【机器人理论 Robotics】D-H表示法（The Denavit-Hartenberg Representation）【新加坡南洋理工大学 Nanyang Technological Univ.】

The Denavit-Hartenberg (D-H) Representation

Introduction

Denavit & Hartenberg, 1955. A systematic notation for assigning right-handed orthonormal coordinate frames to each link of the robot.

Transformations between adjacent coordinate frames can be represented by a single standard 4 * 4 homogeneous coordinate transformation matrix.

Notations

Lk: The frame associated with link k. Lk = {Xk, Yk, Zk}, where 0 <= k <= n.

Lk is attached to the distal end of link k. Last at tip of tool.

Algorithm: D-H Representation

Prerequisite: Number the joints from 1 to n, starting with the base, ending with the tool (1) yaw, (2) pitch, (3) roll. Assign L0 to robot base, with z0 aligning with the axis of joint 1. Set k = 1.

Iteration:

1. The zk axis aligns with the axis of joint k + 1.

2. The intersection of zk and zk-1 axes is selected as the origin of Lk.

3. Select xk to be orthogonal to both zk and zk-1. If zk and zk-1 are parallel, point xk away from zk-1.

4. Select yk to form a right-handed orthonormal coordinate frame Lk.

Follow-up:

(1). Set k = k + 1. If k < n, go to Step 1; else, continue.

(2). Set the origin of Ln at the tool tip. Align zn with the approach vector, yn with the sliding vector, and xn with the normal vector of the tool.

Kinematic parameters:

θk: The angle between xk-1 and xk axes about the zk-1 axis.

dk: The distance between xk-1 and xk axes along the zk-1 axis.

ak: The distance between zk-1 and zk axes along the xk axis.

αk: The angle between zk-1 and zk axes about the xk axis.

Example 1: Simple robot with 2 axes.

Example 2: 5-axis articulated robot Microbot Alpha II.