The main subject-matter of this work was written during 1885 by Peter Schwamb and has been used since then, in the form of printed notes, at the Massachusetts Institute of Technology, as a basis for instruction in mechanism, being followed by a study of the mechanism of machine tools and of cotton machinery. The notes were written because a suitable text-book could not be found which would enable the required instruction to be given in the time available. They have accomplished the desired result, and numerous inquiries have been received for copies from various institutions and individuals desiring to use them as text-books. This outside demand, coupled with a desire to revise the notes, making such changes and additions as experience has proved advisable, is the reason for publishing at this time.

Very little claim is made as to originality of the subject-matter which has been so fully covered by previous writers. Such available matter has been used as appeared best to accomplish the object desired. Claim for consideration rests largely on the manner of presenting the subject, which we have endeavored to make systematic, clear, and practical.

Among the works consulted and to which we are indebted for suggestions and illustrations are the following: "Kinematics of Machinery" and "Der Konstrukteur," by F. Reuleaux, the former for the discussion of linkages, and the latter for various illustrations of mechanisms; "Principles of Mechanism," by S. W. Robinson, for the discussion of non-circular wheels; "Kinematics," by C. W. MacCord, for the discussion of annular wheels and screw-gearing; "Machinery and Mill-work," by Sankine; "Elements of Mechanism," by T. M. Goodeve; and "Elements of Machine Design," by W. C. Unwin.


ELEMENTS OF MECHANISM.

INTRODUCTION,

1. The science of Mechanism treats of the designing and construction of machinery.

2. 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 with certain determinate motions. In general, it may be properly said that a machine is an assemblage of moving parts interposed between the source of power and the work, for the purpose of adapting the one to the other.

No machine can move itself, nor can it create motive power; this must be derived from external sources, such as the force of gravitation, the uncoiling of a spring, or the expansion of steam. As an example of a machine commonly met with, an engine might be mentioned. It is able to do certain definite work, provided some external force shall act upon it, setting the .working parts in motion. We shall find that it consists of a fixed frame, supporting the moving parts, some of which cause the rotation of the engine shaft, others move the valves distributing the steam to the cylinder, and still others operate the governor which controls the engine. These moving parts will be so arranged that they make certain definite motions relative to each other when an external force, as steam, is applied to the piston.

3. The operation of any machine depends upon two things: first, the transmission of certain forces, and second, the production of determinate motions. In dealing, due consideration must be given to both of these, so that each part may be adapted to bear the stresses imposed on it, as well as have the proper relative motion in regard to the other parts of the machine. But the nature of the movements does not depend upon the strength or absolute dimensions of the moving parts, as can be shown by models whose dimensions may vary much from those requisite for strength, and yet the motions of the parts will be the same as those of the machine. Therefore, the force and the motion may be considered separately, thus dividing the science of Mechanism into two parts, viz.:

1. Pure Mechanism, which treats of the motions and forms of the parts of a machine, and the manner of supporting and guiding them, independent of their strength.

2. Constructive Mechanism, which involves the calculation of the forces acting on different parts of the machine; the selection of materials as to strength and durability in order to withstand these forces, taking into account the convenience for repairs, and facilities for manufacture.

A Machine is an assemblage of moving parts so connected that when the first, or recipient, has a certain motion, the parts where the work is done, or effect produced, will have certain other definite motions.

4. A Mechanism b a term applied to a portion of a machine where two or more pieces 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. For example, the combination of a crank and connecting-rod with guides and frame, in a steam engine, serving to convert reciprocating into circular motion, would thus be called a mechanism.

5. Motion and Rest are necessarily relative terms within the limits of our knowledge. We may conceive a body as fixed in space, but we cannot know that there b one so fixed. If two bodies, both moving in space, remain in the same relative position in regard to each other, they are said to be at rest, one relatively to the other; if they do not, either may be said to be in motion relatively to the other.

Motion may thus be either relative, or it may be absolute, provided we assume some point as fixed. In what follows, the earth will be assumed to be at rest, and all motions referred to it will be considered as absolute.

Path, A point moving in space describes a line called its path, which may be rectilinear or curvilinear. The motion of a body b determined by the paths of three of its points selected at pleasure. If the motion b in a plane, two points suffice, and if rectilinear, one point suffices to determine the motion.

Direction. In a given path, a point can move in either of two directions only, which may be designated in various ways: as up, +, or down, - ; to the right, + , or left, - ; with the clock, + , or the reverse, - ; direction, as well as motion, being relative.

6. Continuous Motion. When a point goes on moving indefinitely in a given path in the same direction, its motion is said to be continuous. In this case the path must return on itself, as a circle or other closed curve. A wheel turning on its bearings affords an example of this motion.

7. Reciprocating Motion. When a point traverses the same path and reverses its motion at the ends of such path the motion is said to be reciprocating.

8. Intermittent Motion. When the motion of a point is interrupted by periods of rest, its motion is said to be intermittent.

9. Revolution and Rotation. A point is said to revolve about an axis when it describes a circle of which the centre is in, and the plane is perpendicular to, that axis. When all the points of a body thus move the body is said to revolve about the axis. If the axis passes through the body, as in the case of a wheel, the word rotation is used synonymously with revolution. It frequently occurs that a body not only rotates about an axis passing through itself, but also moves in an orbit about another axis. In order to make the distinction between the two motions more clear, we shall consider the first as a rotation, and the second as a revolution; just as we say, the earth rotates on its axis and revolves around the sun.

An Axis of Rotation is a line whose direction is not changed by the rotation; a fixed axis is one whose position, as well as its direction, remains unchanged.

A Plane of Rotation is a plane perpendicular to the axis of rotation.

Right-handed Rotation is the same in direction as the motion of the hands of a watch, and is generally considered to be positive. Left-handed rotation is in the opposite direction and b consequently considered as negative.

10. Cycle of Motions.  When a mechanism is set in motion and its parts go through a series of movements which are repeated over and over, the relations between and order of the different divisions of the series being the same for each repetition, we have in one of these series what is called a cycle of motions. For example, one revolution of the crank of a steam engine causes a series of different positions of the piston-rod, and the series of positions is repeated over and over for each revolution of the crank.

The Period of a motion is the interval of time elapsing between two successive passages of a point through the same position in the same direction.

11. Driver and Follower.  That piece of a mechanism which is supposed to cause motion is called the driver, and the one whose motion is effected is called the follower.

12. Frame. The frame of a machine is a structure that supports the moving parts and regulates the path, or kind of motion, of many of them directly. In discussing the motions of the moving parts, it is convenient to refer them to the frame, even though it may have, as in the locomotive, a motion of its own.