A textbook of pure mechanism

The discussion in this book does not cover a large number of mechanical appliances, not even a large number of those to be found in common use. An attempt has been made to select representative examples which best illustrate the geometry of machinery and to state them as briefly as possible without a sacrifice of clearness.

The classification is based on the method of transmitting motion. This is radically different from the classification used in several well-known text-books which is according to the method of making contact, i.e., point, line or surface. The former method seems to lead to a somewhat less complex treatment of the subject.

In CHAPTER III, certain fundamental propositions are stated as true of all contact motions and examples in the later parts of the book are constantly referred back to them.

1. Mechanics of Machines or Mechanism is that branch of Applied Mechanics which treats of the design, construction and operation of machinery. The subject has two divisions: Pure Mechanism, sometimes called Kinematics of Machinery, and Constructive Mechanism or Machine Design. Pure Mechanism deals principally with the form and motion of machines; machine design involves questions of the weight and strength of parts and of the forces in operation. The word "mechanism" is used in two senses, first as a general term indicating a branch of the science of Mechanics. It is also used to indicate a body of special shape, as in “a piece of Mechanism” or a group of such bodies so arranged as to transmit motion. In this last sense there is little difference between the definition of a mechanism and a machine, but the word machine implies completeness, something that will do work; this element may be wholly lacking in a piece of mechanism.

2. A Machine is a combination of resistant bodies, fixed or movable, arranged to transmit and modify motion and energy and to do work. Two things are pre-supposed, a source of power and work to be done. The machine is interposed between these two, and its working members may be classed under three heads:

(a) Parts receiving the energy,
(b) Parts transmitting and modifying the energy
(c) Parts performing the required work.

To this might be added two more headings:

(d) Regulators,
(e) Supports or frames.

3. Motion, in the mechanics of machinery, is understood to mean the movement of one part of a mechanism relative to the other parts, the change of position being definite in direction and velocity.

4. Path. If a point changes its position, it traces a line called a path. A path may be of any form whatever, in a plane or in space. There are, however, only a few forms of paths that are made use of in machine design; straight lines and closed loops being the most common. If the path of a moving point and the direction and velocity along the path are given, the motion is completely determined.

6. Cycle, Period, Phase. When a point, which is moving in a given path, makes a complete circuit and returns to the original position, such a circuit is called a cycle. The time required for one such complete cycle is the period of the moving point, and by the phase is meant the position of the point on the path, or the angle turned through at a particular instant.

6. Forms of Motion. Motions available for machine design may be classified with respect to the form of the path under three heads: Plane motion (Rotation, Translation), Helical motion and Spherical motion.

7. Plane Motion. Let a section of a rigid moving body be made by a cutting plane, the plane is extended if necessary in the direction of motion; if the section of the moving body so cut always remains in this cutting plane or its extension, then the body has plane motion. Plane motion may be either rotation or translation. If it is rotation, the body moves around a fixed center located either within or without the body itself. A plane motion of translation may be either rectilinear, in which case its path is a straight line, or curvilinear, where the body moves in such a way as to remain always parallel to its initial position. The wheels of a locomotive furnish an example of plane motion of rotation; the frame of the engine when moving on a straight track has rectilinear translation and the side rods are an illustration of curvilinear translation.

8. Helical Motion. If a body has rotation around an axis combined with rectilinear motion along the axis, the resultant motion is helical, A point moving along a screw thread would have helical motion.

9. Spherical Motion. If a body revolves in two directions at the same time about a fixed point, located outside of the body itself, its motion is spherical. The motion of the governor balls, B, Fig. 1, belongs under this classification.