  The theory of screws clarifies many analogies between apparently unrelated
notions in mechanics, including the duality between forces and angular
velocities. It is known that the real 6-dimensional space of screws can be
endowed with an operator E, E^2 = 0, that converts it into a rank 3 free module
over the dual numbers. In this paper we prove the converse, namely, given a
rank 3 free module over the dual numbers, endowed with orientation and a
suitable scalar product (D-module geometry), we show that it is possible to
define, in a canonical way, a Euclidean space so that each element of the
module is represented by a screw vector field over it. The new approach has the
effectiveness of motor calculus while being independent of any reduction point.
It gives insights into the transference principle by showing that affine space
geometry is basically vector space geometry over the dual numbers. The main
results of screw theory are then recovered by using this point of view.
