The half-round surfaces or gaps here mentioned are such as those belonging to bearer-brasses, concave junctions of crossheads, levers, and bars; also the gaps of U-end connecting-rods, termed gap-end rods, or rods with semi-solid heads. A great number of these curved surfaces are formed by turning, and are consequently treated in the chapter devoted to that subject. But it is sometimes needful to produce half-round gaps by means of shapers and slotters which possess worm-pinions for generating curved motions ; and the paring-processes connected with such motions are here given.

The shaping of curved concave junctions belonging to levers, bars, and crossheads, is frequently executed by means of broad-edge tools, as described in pages 278, 279, and 282, without using the rotary motion of the table by means of the worm-wheel. Such shaping is suitable when only one or two objects are in progress; but whenever a number require to be shaped, the circular motion should be employed. This process involves several additional shiftings and adjustments of each object; but this very circumstance facilitates each adjustment, when several levers or other articles are moved about, because the operators become thereby accustomed to the work.

Perhaps the simplest of the concave surfaces now mentioned, are those belonging to half-round gaps of bearer-brasses ; consequently the shaping of these are first treated. The hidden curve which is to be produced on a bearer-brass is indicated by two curved lines, one on each end of the brass, denoting the boundaries of the intended surface. A brass lined in this manner is shown by Fig. 803, in which one of the two semicircular lines is seen on the front side of the Figure. If the two gauge-lines are of the proper curve, and in their proper places, they correctly show the boundaries of the required surface, according to page 243; and they also serve as lines by which the brass can be adjusted on a machine-table for shaping.

A brass may have its gap formed either on a shaping-machine, or on a slotting-machine, if the machine selected is furnished with the apparatus for generating the necessary curved movement. When a shaper is employed, the brass is held on the table so that the intended gap in the brass is parallel with the table, and, consequently, parallel with the direction of the cutting-tool's motion. The article is adjusted to this position by applying a scriber-block point to both the curved lines, while the block is on the table; and also by fixing a tool-scriber in the tool-holder and observing the scriber-point and the straight gauge-line which is marked on the upper surface or face of the brass. This line is put parallel with the motion of the head, and therefore parallel with the tool's motion, by gradually shifting the brass sideways until the tool-scriber's point moving slowly to and fro, is seen to be exactly parallel with the line. Packing-plates and wedges are also required beneath the brass, to raise either end to a suitable height and cause the bottom of the gap to be produced parallel with the gauge-lines. Poppets also are needed for shifting it sideways.

A bearer-brass may be fixed also by bolting it to an el-chuck on the shaping-table. For this purpose a half-round gap is provided at the upper edge of the chuck, and the brass is put in front of it, so that the gap to be formed in the brass is about midway between the sides of the gap in the chuck. A chuck of this description is shown by Fig. 885. A brass which is to be held against an el-chuck, must have at least one plane surface for contact with the chuck, which surface should also be square to the length of the gap to be formed ; this will cause the brass to be immediately put parallel with the tool's motion by the act of bolting to the chuck, the face of which is placed square to the tool's motion by means of one of the parallel gauge-lines on the table. But if the surface of the brass touching the chuck is not square to the length of the intended gap, the chuck's face must be adjusted square to the gap without regard to any line on the table, in order that the straight gauge-lines on the top of the brass may be properly situated.

As soon as the brass is fixed, the cutting-tool is fixed to the rest in a vertical position; and the brass and tool are next adjusted to each other by placing the centre of the tool-point exactly over the centre of the gap to be made in the brass. To ascertain whether the proper position is obtained, the tool-point is moved in a curved path by rotating the worm-pinion with the handle. For such movement, the point is put very near to the semicircular line to which the metal is to be pared off, or is put very near to another line which is concentric with it; and if, during the rotary movement, the point is seen to be concentric with the half-round gauge-line, the adjustment is effected. The tool can, therefore, be now made to cut by means of the to-and-fro motion combined with the curved motion imparted from the worm-pinion. A convenient tool to remove the metal is an ordinary grooving-tool. A taper tool having a vee-point may also be used, if it has a thin end, which is necessary to prevent the thick part of the tool coming into contact during the time the tool is cutting at the gap-sides. While the tool is at the bottom ample room exists, at which place the operation of cutting is somewhat like planing.

While the tool moves to and fro, its curved motion can be generated by the operator rotating the worm-pinion with the handle on its spindle, which process is suitable for a small gap. But this hand-traverse is avoided by causing the machine itself to rotate the spindle. This is performed by a small rod and lever connected to the machine-carriage and the worm-spindle.

It is not every to-and-fro shaper that will thus shape a half-round gap, because the tool cannot be advanced through the entire semicircle at one travel. Consequently, when such a gap must be formed with a machine whose sector-motion is too short, the gap is shaped by fixing the brass twice instead of only once, half of the gap being shaped at each fixing. The entire gap may also be shaped at only one fixing, if cranked tools are employed ; in which case the tools are shifted instead of the brass.