Some implications of a well-known idea

01. A widespread intuitive idea (and thus a useful definition of) the rigidity of a rigid body is as follows: having fixed any two points A and B in a moving body we argue that, if the body is rigid, the distance from A to B remains constant throughout a movement.

02. A number of important conclusions can be drawn from this fundamental statement. This chapter is devoted to drawing at least one of them, namely that, at any given instant in the motion of a rigid body, an axis with a pitch exists which is unique at the instant. The axis may be called the instantaneous screw axis for the body, or, more simply and often (§ 6.07), the screw in space about which the body is twisting (§ 5.50). Each of its aspects – orientation, location, and pitch – must be known before connections can be made between the so-called angular velocity of the body and the linear velocities of points such as A and B within it.

03. Because the points A and B in their line AB cannot move closer together or further apart, the component along the line of the velocity at B must be the same, at any instant, as the component along the line of the velocity at A. Applying this argument to other points along the line, we see that, for all points along a straight line in a rigid body, the velocity vectors at the points have equal components along the line. This is a general result. It holds for any line which may be drawn in a rigid body.