I have already read a couple of threads on this forum regarding the calculation of forward (direct) kinematics using DH parameters on real examples of KUKA robots.
Most theory books use DH parameters extensively for calculating forward kinematics. I have found an example of DH parameters for KUKA KR500 robot. The datasheet is given here
The table with DH parameters together with joint coordinate frames is given in the attachment.
The direct kinematics is calculated as matrices multiplications (one for each joint) and the result matrix 4x4 matrix, let say denoted M. The last column of this transformation matrix is always in form: X,Y,Z,1. This means that element m41 is the X coordinate of the last coordinate frame in reference to the base coordinate frame, m42 is Y coordinate etc.
Submatrix 3x3 with elements m11, m12, m13, m21,m22,m23,m31,m32,m33) is a rotation part of the transformation matrix M.
So my question is the following:
How to make a connection from the result of direct kinematics and actual position and orientation in KUKA robot language, which is given by X,Y,Z, A,B,C?
It should be: m41 = X, m42 = Y, m43 = Z, and I wonder how to correlate A, B, C with 9 elements of a 3x3 rotation submatrix of matrix M?
I hope you understand my question.
Thank you very much!