Page:The Kinematics of Machinery.djvu/123

. 56.

point of restraint, as c Fig. 56, to the two already examined, is

easily found. We draw the tangent c U and the normal through

c, and also the line R separating the fields of sliding and restraint,

placing the latter so as to pass through the intersection

of the two first normals. It is then evident from the figure that

sliding is no longer possible through

the whole angle P Q, hut that the

field of sliding is diminished to

the angle FOR. Here we see at

once that we have the means of

entirely preventing the sliding of

a figure hy the use of three points

of restraint. Tor as the field of

restraint of each single point covers

180, nothing more is necessary than

to place the third so that its field

of restraint covers the sliding field

of the other two. Fig. 57 represents

this case. The third point c is so

placed that its field of restraint, extending to R 0, entirely covers

the field of sliding P Q (shown Ly dotted lines) left by the other

points a and b. The condition for the attainment of this end is

that the three points of restraint be so placed that the angle

between two consecutive nor- mals should always be less than 180. Figs. 58 and 59 represent separately the relative directions of the normals at the points of restraint in Figs. 56 and 57 re- spectively, and we see from them that in the first case the angles between the normals 1 & 2 and 2 & 3 are each less than 180, but that between 3 and 1 is greater; while in the

second case each of the three corresponding angles is less than

two right angles.

In the case in which the two first directions of restraint are

parallel and opposite, Fig. 60, the third point c is not sufficient to