Page:The Kinematics of Machinery.djvu/461

 SCREWED JOINTS. 439

being the rigid connection of \ with c. We see at once that the screw b is prevented from turning relatively to the piece ^ by the prismatic form given- to its neck (cf. 19), so that as regards rota- tion b and \ form one piece. If the nut a be turned upon the screw, the head of the bolt is brought up to bear upon the piece b r This is brought about by the use of the pair ($), that is to say (as we before expressed it, 47), by pair-closure. Thus the relative turning of b and \ is prevented by suitable restraining profiles, and their relative sliding by pair-closure ; the two parts therefore form kinematically, a single piece.

So far as our engraving goes the piece c can turn relatively to b- In the machine itself, however, such a motion is prevented either by the use of a second screw parallel to the first, or by some other means, and the only motion possible to c before the nut is screwed down is translation in the direction of the axis of b. In other words c is paired with b \ by means of a prism parallel to the axis of b ; c and b l^ form therefore a sliding pair. In reality, therefore, the piece b ~b l contains two kinematic elements, rigidly connected, a screw S + and a prism P + parallel to the screw.

The nut a also consists of two kinematic elements, the hollow screw S~ and the plane cone which forms its under surface and rests upon, or more correctly is paired with, c. This surface is not necessarily plane, its general condition is that it must belong to a re volute con- axial with the screw. The pair of revolutes, or turning pair, thus formed by a and c is incomplete, and here pair-closed. This, how- ever, is accidental ; essentially the piece a consists of an element S~ having conaxial to it a revolute R, the partner element of which belongs to the piece c.