In these notes an attempt is made, first, to give, as clearly and concisely as possible, the principles of mechanical motion in such a manner that their application can readily be made to any mechanism for determining the motion of any of its parts; then to show the methods of dealing with such problems as the designer meets daily. Long and tedious discussions have been avoided as far as possible, it is hoped, fully.

Subjects such as toothed gearing and couplings are taken up only to the extent of the forms that are in the most common use. But with these subjects, as well as all others, references to what are believed to be the best works in their lines are given frequently.

All available works on the subject have been freely consulted, but in no case has any matter which has not become common property by its frequent publication been used without the consent of its author.

The exceedingly clear and concise work of Prof. Albert W. Smith, of Stanford University, entitled "Machine Design," has been of most valuable assistance throughout. This work includes both kinematics and mechanics. To Prof. Smith, especially, the writer would acknowledge his obligations and express his thanks.

The matter presented on the following pages is confined to such subjects as the designer must deal with daily. Equations and formulas are put into such a form as to afford a ready means of application to problems under consideration. Numerical examples and data from practice illustrating principles are introduced wherever it seems that a clear understanding can be brought about in this way. The data thus presented have been gathered from numerous sources during the last fifteen years. That coming from modern practice is always given the preference, however, except where the older matter is undoubtedly the most valuable. Whenever possible, the results of practice or experiments as presented by some engineer or experimenter which fairly well represent the general experience along their lines are given in preference to abstract statements. This is believed to be the most satisfactory method, since it affords a means of studying all the facts incidental to the particular case, in addition to furnishing information fully as well as abstract statements.

The publications of engineering societies and engineering journals have been freely consulted. Much courtesy has been shown by the representatives of engineering and manufacturing concerns, who have invariably been kind in answering inquiries, and many of them have furnished valuable data. Whenever possible, credit for such information is given in connection with the information itself, but much of it was of such a nature as to make it impossible to separate it from general statements.

It is common practice in engineering to fasten together the edges of plates, angles, beams, etc., with rows of rivets. If the plates riveted together are to be used for the retaining-walls of a vessel to contain a fluid under pressure, the joint must be designed for tightness as well as strength. This means that the rivets must be put close enough together to prevent the plates from springing apart between the rivets to any considerable extent. In addition to placing the rivets near together it is generally necessary to calk the joints with a calking-tool, whose typical form is that shown in Fig. 141. This tool resembles a cold-chisel whose chipping edge has been ground off square. It is held in the position indicated in the figure and struck with a hammer to calk the edges of one plate down against the other.

If the joint is for vessels which are to hold solid material, or for the members of bridges and buildings, it is necessary to design it for strength only, there being no necessity for tightness.

In hand-riveting the rivet is heated to a full red heat and then passed through holes previously punched or drilled in the plates and brought into proper position to receive the rivet. The rivet is then held in place with a "dolly-bar" while the opposite end is first upset with hammers and then finished with a "set" or "snap." The "set" resembles a sledge-hammer with a depression cut in its face to conform with the kind of head that is desired, as button-head, cone-head, pan-head, etc. It is held against the rivet and struck with a sledge. Very small rivets are often put in place cold.

Machine-riveting is used much more in modern practice than hand-riveting. A machine-riveter has two dies, cupped to the form the rivet-head is to have, which press on the opposite ends of the Rivet-blank after it has been put in place. The body of the rivet is swelled out in the hole and the head formed by the heavy pressure that is exerted. The dies of riveting-machines are commonly operated by either steam, air, or hydraulic pressure. In hydraulic riveting one method is to press the rivet down so as to form the heads while it is still very hot, then relieve it from the pressure of the die for a short time until it has cooled somewhat, and then put it under pressure again until it has become cold enough to prevent its stretching materially under the tendency which the plates may have to spring apart. In steam and pneumatic riveting the rivet-head is first formed by a steady pressure of the die, then allowed to cool somewhat, after which it is struck a few sharp blows with the die driven out by the action of the steam or air against it in order to bring the plates together so that they will be gripped tightly when the rivet has cooled completely. For very heavy riveting the riveter sometimes has a pair of closing- or gripping-dies, called a "plate-closer," which are used for pressing the plates together and holding them until the rivet has cooled.

If the work is well done, the rivets should fill the holes completely. Since the rivet blank is always smaller in diameter than the hole it is to fill, this necessitates its being upset from end to end so that it may swell to the size of the hole. It has been found that this can be accomplished better by having the blank hottest at the head end, so that it will swell first under the head, gradually filling the hole from the head toward the point, and finally forming the second head.

When the holes are made by punching, they are larger at one end than the other, being roughly conical on account of the punch being smaller than the die on which the plate rests during the operation of punching. The plates should be placed so that the small ends of the holes come together. When so placed, the end contraction of the rivet tends to draw it more tightly against the conical walls, thus eliminating, in a measure at least, the loosening effect of the decrease in diameter due to cooling, and giving the rivet a better fit in the hole; the rivet also grips the sides of the holes and draws the plates together, thus relieving the heads of a portion of the strain. If, on the contrary, the large ends of the holes are placed together, the swelling of the rivet when under the dies tends to force the plates apart, and its contraction to loosen it in the hole; also the end contraction is resisted by the heads only.

Numerous styles of riveted joints are in common use. Some of the simpler ones will be shown in order to explain the nature of the stresses that act upon the plate and rivets. The seams most commonly used are of two general classes, namely, lap-joint and butt-joint. The names are derived from the manner in which the edges of the plates are placed relatively to each other. In the lap-joint the plates overlap each other, examples of this form of seam being shown in Figs. 142, 143, and 144; in the butt-joint the edges of the plates are butted against each other, and one or two cover plates, straps, or welts placed over their junction, the rivets passing through one plate and one side of the strap or straps, as shown in Figs. 146 and 147. Fig. 145 is a lap-joint with cover-plate.

The seams are further classified according to the number of rows of rivets that are used, and the positions of the rivets of one row relatively to those of the other rows. The rows of rivets run parallel to the length of the seams. Single-riveted joints are shown in Figs. 142, 146, and 147; in each of these joints the edges of the plates are pierced by bat a single row of rivets, although two rows are embodied in the seam in two of these three cases. Double riveting is shown in Figs. 143 and 144, the edges of the plates being pierced with two rows of rivets. The rivets are said to be staggered when those of one row are opposite the spaces of the adjacent row, as in Figs. 143 and 145; when they are opposite each other, as in Figs. 144, 146, and 147, the seam is chain-riveted.

The pitch of rivets is the distance between the centres of adjacent rivets in the same row.

The margin is the distance from the edge of the plate to the edge of the rivet-hole. (See w, Fig. 142.)

The overlap is the distance one plate laps over the other.

All the rows of a seam do not need to have the same pitch, as can be seen by reference to Fig. 145, where the pitch of the outer rows is double that of the middle one.

139. A single-riveted joint may yield in one of the five following ways when forces are applied as indicated by the arrows in Fig. 142:

1st. Shearing the rivets in the plane of the plate surfaces that are in contact.

2d. Crushing the rivets, or the plate in front of them, by the "bearing-pressure" of the rivets against the plate.

3d. Tearing the plate between the rivets.

4th. Splitting or tearing the plate between the rivet and the edge of the plate.

5th. Shearing out the plate in front of the rivet, the piece sheared out having a width approximately equal to the diameter of the rivet.

Double-riveted joints may fail by either the first or third method, or by crushing the rivets. Any other manner of failure would be a combination of two or more of the five methods given above. The failure of joints with several rows of rivets may be still more complicated.

The frictional resistance to the slipping of the plates over each other, due to their being clamped together by the end contraction of the rivets, is, in a carefully made hydraulic machine-riveted joint, generally from one third to one half of the total strength of the joint. A hand-riveted seam generally offers less frictional resistance to the slipping of the plates over each other than one which is machine-riveted. In designing riveted seams it is not customary to take this frictional resistance into consideration.

A rivet is in single shear when the shearing force acts only in one plane, as in a lap-joint, or a butt-joint with one cover-plate. It is in double shear when the tendency is to shear it off in two planes, as in the double-welt butt-joint, Fig. 147.

Table XLYI gives ultimate values that can be safely used in practice with good material. A suitable factor of safety must be introduced. The common practice in this country is to use steel plates with iron rivets for boiler construction. Steel plates with mild steel rivets are used to a considerable extent for other classes of work.