Page:The Kinematics of Machinery.djvu/101

 PQR relatively to A B C may be obtained by combining a simple translation and a simple rotation about an axis; and this in an endless number of ways. It is in no way essential that the translation should be parallel to the line joining the two positions of one of the points (as PP l above). Among the infinite number of possible methods just mentioned one is of special simplicity, that, namely, in which the translation takes place

parallel to the axis of rotation. Here the motion resolves itself into an endlong sliding upon and rotation about one and the same axis; and if in such a case the changes of position of P Q R in reference to A B C be taken indefinitely small, the instantaneous axes of rotation, along which also simultaneous sliding takes place, become infinitely near together.

§13. Twisting and Rolling of Ruled Surfaces.

Many attempts have been made to render easy the comprehen- sion of the kind of motion just described, but the task is far from