Figs. 748.

Sawing Rectangular Pieces Part 4 200190

749.

Sawing Rectangular Pieces Part 4 200191

Irregular polygons have frequently the angles alike, hut the sides dissimilar; thus it may be considered that in a, fig. 740, a parallel piece is added between the halves of the regular hexagon, whereas in b, a piece is abstracted, and in c, two of the sides disappear. These and the entire group, a to y, fig. 749, may be sawn with the bed B, fig. 748, of 60 degrees.

It is most convenient, especially when many pieces are wanted, to prepare for a, a rectangular prism, and then to cut off the four dotted triangles at four cuts, leaving the stop s, in the same position throughout; b may be treated in the same manner as a, or else as in c, the two exterior cuts may be made on the edge of a wide piece of board, and then two interior cuts remove the rhombus c, and leave a hollow angle of 120 degrees, as explained by the dotted lines.

The several inverted angles of the piece g, may be also produced in this manner by two cuts each; two of the cuts in g, are however made on the horizontal table, and not the inclined bed, B. The inverted angles are convenient as troughs, to support prismatic pieces on their angles, instead of their surfaces.

Pieces analogous to those, a to g, may be cut on beds of any other angles; but when the prismatic pieces have dissimilar angles, unless they are complementary one to the other, separate inclined beds are generally required for every angle.*

10. Sawing geometrical solids and irregular pieces, or those in which the angular variations, are in both the horizontal and vertical planes. - It is proposed to illustrate this part of the subject, by some remarks on the formation of various solids illustrative of geometry, and crystallography; such as erect and oblique prisms, pyramids, double pyramids, the five regular solids or platonic bodies, (namely, 1st, the tetrahedron, 2nd, the hexahedron, 3rd, the octahedron, 4th, the dodecahedron, 5th, the icosahedron,) and some other polyhedra. And, although in the formation of the models of these solids, various modes are employed, those methods will be selected, in which all, or nearly all the work, may be performed by the saw machine alone, independently of the various other means.

• It will be shown in the succeeding section that, in some cases, prismatic works are mounted upon an axis, placed at various angles by a dividing plate, and then applied to the saw. And in the subsequent volumes, it will be likewise explained that most lathes for ornamental turning, possess very ready means of producing, both in wood and metal, an infinite variety of polygonal and polyhedral works, with great precision and smoothness.

The models above referred to, are generally made in sycamore, maple, or horse chesnut, and in the majority of cases, the wood is prepared as prisms, the sawing of which has been fully described. Sometimes, before the subsequent processes, the prisms are very carefully planed in angular beds, mostly so arranged, that the surface to be planed is horizontal.

A long prismatic rod, carried to the saw at right angles, is readily cut into short erect prisms of various heights; and the same prisms, carried obliquely to the saw, become oblique prisms.

For pyramids of 3 to 12 sides, long prisms should be first prepared also of 3 to 12 sides, the sections of which are exactly equal to the bases of the required pyramids.

The prisms are usually cut into short pieces equal to the vertical height of the pyramids, and one guide-block suffices for making all pyramids the sides of which meet at the same angle. The ordinary guide or gage-block, is simply a piece of wood having at the end a rectangular and perpendicular notch B C D, fig. 755, which may be made at the saw machine by aid of the protractor. For pyramids, the sides of which meet at 60 degrees, as in fig. 750, the side B C, of the notch in fig. 755, measures 30 degrees with the principal edge A B, of the guide; for pyramids of 40, 50, or 70, the angle of the guide is respectively 20, 25, and 35 degrees, or half the angles at which the sides meet.

The side A B, of the guide is placed in contact with the parallel rule, and the short prism is placed in the nook, so that in every case the base of the prism rests against the face C D, and one of its sides, whatsoever their number, touches the vertical face B C; the parallel rule is then adjusted to direct the saw s s, through the dotted line proceeding from the apex to the base of the pyramid. One cut having been made, the guide and work are quickly withdrawn, the waste piece removed by the saw, is thrown away, and the block is shifted round until the succeeding face of the prism, (or so much of it as remains,) touches the face B C, and so on to the last face of the pyramid.

Sometimes, as in fig. 751, a pyramid is cut at each end of a prism, the method is almost the same; but the wood and guides are each longer, as in fig. 756. The square end of the prism is placed against the stop, rod the first pyramid having been cut, the piece is changed end for end, and the process is repeated; in cutting the second pyramid, the point of the first touches the stop, or a notch may be made in the stop to prevent the extreme point of the prism from being bruised.

When the pyramids meet base to base, as in fig. 752, other methods are pursued, dependent on the parallelism of the opposite sides or angles of equal pyramids. Sometimes the prism is cut off to the exact length of the double pyramid; and the first pyramid bating been cut as shown in fig. 756, the second pyramid is produced as is fig. 753, by laying the sides of the first pyramid against the parallel rule, and placing a wedge beneath the point of the first pyramid, to support the axis of the piece horizontally.

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