Fig. 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
