Kinematics Calculator

Denavit-Hartenberg (DH) 4x4 Matrix Generator

Interactive mathematical tool that takes standard DH link parameters and outputs the exact 4x4 transformation matrix and spatial rotation/translation components.

Denavit-Hartenberg (DH) 4x4 Transformation Matrix Generator

Link Length a_i (m)

Link Twist α_i (deg)

Link Offset d_i (m)

Joint Angle θ_i (deg)

Resulting 4x4 Homogeneous Transformation Matrix T_i:

0.7071-0.70710.00000.21210.70710.70710.00000.21210.00000.00001.00000.00000.00000.00000.00001.0000

Cyan columns = 3x3 Rotation SO(3)Green column = 3D Position [X, Y, Z]

Mathematical Formulation & Engineering Notes

T = Rot_z(θ) · Trans_z(d) · Trans_x(a) · Rot_x(α).