Denavit–Hartenberg, Completely: Building and Solving a 6-Axis Robot Arm

Build the DH table for a six-axis arm from its geometry, turn each row into a matrix, multiply through to the tool, and then run it backwards. The closed-form inverse kinematics is shown step by step: wrist centre, law of cosines, the wrist rotation, the eight solutions.

Then the places it breaks: the classic–modified mix-up, parallel axes, singularities, and calibrating the table against a real arm with a laser tracker.

In this video

• Frame assignment rules and the common normal
• Measuring d, θ, a, α on a real arm
• The 4×4 matrices and their closed form
• Forward kinematics to the tool, live
• Inverse kinematics in closed form, eight solutions
• Singularities and calibration