This lesson introduces the Denavit–Hartenberg (DH) convention and explains how it organizes coordinate frames along a robot’s links. Consistent frames make it possible to describe a manipulator’s pose using a sequence of transformations.
A robot manipulator is a chain of links connected by joints. To calculate the position and orientation of its end link, we need to describe how each link is positioned relative to the previous one. Many frame conventions are possible, but using a consistent convention makes those calculations systematic.
All flashcards
What is the purpose of the DH convention?
It provides a standard way to assign coordinate frames to robot links and express transformations between neighboring frames.
What does the joint axis represent?
It is the line about which a revolute joint rotates or along which a prismatic joint slides.
How are the classic DH z-axes assigned?
Each z-axis is placed along the corresponding joint axis.
What is a common normal?
A line perpendicular to two consecutive joint axes; it gives a natural direction for the x-axis and measures their separation.
How is the y-axis chosen in a DH frame?
It is chosen so the x, y, and z axes form a right-handed coordinate system.
Quiz questions
In a classic DH homogeneous transformation matrix, what does the upper-left 3×3 block represent?Answer: The relative orientation of the two frames.
Frames i and k are connected through frame j. How is Mi,k composed from the two neighboring transforms?Answer: Multiply Mi,j by Mj,k in that order.
For a rigid transform M=[R0T1], what is the translation column of M−1?Answer: −RTT
In a common modified DH transform, which pair of axis operations comes first?Answer: Twist rotation and link translation about or along the preceding x-axis.
Which statement describes transformation order in general?Answer: Changing the order of operations about different axes can change the resulting transform.