This lesson covers forward and inverse kinematics for robotic manipulators.

Forward Kinematics

Given joint angles \(\theta_1, \theta_2\), the end-effector position of a 2R planar robot is:

\(x = l_1\cos\theta_1 + l_2\cos(\theta_1+\theta_2)\) \(y = l_1\sin\theta_1 + l_2\sin(\theta_1+\theta_2)\)

Try it live:

🔬 Interactive: Robot Arm Simulator

θ₁ = 0°

θ₂ = 0°

End-effector:
x = 0.00
y = 0.00

Coding FK

Run the FK calculation yourself:

🐍 Python Sandbox

import numpy as np # 2R planar robot forward kinematics L = [1.0, 0.8] # link lengths theta = [45, -30] # joint angles in degrees theta_r = np.radians(theta) x = L[0]*np.cos(theta_r[0]) + L[1]*np.cos(theta_r[0]+theta_r[1]) y = L[0]*np.sin(theta_r[0]) + L[1]*np.sin(theta_r[0]+theta_r[1]) print(f"End-effector: x={x:.3f}, y={y:.3f}")

NumPy available.