Base Coordinate Transformation
x_0 = 0, \quad y_0 = 0
Joint 1 (Shoulder) Position
x_1 = L_1 \cos(\theta_1), \quad y_1 = L_1 \sin(\theta_1)
Joint 2 (Elbow) Position
x_2 = x_1 + L_2 \cos(\theta_1 + \theta_2), \quad y_2 = y_1 + L_2 \sin(\theta_1 + \theta_2)
End Effector Tool Tip Position
x_e = x_2 + L_3 \cos(\theta_1 + \theta_2 + \theta_3), \quad y_e = y_2 + L_3 \sin(\theta_1 + \theta_2 + \theta_3)
Planar forward kinematics calculates workspace positions using direct trigonometric projections.
Angles are relative, representing coordinate rotation accumulated from base link reference frames.
Singular configurations occur when the arm is fully extended or folded back, reducing active degrees of freedom.