ABSTRACT
Denavit-Hartenberg in 1955 developed a notation for assigning orthonormal coordinate frames to a pair of adjacent links in an open kinematic chain. The procedure involves finding the link coordinates and using them to find the 4×4 homogeneous transformation matrix composed of four separate submatricies to perform transformations from one coordinate frame to its adjacent coordinate frame. D-H notation is valuable to the area of robotics in which robot manipulators can be modeled as links of rigid bodies. Most industrial robot manipulators are open loop kinematic chains consisting of a base, joints, links, and an endeffector. The ability to control a robot endeffector in three-dimensional space requires the knowledge of a relationship between the robot’s joints and the position and orientation of the endeffector. The relationship requires the use and an understanding of the rotation matrix and the translation vector.
Figure 8.1 shows a schematic of two orthonormal reference frames; one is the fixed (inertial) frame and the other is the moving (noninertial) frame. The fixed reference frame comprising the triad of unit vectors (−→e1 , −→e2 , −→e3 ) has the origin at point O . The moving frame comprising the triad of unit vectors (−→e1 ′, −→e2 ′, −→e3 ′) has the origin at point O ′. The rotation matrix transforms coordinates from one reference frame to another. Since most robotic manipulators have individual joint reference frames, which are displaced by a finite distance and rotation, it is necessary to develop a uniform methodology for deriving the transformation from one reference frame to the next. The D-H parameters for a robot manipulator help to systematically derive the transformation from one joint to the next. As a result, it is possible to derive the transformation from the robot endeffector to the base coordinate frame of the robot arm.
