A Mathematical Introduction to Robotic Manipulation

Textbook:

• A Mathematical Introduction to Robotic Manipulation, Richard M. Murray, Zexiang Li, S. Shankar Sastry
  • In short as RM in the following description.

Note:

***** Chapter 2 Rigid Body Motion *****

***** Chapter 3 Manipulator Kinematics *****

• Denavit-Hartenberg Parameters
  • While it is possible to carry out all the analysis using an arbitrary frame, a commonly used frame of reference in robotic applications is the Denavit-Hartenberg or D-H convention.
  • Wikipedia: The Denavit–Hartenberg parameters (also called DH parameters) are the four parameters associated with a particular convention for attaching reference frames to the links of a spatial kinematic chain, or robot manipulator.
  • DH1: The axis x1 is perpendicular to the axis z0.
  • DH2: The axis x1 intersects with the axis z0.
  • The following four transformation parameters are known as D–H parameters:.^[4]
    • : offset along previous  to the common normal
    • : angle about previous , from old  to new 
    • : length of the common normal (aka , but if using this notation, do not confuse with ). Assuming a revolute joint, this is the radius about previous .
    • : angle about common normal, from old  axis to new  axis
  • In summary, the reference frames are laid out as follows:
    1. the -axis is in the direction of the joint axis
    2. the -axis is parallel to the common normal: 
       If there is no unique common normal (parallel  axes), then  (below) is a free parameter. The direction of  is from  to , as shown in the video below.
    3. the -axis follows from the - and -axis by choosing it to be a right-handed coordinate system.

Reference: