Engineering Descriptive Geometry;

Class _X 3 53 Book >Ba5 ; ~" Copyright^ ' COPYRIGHT DEPOSIT- ENGINEERING DESCRIPTIVE GEOMETRY Engineering Descriptive Geometry A Treatise on Descriptive Geometry as the Basis of Mechanical Drawing, Explaining Geometrically the Operations Customary in the Draughting Room F. W. BARTLETT COMMANDER, U. S. NAVY HEAD OF DEPARTMENT OF MARINE ENGINEERING AND NAVAL CONSTRUCTION AT THE UNITED STATES NAVAL ACADEMY THEODORE W. JOHNSON PROFESSOR OF MECHANICAL DRAWING, UNITED STATES NAVAL ACADEMY MEMBER OF AMERICAN SOCIETY OF MECHANICAL ENGINEERS ANNAPOLIS, MD., U.S. A. 1910 Copyright, 1910, by T. W. Johnson BALTIMORE, MB. , U. S. A. CO!. A 26 JO': PBEFACE. The aim of this work is to make Descriptive Geometry an integral part of a course in Mechanical or Engineering Drawing. The older books on Descriptive Geometry are geometrical rather than descriptive. Their authors were interested in the subject as a branch of mathematics, not as a branch of drawing. Technical schools should aim to produce engineers rather than mathematicians, and the subject is here presented with the idea that it may fit naturally in a general course in Mechanical Drawing. It should follow that portion of Mechanical Drawing called Line Drawing, whose aim is to teach the handling of the drawing instru- ments, and should precede courses specializing in the various branches of Drawing, such as Mechanical, Structural, Architectural, and Topographical Drawing, or the " Laying Off " of ship lines. The various branches of drawing used in the different industries may be regarded as dialects of a common language. A drawing is but a written page conveying by the use of lines a mass of informa- tion about the geometrical shapes of objects impossible to describe in words without tedium and ambiguity. In a broad sense all these branches come under the general term Descriptive Geometry. It is more usual, however, to speak of them as branches of Engineer- ing Drawing, and that term may well be used as the broad label. The term Descriptive Geometry will be restricted, therefore, to the common geometrical basis or ground work on which the various industrial branches rest. This ground work of mathematical laws is unchanging and permanent. The branches of Engineering Drawing have each their own abbreviations, and special methods adapting them to their own particular fields, and these conventional methods change from time to time, keeping pace with changing industrial methods. Descriptive Geometry, though unchanged in its principles, has recently undergone a complete change in point of view. In changing its purpose from a mathematical one to a descriptive one, vi Preface from being a training for the geometrical powers of a mathematician to being a foundation on which to build up a knowledge of some branch of Engineering Drawing, the number and position of the planes of projection commonly used are altered. The object is now placed behind the planes of projection instead of in front of them, a change often spoken of as a change from the " 1st quadrant " to the "3d quadrant," or from the French to the American method. We make this change, regarding the 3d quadrant method as the only natural method for American engineers. All the principles of Descriptive Geometry are as true for one method as for the other, and the industrial branches, as Mechanical Drawing, Structural Drawing, etc., as practiced in this country, all demand this method. In addition, the older geometries made practically no use of a third plane of projection, and we take in this book the further step of regarding the use of three planes of projection as the rule, not the exception. To meet the common practice in industrial branches, we use as our most prominent method of treatment, or tool, the use of an auxiliary plane of projection, a device which is almost the draftsman's pet method, and which in books is very little noticed. As the work is intended for students who are but just taking up geometry of three dimensions, in order to inculcate by degrees a power of visualizing in space, we begin the subject, not with the mathematical point in space but with a solid tangible object shown by a perspective drawing. ]STo exact construction is based on the perspective drawings which are freely used to make a realistic ap- pearance. As soon as the student has grasped the idea of what orthographic projection is, knowledge of how to make the projection is taught by the constructive process, beginning with the point and passing through the line to the plane. To make the subject as tangible as possible, the finite straight line and the finite portion of a plane take precedence over the infinite line and plane. These latter require higher powers of space imagination, and are therefore postponed until the student has had time to acquire such powers from the more naturallv understood branches of the subject. F. W. B. T. W. J. March, 1910. CONTENTS. CHAPTER PAGE I. Nature of Orthographic Projection 1 II. Orthographic Projection of the Finite Straight Line. 18 III. The True Length of a Line in Space 27 IV. Plane Surfaces and Their Intersections and Develop- ments 38 V. Curved Lines 49 VI. Curved Surfaces and Their Elements 62 VII. Intersections of Curved Surfaces 70 VIII. Intersections of Curved Surfaces; Continued 81 IX. Development of Curved Surfaces 91 X. Straight Lines of Unlimited Length and Their Traces . 98 XI. Planes of Unlimited Extent: Their Traces 108 XII. Various Applications 121 XIII. The Elements of Isometric Sketching 133 XIV. Isometric Drawing as an Exact System 142 Set of Descriptive Drawings 149 CHAPTER I. NATURE OF ORTHOGRAPHIC PROJECTION. 1. Orthographic Projection.—The object of Mechanical Draw- ing is to represent solids with such mathematical accuracy and precision that from the drawing alone the object can be bnilt or constructed without deviating in the slightest from the intended shape. As a consequence the "working drawing" is the ideal sought for, and any attempt at artistic or striking effects as in " show drawings " must be regarded purely as a side issue of minor importance. Indeed mechanical drawing does not even aim to give a picture of the object as it appears in nature, but the views are drawn for the mind, not the eye. The shapes used in machinery are bounded by surfaces of mathematical regularity, such as planes, cylinders, cones, and surfaces of revolution. They are not random surfaces like the surface of a lump of putty or other surfaces called " shapeless." These definite shapes must be represented on the flat surface of the paper in an unmistakable manner. ft The method chosen is that known as orthographic projection" If a plane is imagined to be situated in front of an object, and from any salient point, an edge or corner, a perpendicular line, called a " projector," is drawn to the plane, this line is said to project the given point upon the plane, and the foot of this perpendicular line is called the projection of the given point. If all salient points are projected by this method, the orthographic drawing of the object is formed. 2. Perspective Drawing.—The views we are accustomed to in artistic and photographic representations are " Perspective Views." They seek to represent objects exactly as they appear in nature. In their case a plane is supposed to be erected between the human eye and the object, and the image is formed on the plane by sup- posing straight lines drawn from the eye to all salient points of Engineering Descriptive Geometry the object. Where these lines from the eye, or " Visual Kays," as they are called, pierce the plane, the image is formed. Fig. 1 represents the two contrasted methods applied to a simple object, and the customary nomenclature. An orthographic view is sometimes called an " Infinite Perspec- tive View," as it is the view which could only be seen by an eye at an infinite distance from the object. " The Projectors " may then be considered as parallel visual rays which meet at infinity, where the eye of the observer is imagined to be. Projector Perspective Vie w. Orthographic View. Fig. 1. 3. The Regular Orthographic Views.—Since solids have three " dimensions," length, breadth and thickness, and the plane of the paper on which the drawing is made has but two, a single orthographic view can express two only of the three dimensions of the object, but must always leave one indefinite. Points and lines at different distances from the eye are drawn as if lying in the same plane. From one view only the mind can imagine them at different distances by a kind of guess-work. If two views are made from different positions, each view may supplement the other in the features in which it is lacking, and so render the representa- tion entirely exact. Theoretically two views are always required to represent a solid accurately. To make a drawing all the more clear, other views are generally advisable, and three views may be taken as the average requirement for single pieces of machinery. Six regular views are possible, " however, and an endless number of auxiliary views and " sections in addition. For the present, we shall consider only the " regular 7 views. '' which are six in number. Nature of Orthographic Projection 4. Planes of Projection.—A solid object to be represented is supposed to be surrounded by planes at short distances from it, the planes being perpendicular to each other. From each point of every salient edge of the object, lines are supposed to be drawn perpendicular to each of the surrounding planes, and the succes- sion of points where these imaginary projecting lines cut the planes are supposed to form the lines of the drawings on these planes.

Load more