I am trying to solve inverse kinematics (using the Jacobian pseudoinverse method) for a 7 DoF arm, but because of the way the robot is mounted, the base frame does not coincide with the frame of the first joint, so there is a transformation between base and frame 0. As the Jacobian expresses the joint-end effector velocity relationship w.r.t. the base frame, and also because my target poses etc. are expressed w.r.t the base frame, I encoded the transformation as an extra row in my DH parameters, but these angles are always fixed. Hence, I ended up with 8 rows in my DH although I have only 7 joints.
Because of this, my inverse kinematics algorithm, when trying to minimize the end effector pose error, continuously attempts to change the angle of the "first" joint which really isn't a joint at all. Hence, although the algorithm thinks the end effector has reached the target position, in real world it would not, because that base-robot transformation would be invalid for my setup. If I force this angle to be constant after every update of the iteration, the algorithm fails to converge and gets stuck at some pose. So I am guessing my approach for encoding the fixed base-first joint transformation is wrong? How are these transformations usually dealt with?