+L2*math.sin(theta_2)

file_name = str(ct)+'.png'

plt.figure(ct)

plt.plot([x0,x1],[y0,y1])

plt.plot([x1,x2],[y1,y2])

plt.xlim([0,10])

plt.ylim([0,6])

plt.savefig(file_name)

ct = ct+1

2.Code explanation

• Initially, we should import the libraries that are required to run the program.
• The input parameters such as L1 & L2 and Xo & Yo are considered.
• We will consider theta values in the form of an array using the “np.Linspace” command.
• By using the for loop for each value from the array we can calculate the points X1, Y1, and X2, Y2.
• By using the plt.plot command we can plot the links L1 & L2 using these points.
• At this point, we will get individual plots for each value of theta_1 and theta_2.
• I have converted all this plot into GIF using Imagick fie.

3.Results