Page:The Kinematics of Machinery.djvu/129

 been so placed that its normal passed through the left-handed field a b ', the case would have been reversed, and a triangle would have been left about points in which L. H. turning only could have occurred.

It will now be easily seen how the turning can be still further limited. For this purpose it is only necessary to diminish the size of the triangle P Q. This becomes a minimum, that is, a single point, if c be so placed (Fig. 71) that its nor- mal passes through the in- tersection Oof the two first normals. The turning is then reduced as far as it can be, but it still remains pos- sible about one point.

. 71.

If the two first points of

restraint have parallel normals we obtain other and entirely different results.

If the parallel normals to a and b have opposite directions (Fig 72), the normal to any point c between them divides the field of turning into two parts, of which one remains a field of turning, being covered by a pair of similar fields, while the other,

. 72.

. 73.

which is covered by dissimilar fields, becomes a field of restraint. If the field of turning of the first two points be a line only, (the normals, coinciding, Fig. 73), about points in which, as we saw above by Fig. 66, both right- and left-handed turning may take place, the normal to c divides the line at P into two parts, about points in one of which, Pa, right-handed turning, and in the oth er, P b, 1 e f t - h a n d e d turning, is possible.