Denavit-Hartenberg Kinematics

Robotics Engineering

How It Works

The Denavit-Hartenberg (D-H) convention establishes a standardized mathematical procedure for attaching coordinate reference frames to interconnected links in spatial robotic manipulators. Four geometric parameters—link length a_i, link twist α_i, joint offset d_i, and joint angle θ_i—uniquely construct the 4×4 homogeneous transformation matrix between adjacent link frames. Chaining successive transformation matrices evaluates the complete forward kinematics pose of the tool end-effector in Cartesian space.

Governing Equation
^(i-1)T_i = Rot_z(θ_i) Trans_z(d_i) Trans_x(a_i) Rot_x(α_i) , ^0T_n = ∏_{i=1}^n {^(i-1)T_i}