Kinematics

Denavit–Hartenberg parameters

The Denavit–Hartenberg parameters are a tidy, agreed-upon bookkeeping system for describing the shape of a robot arm joint by joint. The trouble with a many-jointed arm is that you could measure and label its geometry in countless inconsistent ways. The DH convention solves this by saying: for each link, attach a coordinate frame (a little set of reference axes) following one fixed set of rules, and then the relationship between one frame and the next can always be captured by just four numbers. Those four — usually called link length, link twist, link offset, and joint angle — are the DH parameters, and one such row of four describes each joint in turn.

Why bother with only four numbers per joint? Because it makes the whole arm describable by a small, standardized table that any robotics tool can read the same way, and it makes computing forward kinematics almost mechanical: each row turns directly into one transform, and multiplying them down the table gives the end-effector's pose. It is like agreeing on a single standard form for an address — house number, street, city, country — so that anyone, anywhere, can locate the place without confusion. The convention dates back to 1955 and remains one of the first things taught in robot kinematics, though some modern software prefers other equivalent descriptions.

A six-joint industrial arm is fully described by a six-row table, each row holding its four DH numbers; software reads the table and immediately knows the arm's exact geometry.

Four numbers per joint, one row per joint — a whole arm in one small table.

Two slightly different conventions exist ("standard" and "modified" DH); they encode the same arm but order the four steps differently, so a table must say which one it uses.

Also called
DH parametersDH conventionDH 参数DH 表示法