Denavit-Hartenberg parameters

Four parameters for each link transform#

A DH table describes the geometry of a kinematic chain after assigning coordinate frames to its links. In the standard convention, the four parameters are:

• Joint angle, theta: rotation about the preceding frame's z-axis.
• Link offset, d: translation along that z-axis.
• Link length, a: translation along the new frame's x-axis, the common normal between the joint axes.
• Link twist, alpha: rotation about that x-axis to align the successive z-axes.

For a revolute joint, theta is the joint variable. For a prismatic joint, d is the variable. The Robotics Toolbox documentation gives the corresponding link transforms for both types.

Standard and modified conventions#

Standard DH multiplies the z rotation and translation before the x translation and rotation. The modified convention documented by the Toolbox places the preceding link's x operations before the current joint's z operations. Frame placement and parameter indexing therefore differ.

A table is incomplete without its convention, frame definitions, joint zero offsets, and units. Copying values between conventions without converting the frames can produce incorrect forward kinematics.

Geometry, not a dynamics model#

Multiplying the link transforms gives an end-effector pose. The DH parameters alone do not describe link masses, inertias, friction, or motor limits; the Toolbox stores those as separate model properties.