e e and//' pass left and right of 0, covering it with unlike fields as before. The moment of the pressure in the direction of the normal has here, however, a much smaller arm than in the former case, on which account it is employed only where the effort tending to cause turning is small.
Large heavy water-wheels are frequently secured upon the shaft with three, or more often with four keys, a space being left be- tween the solid and hollow cylindric surfaces, which are therefore altogether dispensed with for restraining purposes (Figs. 83 and 84). Such fastenings can offer obviously but small resistance to turning forces, as the normals to the faces of the key pass so very near to the centre 0. On this account such modes of keying the shaft are employed rather as methods of centering, that is, as restraints against the cross sliding of the shaft in the wheel boss in the manner indicated in Figs. 57 and 60, and for this purpose they are correctly designed. Where, however, there is any considerable torsion to be resisted, as in the driving pinions of rolling mills,
Fig. 83.
Fig. 84.
such an arrangement as shown in Fig. 85 is used which serves
as a restraint both against sliding and tinning.
Theoretically, complete restraint might be effected by four of these keys only (as / g, b and c), or the arrangement of Fig. 80 might be used, where a, 6, and c are arranged as in Fig. 76, while d and e are added as in Fig. 60. But the arrangement shown in
Fig -85 is very much better, for the torsion is resisted at four
