Page:The Kinematics of Machinery.djvu/122

. 54.

3 or 4, must have a component parallel to one or other of the

directions of restraint 1 and 2. If the division line between

the fields of sliding and of restraint for each of the points a and I

be drawn through the intersec- tion of their normals, the shaded angle P Q enclosed be- tween them is the field of slid- ing, and the exterior angle Q OP the field of restraint, for the case before us. Both points of support would equally prevent sliding in any direction falling within the opposite angle to POQ.

By reducing the angle a T b between the tangents the field of sliding is made smaller and smaller. When they become parallel, as in Fig. 55, the angle

covered by the field becomes infinitely small. But just as sliding

could take place before along the lines of separation P and Q,

it can still occur along those lines now that they have become

coincident, that is, it can take place in

a direction parallel to the two tangents.

Motion is possible, therefore, not only

along P, but also along R, the

arms of the now infinitely small

opposite angle. In other words, the

field of sliding is now reduced simply

to a line parallel to the tangents, and along this sliding can take place in both directions.

If the parallel directions of restraint 1 and 2 had not been opposite, as here shown, but in the same direction, the resulting restraint, so far as sliding is concerned, would not have differed from that given by a single point, so that it is not a case which need be further considered.

. 55.

Three Points of Restraint. The result of adding a third