[Fig. 1214] shows the manner in which the lathe centres and the work centres have contact, l being the live and b the dead centre; hence c c is the axis of the live spindle which is parallel to the lathe shear slides, which are represented by g; obviously a is the work axis. The wear is greatest at the dead centre end of the work, but there is some wear at the live centre end, because there is at that end also a certain amount of motion of the work centre upon the live centre. Thus, in [Fig. 1215], let c represent the live centre axis, a the work axis, d the lathe face plate, and e f the plane of the driver or dog upon the work, and it is obvious that the tail of the driver will when at one part of the lathe revolution stand at e, while when diametrically opposite it will stand at f; hence, during each work revolution the driver moves, first towards and then away from the face plate d, and care must be taken in adjusting the position of the driver to see that it has liberty to move in this direction, for if obstructed in its motion it will spring or bend the work.
Fig. 1216.
Fig. 1217.
To determine how much the tailstock of a lathe must be set over to turn a given taper, the construction shown in [Fig. 1216] may be employed. Draw the outline of the work and mark its axis d, draw line c parallel to one side of the taper end, and the distance a between this line and the work axis is the amount the tailstock requires to be set over. This construction is proved in [Fig. 1217], in which the piece of work is shown set over, c representing the line of the lathe ways, with which the side f of the taper must be parallel. d is the line of the live spindle, and e that of the work, and the distance b will be found the same as distance a in [Fig. 1216].
It may be remarked, however, that in setting the tailstock over it is the point of the dead centre when set adjusted to the work length that must be measured, and not the tailblock itself.
Other methods of setting tailstocks for taper turning are as follows: If a new piece is to be made from an old one, or a duplicate of a piece of work is to be turned, the one already turned, or the old piece as the case may be, may be put in the lathe and we may put a tool in the tool post and set the tailstock over until the tool traversed along the work (the latter remaining stationary) will touch the taper surface from end to end.