For a more detailed description of Denavit-Hartenberg notation see Craig, J. J., 1989, Introduction to Robotics: Mechanisms and Control, Addison Wesley, New York.
The first step in calibrating a manipulator is to understand its nominal kinematic parameters, and the controller's ability to accept new, calibrated values for these parameters. This section will describe how to represent a robot's kinematics. Most manipulators are serial devices, meaning they are composed of a series of links and joints connected in an open chain. Denavit-Hartenberg notation is a standard means for specifying the kinematics of a manipulator. See the example table below, then a brief description of the meaning of the parameters.
Links are rigid members; joints allow relative motion between the links. The chain starts at the base, or ground link, and ends at the working tool. Except for the tool link and the base, each individual link in the chain begins and ends with a joint. The tool may be a grip per, paint sprayer, welding tip, electro-magnet or any of a wide variety of devices. Common manipulators use only revolute (turning) or a prismatic (sliding) joints to connect links. More complicated forms of joints can always be modeled as a combination of these simple elements. The function of a link is merely to fix the relationship be tween the joints at either end of the link. As long as the two joints are held at the same relative position and orientation with respect to one another, the link serves only as a rigid connector. The actual physical shape of the link can be changed without altering the kinematic relationship between the two interconnected joints.
A kinematic description of the manipulator is generated by SpatialAnalyzer using the standard Denavit-Hartenberg notation. This remark ably simple representation uses only two values to describe each link, and two additional values to describe the joint connection between adjacent links. Links are described in terms of their length (a) and the twist they maintain between adjacent joints (a), as explained below.
Twist Angle (a). The angle between the first and second joint axes on a link. This angle is measured in a right-hand sense when viewed directly along the common normal.
Link Length (a). The distance between the two joint axes of a link. This distance must be measured along a line that is normal (i.e. perpendicular) to both joint axes. This line is referred to as the common normal between the joint axes. If the joint axes intersect (a common arrangement in industrial manipulators), the link will have zero length. The joint connection between adjacent links is described in terms of the offset (d) and the joint angle (8), as explained below.
Offset (d). The distance between the common normal of one link and the common normal of the next, measured along the axis of the joint connecting the two links.
Joint Angle (8). The angle between the common normal of one link and the common normal of the next, measured about the axis of the joint connecting the two links.
The four parameters a, a, d, and 8, when taken for each link and joint in the chain, provide a complete kinematic description of the manipulator. When taken together with a description of the physical shape of each link and limits on joint motion, an accurate simulation of ro bot motion and operating workspace can be developed.
In addition, there is usually a JointOffsetvalue computed during the calibration. This value represents the difference between the "kinematic zero" of a joint, and the mechanical zero based on how the encoder was set in the joint mechanism.
For a more detailed description of Denavit-Hartenberg notation see:
Craig, J. J., 1989, Introduction to Robotics: Mechanisms and Control, Addison Wesley, New York