The right lines in a moving body

01. I began to explain in chapter 3 the importance of and the ubiquitous nature of that special kind of line in a moving body which I called there, for the want of a better name, right line. There and in other places the n-line and the contact normal are also mentioned (§ 3.01, § 3.05, § 3.06) and a distinction made between a line which is obliged by virtue of some constraint to be a right line in a body as soon as the body moves and other lines in the body which may or may not be right lines according to how the body moves. Because I am speaking here in chapter 9 about the kinematics of a body, I am speaking about the motional (not the actional) right lines within the body; the distinction between the two is explained at § 3.43.

02. In any event it is taken for granted here that the reader is aware of the practical significance of the right line in the kinematics of mechanism. The objective of this chapter is not to study the significance of right lines but to plot the overall distribution of them in a moving body or in a body which has the capacity to move with one degree of freedom only (§ 3.24). We are trying to discover, not only where the right lines in a body are, but also how many of them there are.