Denavit-Hartenberg (DH) Parameters

A convention for modeling an arm where just four numbers per joint describe the transform between neighboring link frames.

DH parameters are a convention introduced by Jacques Denavit and Richard Hartenberg in a 1955 paper in the Journal of Applied Mechanics: following a fixed rule, each link gets its own coordinate frame, and the transform between neighboring frames then needs only 4 numbers — the offset d along the previous z-axis, the rotation angle θ about the previous z-axis, the length a of the common perpendicular between the two joint axes (the link length), and the twist angle α about that common perpendicular. For a revolute joint, θ is the joint variable and the other three are fixed constants. Multiplying each joint's 4×4 homogeneous transformation matrix together in sequence gives the forward kinematics from base to end effector. Richard Paul extended the convention to robotics broadly in 1981. The “modified DH” convention used in John Craig's textbook places the frames and orders the transforms differently, so the two parameter tables are not interchangeable.

ExampleUniversal Robots' official standard DH parameters for the UR5e: joint 1 has d = 0.1625 m and α = π/2; joints 2 and 3 have a = −0.425 m and −0.3922 m (the upper-arm and forearm lengths); joints 4–6 have d = 0.1333, 0.0997, and 0.0996 m. Plugging these into the formula computes the end-effector pose from the 6 joint angles.

Also called

DH Parameters, Standard DH, DH Convention

Related

Modified Denavit-Hartenberg Parameters · Forward Kinematics (FK) · Homogeneous Transformation Matrix · Product of Exponentials Formula · Unified Robot Description Format · Link

Sources

Denavit–Hartenberg parameters - Wikipedia
DH Parameters for calculations of kinematics and dynamics - Universal Robots