Page:The Kinematics of Machinery.djvu/121

 concern ourselves about the shape of the restraining- figure B (Fig. 52); we require only to draw a tangent T T to the re- strained figure A at a, and erect upon this through a the normal NN'; the direction from A towards a and N' is then that in. which the point of restraint renders sliding impossible (Fig. 53).

No sliding therefore which has a component in this direction can occur. The only motions, however, which have not such components are those whose directions are included in the angle TNT', as indicated by the arrows. This straight-angle may be called the field of sliding for a figure restrained only at a, and having the normal N'a to the tangent T T' as the direction of restraint. All the directions in which motion is prevented by the restraining point fall within the second straight-angle TN' T,

. f.2.

. 53.

this we may therefore call the field of restraint for the point a. The fields of sliding and restraint for any point of restraint contain together four right angles. They are sepa- rated at the point of restraint by the tangent T T; but as the essential difference between them is a question only of angle or direction, this line of separation may take different positions, such as it' or ^ t' v so long as it remains parallel to T T '. In general we may therefore say that any normal to the direction of restraint is a division line between the fields of sliding and restraint.

Two Points of Kestraint. If a figure have two restraining points, a and b, Fig. 54, these limit the possible directions of sliding to the angle enclosed between the two tangents a T and IT, be- cause all directions falling outside this angle, as those marked