Denavit–Hartenberg parameters

The Denavit -Hartenberg transformation (DH transformation) from the year 1955 is a mathematical method based on homogeneous matrices and the so-called Denavit -Hartenberg convention ( DH- convention ) that the transfer of local coordinate systems ( OKS ) within the kinematic chains describes. It facilitates so primarily to calculate the direct kinematics ( forward kinematics ) and is here now than the standard methods, particularly in the area of ​​robotics.

DH- convention

The following requirements are necessary:

For the first joint, the axis is taken from the second joint.

DH transformation

The actual DH transformation from object coordinate system ( OKS ) in the OKS is the sequential execution of the following individual transformations:

• Of rotation ( joint angle ) around the axis so that the axis is parallel to the axis

• A translation ( joint spacing ) along the - axis to the point where cutting and

• A translation ( Armelementlänge ) along the axis to bring the origins of the coordinate systems in the cover

• Of rotation ( twisting ) about the axis to transfer the axis in the axis

In matrix notation, the total transformation is then ( to be interpreted from left to right):

The inverse of this matrix

Describes the transformation of a point on the OKS OKS. Accordingly, the original matrix can be interpreted as the transformation of a point on the OKS OKS when the position vector of the point is multiplied from the right in the matrix.

The parameters and are thereby also called the Denavit -Hartenberg parameters.

Are for open kinematic chains and variable sizes during the movement of the robot, depending on the specific geometry and dimensions. With a rotary joint is variant and constant, conversely, a sliding joint. and on the other hand, both in rotation, as well as shear joints invariant variables and must be determined only once for each arm member of the subsequent calculation of direct kinematics.