I'm going through a robotics textbook Introduction to Robotics Mechanics and Control 3rd edition by John J. Craig and am currently on a section describing the relationships between links of some robotic manipulator.
The text contains a figure shown below that has two axes and a link connecting them. There are two numbers that relates the location of the two axes in space - the distance between them written as a, and the link twist alpha.
The text claims "For any two axes in 3-space, there exists a well defined measure of distance between them (a as written above). This distance is measured along a line that is mutually perpendicular to both axes. The mutual perpendicular always exists; it is unique except when both axes are parallel."
But I'm pretty sure a mutual perpendicular won't always exist. Won't a mutual perpendicular only exist if the two axes are parallel in the plane that cuts through both of them? If the two axes will intersect at some point, there shouldn't be a line that is perpendicular to both axes at any point. Is my reasoning incorrect?