The purpose of this revision has been to make more clear those points that have been the most difficult for the students. The definitions and rules have been italicized as it has been our experience that the student in going over the text for the first time is at a loss to know just what are the most important points.

Very little new subject matter has been added as it is felt that the size of the text is all that can be covered in the time usually allotted to this subject, and it has been the writer's experience that it is better to cover the entire text than to omit certain parts in order to complete the course.

The number of problems has been doubled and most of the illustrations for those problems suitable for drafting room practice have been enlarged to make them more clear than they were in the first edition.

Experience has shown us that the class and drafting room work can be more closely coordinated if the time allowed for the course be made one recitation and three two-hour drafting periods per week, using the third drafting period for a lecture or second recitation when necessary to keep ahead of the drafting room work.

The writer wishes to express his appreciation for the very helpful assistance of his former colleague Professor P. H. Hyland of the Department of Machine Design, University of Wisconsin, for his suggestions as to changes, preparation of drawings, and assistance in reading proof.

The writer's aim has been to cover the subject of mechanism as briefly, simply and clearly as possible. The text is designed for a half year's work of one lecture, one recitation and four hours drafting work per week.

No especial claim to originality of subject matter can be made, nor has the writer found need for a special effort in this direction. The arrangement and method of treatment are new, and these the author bases upon satisfactory results obtained in the work of his classes in the College of Engineering of the University of Wisconsin.

After a brief discussion of motions and velocities, linkages are taken up, as they are comparatively easy for the student to understand, and simple problems can be given out while the subject is yet new to him.

Cams are taken up in detail, as they form a part of the subject in which the student needs considerable practice in order to work out original problems, and practically all cam problems are original.

The involute system of gearing is taken up before the cycloidal system, because it seems to the writer easier for the student to grasp. Having once become familiar with the involute system, the student can more readily understand the cycloidal. Further-more, the involute system is in more general use at the present time.

Problems are given at the end of each chapter. Some of these are designed especially for drafting-room work, and the necessary instructions as to scale, position of drawing on the sheet, method of procedure and time, etc., are given. These few problems are not intended to exhaust the subject, but rather to serve as a guide for instructors in giving the drafting-room work in connection with the recitations.

Quotations have been made from the various authorities, and credit given where the quotations appear. The writer wishes to express his thanks to the several authors from whom he has made quotations, the manufacturing companies who have furnished cuts and to all others who have aided in the preparation of the manuscript.

The science of Mechanism treats of the design and construction of machinery.

“A machine is a combination of resistant bodies so arranged that by their means the mechanical forces of nature can be compelled to produce some effect or work accompanied by certain determinate Motions” Reuleaux. In general it may be said that a machine is an assemblage of fixed and moving parts interposed between the source of power and the work for the purpose of adapting one to the other.

1. Design of a Machine. - In the design of a machine there are three distinct parts to be considered:

First, - The general outline is sketched without any regard to the detailed proportions of the individual parts, and from this sketch or skeleton, by means of pure geometry alone, the displacement, velocity, and acceleration of each of the moving parts can usually be accurately determined.

Second, - The forces acting on each part must be determined, and each part given its proper form and dimensions to withstand these forces.

Third, - Having designed the machine, the dynamical effects of the moving parts can be accurately determined.

The first part belongs to the subject known as the Kinematics of Machines, the second to the Design of Machine Parts, and the third to the Dynamics of Machines.

This course will treat only of the first part dealing with the motions of the machine parts, and the manner of supporting and guiding them without regard to their strength. This is some- times called Pure Mechanism or the Geometry of Machinery.

Since Mechanism is a study of relative motion it will be well to discuss the different kinds of motion.

2. Motion. - Motion is a change of position. The change of position can be noted only with respect to the position of some other body which is at rest, or assumed to be at rest, or with respect to somebody, the motion of which is known or assumed to be known. That is, the motion is purely a relative one.

Two bodies may be at rest relatively to each other but in motion relatively to a third body, as for example, two car wheels fastened to the same axle have no motion with respect to each other, but may be in motion relatively to the truck or track.

In problems dealing with machinery the motions of the various parts are usually taken with reference to the frame of the machine. This is not always the case, however, as sometimes it is easier to compare the motion of one part of a machine directly with that of some other moving part, as for example the number of revolutions that the cylinder of a printing press makes to each revolution of the knife for cutting off the sheets.

3. Forms of Motion. In order to be of any use in machine construction, the motions must be completely controlled or constrained. Most of the motions used are, or can be reduced to one of three forms, plane, helical and spherical.

4. Plane Motion. Plane motion is the most common as well as being the most simple. In order to have plane motion all points in a plane section of the body must remain in that plane and all points outside that section will move in parallel planes.

In Fig. 1, if the lower face abed of a cube is kept in contact with a flat table top, all points in the lower face will move in a plane, and all points similarly located in any other plane section will move in parallel planes, no matter what path the cube describes in moving from one position to another.

Thus if we know the motions of two points in a body that has plane motion, the motions of other points in the body are also known. Plane motion is always found as rotation or translation, or a motion that can be reduced to a combination of rotation and translation.

5. Rotation. In rotation all points in the body move in circles, that is, they remain at a fixed distance from a right line called the axis of rotation. For example, shafts, pulleys, fly-wheels, etc., have a motion of rotation.

6. Translation. Translation may be divided into two classes, Rectilinear Translation and Curvilinear Translation. A body has rectilinear translation when all points in it move in straight lines, as the carriage of a lathe, piston of an engine, or spindle of a drill press.

The crank pin of a locomotive driving wheel is an example of curvilinear translation. It moves in a circle around the center of the wheel and at the same time moves along the track.

7. Helical Motion. The path traced by a point moving at a fixed distance from an axis and with a uniform motion along the axis is a helix, and a point moving in such a path is said to have helical motion.

Perhaps the most common example of helical motion is that of a screw being turned into a nut. All points in the screw, except those in the axis, have helical motion. Both limits of helical motion are plane motion, that is, if the pitch of the screw is zero the resulting motion is rotation, while if the pitch is infinity, the motion will be that of translation.

8. Spherical Motion. Spherical motion may be defined as the motion of a body moving so that every point in it remains at a constant distance from a center of motion, but does not remain in a plane.

9. Path. A point in changing from one position to another traces a line called its path. The path may be of any form. The path traced by any point on a pulley revolving on its shaft is a circle, but a path need not be continuous, as for example the path traced by a rifle bullet.

In general, the motion of a body is determined by the paths of three of its points not in a right line. If the motion is in a plane, two points are sufficient, and if rectilinear, one point determines the motion.

10. Velocity. In addition to knowing the path and direction of a moving body, there is another element necessary to completely determine its position, and that is its velocity. Heretofore we have not considered the time necessary for a body to complete a certain motion.

Velocity is measured by the relation between the space passed over and the time occupied in traversing that distance. It is expressed numerically by the number of units of distance passed over in one unit of time, as miles per hour, feet per minute, inches per second, etc. It is the rate of motion of a point in space.


CHAPTER II - INSTANTANEOUS CENTERS, KINEMATIC CHAINS.

16. Mechanisms. A mechanism or train of mechanism is the term applied to a portion of a machine where two or more parts are combined so that the motion of the first compels the motion of the others according to a law depending on the nature of the combination. The two parts connected together are known as an elementary combination, so that a train of mechanism consists of a series of elementary combinations.

If a part is considered separately from the others it is at liberty to move in the two opposite directions and with any velocity, as the crosshead of an engine that is not connected to the connecting rod.

Wheels, shafts and rotating parts generally are so connected with the frame of the machine that any given point is compelled when in motion, to describe a circle around the axis, and in a plane perpendicular to it. Sliding parts are compelled by fixed guides to describe straight lines, other parts to move so that points in them describe more complicated paths and so on.

These parts are connected in successive order in various ways so that when the first part in the series is moved, it compels the second to move, which again gives motion to the third, etc. The various laws of motion of the different parts of a train are affected by the mode of connection.

17. Modes of Connection. Connection between the different parts of a machine may be made in any of the following ways:

1. By direct contact
a. Turning pairs - connected links.
b. Slide connector - crosshead.
c. Cams without rollers.
d. Friction contact - friction cylinders.
e. Rolling and sliding contact - toothed gears.

2. By intermediate connectors
a. Cams with rollers.
b. Rigid links.
c. Flexible connectors ropes, belts and chains.

3. Without material connectors
a. Electricity and magnetism.
b. Gravity.
c. Centrifugal force governor.

The first two methods are perhaps the most important in this subject, and will be discussed later on.

18. Instantaneous Motion. When a body changes its position its motion at any instant may be said to be its instantaneous motion.