## CHAPTER III.

PAIRS OF ELEMENTS.

### §14.

Different Forms of Pairs of Elements.

We have already found, in the general solution of the machine problem (p. 35 et seq.), that the elementary or what may be called the elementary parts of a machine are not single, but occur always in pairs, so that the machine, from a kinematic point of view, must be divided rather into pairs of elements than into single elements. It is the geometrical form of these pairs with which we must first of all make ourselves acquainted.

We shall in the first instance limit our investigations to rigid bodies, that is, to such as possess approximately complete rigidity; the problem before us in the construction of pairs of elements will then be the determination of a given or required motion by means of two such bodies or elements only. As we have found in the last chapter, these elements must satisfy the following conditions::

1. That one element be fixed relatively to the surrounding portion of space, itself assumed to be stationary.;

2. That this element be so formed as to carry upon or within itself the envelope of the second and moving element, which