Denavit-Hartenberg Parameters

A commonly used convention for selecting frames of reference in robotics applications is the Denavit and Hartenberg (D-H) convention which was introduced by Jaques Denavit and Richard S. Hartenberg. In this convention, each homogeneous transformation is represented as a product of four basic transformations. The common normal between two lines was the main geometric concept that allowed Denavit and Hartenberg to find a minimal representation. The transformation is described by the following four parameters known as D-H Parameters: [Spong, M., M. Vidyasagar, ”Robot Dynamics and Control”, John Wiley and Sons, 1989, ISBN 047161243X]
* $a,$: length
* $alpha,$: twist
* $d,$: offset
* $heta,$: angle

Since only four parameters are used, the frames that can be represented this way has to satisfy two more constraints

# the $x\_n$-axis is perpendicular to the $z\_\{n\; -\; 1\}$ axis
# the $x\_n$-axis intersects $z\_\{n\; -\; 1\}$ axis

Every link/joint pair can be described as a coordinate transformation from the previous coordinate system to the next coordinate system.

: $\{\}^\{n\; -\; 1\}T\_n\; =\; operatorname\{Rot\}\_\{z\_\{n\; -\; 1(\; heta\_n)\; cdot\; operatorname\{Trans\}\_\{z\_\{n\; -\; 1(d\_n)\; cdot\; operatorname\{Trans\}\_\{x\_n\}(a\_n)\; cdot\; operatorname\{Rot\}\_\{x\_n\}(alpha\_n)$

Note that these are 2 screws after oneanother. See Screw (motion).

The matrices mentioned above are as follows:

:

:

:

:

This gives:

:

References