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A MANUAL OF MACHINERY AND MILLWORK.

INTRODUCTION

ART. 1. Nature and Use of Machinery in General.-The use of machinery is to transmit and modify motion and force. The parts of which it consists may be distinguished into two principal divisions,— the Mechanism, or moving parts; and the Frame, being the structure which supports the pieces of the mechanism, and to a certain extent determines the nature of their motions. In the action of a machine the following three things take place:-First, Some natural source of energy communicates motion and force to a part of the mechanism called the Prime Mover; Secondly, The motion and force are transmitted from the prime mover through the train of mechanism to the working piece; and during that transmission the motion and force are modified in amount and in direction, so as to be rendered suitable for the purpose to which they are to be applied; and, Thirdly, The working piece, by means of its motion, or of its motion and force combined, accomplishes some useful purpose.

2. Distinction between the Geometry and the Dynamics of Machinery.—The modification of motion in machinery depends on the figures and arrangement of the moving pieces, and the way in which they are connected with the frame and with each other; and almost all questions respecting it can be solved by the application of geometrical principles alone. The modification of force depends on the modification of motion; and those two phenomena always take place together; but in solving questions relating to the modification of force, the principles of dynamics have to be applied in addition to those of geometry. Hence, in treating of the art of designing machinery, arises a division into two departments, the "Geometry of Machinery," or "Science of Pure Mechanism” (to use a term introduced by Professor Willis), which shows how the figure, arrangement, and mode of connection of the pieces of a machine are to be adapted to the modification of motion which they are to

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produce; and the "Dynamics of Machinery," which shows what modifications of force accompany given modifications of motion, and what modifications of motion are required in order to produce given modifications of force.

3. Strength of Machinery.—In order that a machine may be fit for use, every part, both of the machinery and of the framework, must be capable of bearing the utmost straining action which can be exerted upon it during the working of the machine, without any risk of being broken or overstrained; and the dimensions required for that purpose are to be determined by the proper application of the principles of the strength of materials.

4. The Art of the Construction of Machinery Consists of three departments, the selecting and obtaining of suitable materials for the parts of the mechanism and framework; the shaping of those parts to the proper figures and dimensions by means of suitable tools; and the fitting-up of the machine, by putting its parts together.

5. Division of the Subject. For the reasons explained in the preceding Articles, the subjects of this work are treated of under four principal heads,-Geometry of Machinery, or Pure Mechanism; Dynamics of Machinery; Materials, Construction, and Strength of Machinery.

PART I.

GEOMETRY OF MACHINERY.

CHAPTER I.

ELEMENTARY RULES IN DESCRIPTIVE GEOMETRY.

SECTION I.-General Explanations-Projection of Points and Lines.

6. Descriptive Geometry is the art of representing solid figures upon a plane surface. In the present chapter are given some general elementary rules in that art, whose application is of very frequent occurrence in designing mechanism. The more special and complex rules will be given in the ensuing chapters, in treating of the particular kinds of mechanism to which those rules belong.*

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7. By the Projection of a Point upon a given plane is meant the foot of a perpendicular let fall from the point on the plane. For example, in fig. 1, X Z ZX represents a plane (called a plane of projection), A a point, and A B a perpendicular let fall from the point on the plane; the foot, B, of that perpendicular is the projection of the point A on the plane X Z Z X.

8. The Position of a Point is completely deter

Fig. 1.

mined when its projections upon two planes not parallel to each other are known. In descriptive geometry a pair of planes of projection at right angles to each other are used; and in general one of these is vertical and the other horizontal. Thus, in fig. 1,

*For complete information on the subject of descriptive geometry, reference may be made to the works of Monge and Hachette in French, and of Dr. Woolley in English.

XZ ZX is the vertical plane of projection, and X Y Y X the horizontal plane of projection; B is the vertical projection, and C the horizontal projection of the point A; and those two projections tompletely determine the position of the point A; for no other point can have the same pair of projections.

9. The Axis of Projection is the line X X, in which the two planes of projection cut each other.

10. Rabatment.-When the two projections of an object are shown in one drawing, it is convenient to represent to the mind that the following process has been performed:-Suppose that the vertical plane of projection is hinged to the horizontal plane at the axis X X, and that after the projection of the object on the vertical plane has been made, that plane is turned about that axis until it lies flat in the position X zz X, so as to be continuous with the horizontal plane: thus bringing down the projection B to b. This process is called the rabatment of the vertical plane upon the horizontal plane (to use a term borrowed from the French "rabattement" by Dr. Woolley). The two points C and b are in one straight line perpendicular to X X. The process of rabatment may be conceived also to be performed upon a plane in any position when a figure contained in that plane is shown in its true dimensions on one of the planes of projection.

11. Projections of Lines. The projection of a line is a line containing the projections of all the points of the projected line. The projection of a straight line perpendicular to the plane of projection is a point; for example, the projection on the vertical plane, X Z Z X (fig. 1), of the straight line A B, perpendicular to that plane, is the point B. The projection of a straight line in any other position relatively to the plane of projection is a straight line. If the projected line is parallel to the plane of projection, its projection is parallel and equal to the projected line itself; thus the projection on the horizontal plane, X Y Y X, of the horizontal straight line A B, is the parallel and equal line C D. If the projected line is oblique to the plane of projection, the projection is shorter than the original line.

The projections, on the same plane, of parallel and equal straight lines are parallel and equal. The projections, on the same plane, of parallel lines bearing given proportions to each other are parallel lines bearing the same proportions to each other. When the plane of a plane curved line is perpendicular to a plane of projection, the projection of the curve on this plane is a straight line, being the intersection of the plane of the curve with the plane of projection. When the plane of the projected curve is parallel to a plane of projection, the projection of the curve on this plane is similar and equal to the original curve. In all other cases, it follows from the preservation of the proportions of a set of parallel

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