Fig. 233.
It is obvious also that the lines s, z, drawn from the extremes of the face to be projected will define the width of the ellipse, hence we have four of the points (marked respectively 1, 2, 3, 4) in the ellipse. To obtain the remaining points, lines t, u, v, w, x, y (which start from the point on the face F where the lines m, n, o, p, q, r, respectively meet it) are drawn across the face of B as shown. The compasses are then set to the radius g; that is, from centre line D to division a on the circle, and this radius is transferred to the face to be projected the compass-point being rested at the intersection of centre line G and line t, and two arcs as 5 and 6 drawn, giving two more points in the curve of the ellipse. The compasses are then set to the length of line h (that is, from centre line D to point of division b), and this distance is transferred, setting the compasses on centre line G where it is intersected by line u, and arcs 7, 8 are marked, giving two more points in the ellipse. In like manner points 9 and 10 are obtained from the length of line i, 11 and 12 from that of j; points 13 and 14 from the length of k, and 15 and 16 from l, and the ellipse may be drawn in from these points.
It may be pointed out, however, that since points 5 and 6 are the same distance from G that points 15 and 16 are, and since points 7 and 8 are the same distance from G that points 13 and 14 are, while points 9 and 10 are the same distance from G that 11 and 12 are, the lines, j, k, l are unnecessary, since l and g are of equal length, as are also h and k and i and j. In Figure 232 the cylinders are line shaded to make them show plainer to the eye, and but three lines (a, b, c) are used to get the radius wherefrom to mark the arcs where the points in the ellipse shall fall; thus, radius a gives points 1, 2, 3 and 4; radius b gives points 5, 6, 7 and 8, and radius c gives 9, 10, 11 and 12, the extreme diameter being obtained from lines S, Z, and H, H.
CHAPTER XI.
DRAWING GEAR WHEELS.
The names given to the various lines of a tooth on a gear-wheel are as follows:
In Figure 233, A is the face and B the flank of a tooth, while C is the point, and D the root of the tooth; E is the height or depth, and F the breadth. P P is the pitch circle, and the space between the two teeth, as H, is termed a space.