Page:The Kinematics of Machinery.djvu/112

 the solid is generated, and we have as the result a closed pair consisting of two solids of revolution, of which the profiles are such as to prevent all motion in the direction of the axis. Fig. 40 is an illustration of such a pair, in which the nut has become an eye (shown in section); the only motion which is possible for it being rotation.

If we now suppose the pitch-angle to increase instead of diminishing, the screw becomes steeper and steeper. If we make the angle = 90, the screw lines become parallel to the axis.

. 40.

. 41.

the screw becomes a prism, and the nut a corresponding hollow prism. The normal profile of the screw thread is now at right angles to the axis, and so is transformed into the normal section of a prism, which always retains a profile preventing cross- motions, that is, a non-circular profile. As a result we have a closed pair consisting of two prisms having such profiles as to prevent any turning about their axes (Fig. 41). The single possible motion of the open prism is here sliding in the direction of the edges of the full one.

Further alteration of the pitch-angle gives no new result if we make it > 90 the screw passes from right to left-handed; it remains, however, always a screw; and we have found it unneces- sary to make any distinction between a right and left-handed thread. The problem of the closed pair has thus been ex- hausted by our investigation. It will be well to consider the