Page:The Kinematics of Machinery.djvu/152

 on opposite sides are at the same distance apart. The circle gives us a familiar example of this. If on any figure having this property we place two pairs of the restraining tangents supposed, they touch it in four points and completely restrain it as was shown in 18 from sliding. This restraint, however, does not prevent the turning of the figure, and this turning may be so arranged that it can take place about one point only. That this may be the case the normals to the four points of restraint must intersect in that point the opposite normals, that is to say, must coincide, as in Fig. 100, where the normal on a passes through c t and that on I through d.

. 99.

. 100.

Then, the breadth of the figure being constant, the restraint is un- interrupted or continuous for all alterations of its position within the four tangents, from which it follows (see 21) that the normals always intersect in one point. This shows that figures of constant breadth have the property that on any radius there lies not only the centre of curvature of the element of the circumference to which that radius belongs, but also the centre of curvature for the opposite element. The four tangents enclose a square, or more generally a rhombus, as ABGD. The foregoing shows also that every figure of constant breadth can be constrained in such a rhombus, so that from it and the rhombus a pair of elements may be formed.