  Numerical methods for Inverse Kinematics (IK) employ iterative, linear
approximations of the IK until the end-effector is brought from its initial
pose to the desired final pose. These methods require the computation of the
Jacobian of the Forward Kinematics (FK) and its inverse in the linear
approximation of the IK. Despite all the successful implementations reported in
the literature, Jacobian-based IK methods can still fail to preserve certain
useful properties if an improper matrix inverse, e.g. Moore-Penrose (MP), is
employed for incommensurate robotic systems. In this paper, we propose a
systematic, robust and accurate numerical solution for the IK problem using the
Mixed (MX) Generalized Inverse (GI) applied to any type of Jacobians (e.g.,
analytical, numerical or geometric) derived for any commensurate and
incommensurate robot. This approach is robust to whether the system is
under-determined (less than 6 DoF) or over-determined (more than 6 DoF). We
investigate six robotics manipulators with various Degrees of Freedom (DoF) to
demonstrate that commonly used GI's fail to guarantee the same system behaviors
when the units are varied for incommensurate robotics manipulators. In
addition, we evaluate the proposed methodology as a global IK solver and
compare against well-known IK methods for redundant manipulators. Based on the
experimental results, we conclude that the right choice of GI is crucial in
preserving certain properties of the system (i.e. unit-consistency).
