From all this we see that the three closed pairs represent the three typical cases of the most general form of relative motion described in 12 and 13; viz. (reversing their order), simple sliding or translation, simple rotation, and simple sliding combined with simple rotation proportional to the sliding.
This is one of the characteristics of the closed pairs. Another very notable one we have already noticed, but without enlarging
Fig. 44.
Fig. 45.
Fig. 46.
upon it. It is this, that the exchange of the fixed element with the movable one causes no alteration in the resulting absolute motion. The equality of the axoids proves this generally. It is however extremely important, and for the purposes of machine construction extraordinarily valuable. The exchange of one element of a pair with the other, or, as we can say, the exchange, in respect to its fixedness or movability, of an element with its partner, we shall call the inversion of the pair: the inver- sion of closed pairs causes no alteration in the motion belonging to them.
Continual use is made of this principle in machine construction. Where, for example, a screw with a head (Fig. 44 a) is employed
