Page:The Kinematics of Machinery.djvu/125

 complete restraint are fulfilled, shows. Indeed, the investigation already made points this out, although in another way, for the second figure B, Fig. 52, which carries the point of restraint for the first, A, must be open or hollow if the first have an external profile (such as we have shown), while the action of the figures as to restraint is reciprocal, just as we have found to be the case with the elements from which pairs are formed.

§19. Restraint against Turning.

Here also we shall consider first the case of plane motions of a plane figure, and shall understand by " turning " such a motion of the figure that some one point connected with it retains continuously or for an instant its position relatively to the plane. Two kinds of turning must be distinguished, that which takes place in the same direc- tion as the hands of a watch we call right-handed (R. If.), and that occurring in the opposite direction left-handed (L. H.), turning.

Single Point of Kestraint. If the figure A, Fig. 62, have a single point of restraint a, at which T T and N N' are again tangent and normal, a right-handed turning may be given to it about any point in the quadrants N a T and TaN',

while left-handed turning cannot occur about any of these points, because the motion of the point a in these cases would always have a component in the direction of restraint. L. H. turning is possible, and R. H. impossible, about every point in the re- 'maining quadrants N'aT' and T'aN. The turnings possible from points upon both sides of the normal N N' are indicated in the figure by the letters rand I. The whole field NT N'T' is thus a field of turning, and is divided by the normal N N' into fields of right- and left- handed turning. The normal

52.