In this treatise, several relationships are improved for the axodes of one-parameter
spatial movements. Results are devised in some theorems which characterize many kinematical and
geometrical properties of the movements employing the geometrical data of the stationary and movable
axodes. An example illustrates the application of the formulae derived. Our findings contribute
to a greater understanding of the similarities between spatial movements and axodes, with possible
applications in fields such as mechanical engineering.