This paper formally documents a method that enables the scaling of displacements, elements of the group of rigid body motions, in all their six degrees of freedom individually in linear manner. In particular, the method incorporates a suitable modulation method for the rotational part of a displacement. This simple, yet non-trivial function has not been reported in the literature as of today. The rotation scaling relies on the representation of a rotation in terms of its angle and its axis as given via Euler’s rotation theorem. It is argued that the overall workspace scaling falls in the class of ‘regularized linear functions’ in the tangent space.