Fig. 2186.
Thus in [Fig. 2185] d b e represents the bottom of the moulding and line of motion of the cutter, and a b the cutter perpendicular to it, the highest point of the cutting edge, as c of [Fig. 2184], being at c, [Fig. 2185]. The height or thickness of the moulding cut would be the space between the lines e b d and e c f, but the cutter assuming the position b c at an angle of 30° from a b, the point c is brought to d; consequently the highest line of the moulding would now be g d h, and its thickness less. This is further exhibited in [Fig. 2186], where a represents the original depth section of [Fig. 2184] that would be formed by knife b of [Fig. 2184] when standing perpendicular; and g shows the depth with the same knife when placed as b c, [Fig. 2185], or at 30° inclination, and h shows the depth that would be cut with the same knife or cutter at 45°. It is now evident that every change in the inclination of the same cutter would effect a change in the shape of moulding which it cuts, and to produce a given style of moulding the shape of the cutter must be decided by its inclination, or the angle at which it is used.
Fig. 2187.
The method of projecting a given section of moulding in order to exhibit the form that the curve of the opening should assume on the face of the knife, is shown in [Fig. 2187]. Upon a horizontal line a b c d draw a section of the required style of moulding, as shown at a e b. To the right of this draw a line, as f c, to meet the base line a b c d, and as f c represents the cutter, it must stand at the same angle that the proposed cutter is to have—in this particular example 30° from the perpendicular. From the highest point of the section a e b draw a horizontal line e g, meeting f c in g. From points g and c draw lines, as c j and g h, of any convenient length, at right angles to f c. At any distance from g h draw k l parallel to g h, and upon k l trace the section of moulding a e b, as k m l. Draw lines from the extreme edges k and l of k m l, as k n, l j, perpendicular to k l, cutting g h and meeting c j at n and j. e g being parallel to a b c d, g will be the point on the cutter where the top e of the moulding will come on the highest point of the cutting edge, and c g will be the entire length of cutting edge or height of opening measured on the face of the cutter f c. c j being drawn from the lowest point c of the cutter and g h being drawn from g, the highest cutting point, both lines at right angles to g c, then their distance from each other, as p o, must obviously represent the extreme height of opening in the cutter in its new position or front view, and k l, representing the width of moulding transferred to n j by the parallel lines k n and l j, will show the width of opening in the cutter. Having now the height and width, it only remains to project an indefinite number of points and trace the curve through them. Divide a b into a number of parts, and to avoid confusion mark the points of division thus obtained upon a b—1, 2, 3, 4, &c. Divide k l in an exactly similar manner and into the same number of parts, and mark the divisions i., ii., iii., iv., &c. Erect perpendiculars from points 1, 2, 3, 4, &c., meeting the curve a e b, and from the points thus found on a e b draw horizontal lines to f c; from the termini of these horizontals on f c draw the remaining lines parallel to and between g h and c j. From the divisions i., ii., iii., iv., &c., on k l, let drop the perpendiculars, cutting the other series of lines at right angles. A point of the curve will then be at the intersection of the line from 1 on a b, with line i on k l; another at the intersection of the line originating at 2 with that from ii, and so on, and the proper curve is found by tracing from n through the intersections to p, and from p to j. Then k n being one side of the cutter and l j the other, n p j is the curve that the opening or cutting edges must have to cut the profile a e b, with the cutter set at f c, or 30°.
Fig. 2188.