Class Book COPYRIGHT DEPOSm / THE THEORY OF ENGINEEEING DRAWING BY ALPHONSE A. ADLER, B.S., M.E. Member American Society of Mechanical Engineers; Assistant Professor of Mechanical Drawing and Design, Polytechnic Institute, Brooklyn, N. Y. 273 ILLUSTRATIONS SECOND EDITION, CORRECTED NEW YORK D. VAN NOSTRAND COMPANY 25 PARK PLACE 1915 ^Vx \<^- Copyright, 1912, by D. VAN NOSTRAND COMPANY Copyright, 1915, by D. VAN NOSTRAND COMPANY THE SCIENTIFIC PRESS HOBERT DRUMMOND AND COMPANY BROOKLYN. N. Y. iyi5 JUL I ©CIA406530 X. PREFACE TO THE FIRST EDITION Although the subject matter of this volume is, in large measure, identical with that of many treatises on descriptive geometry, the author has called it ''Theory of Engineering Drawing," beheving that this title indicates better than could any other, the ultimate purpose of the book. That texts on descriptive geometry appear with some degree of frequency, with but few, if any, additions to the theory, indicates that teachers are aware of certain weaknesses in existmg methods of presenting the subject. It is precisely these weaknesses that the present work aims to correct. The author emphasizes the fact that the student is concerned with the representation on a plane of objects in space of three dimensions. The analysis, important as it is, has for its primary purpose the development of methods for such representation and the interpretation of the resulting drawings. It is nowhere regarded as an end in itself. The number of fundamental prin- ciples has been reduced to a minimum; indeed it will be found that the entire text is based on the problem of finding the piercing point of a given line on a given surface, and a few additional operations. The accepted method of presenting the subject, IS to start with a set of definitions,to consider in detail the ortho- graphic projection of a point, and then, on the foundation thus laid, to build the theory of the projection of lines, surfaces, and sohds. Logical and beautiful as this systematic development may be, it nevertheless presents certain inherent difficulties, chief of which is that the student is confronted at the outset with that most abstract of all abstractions, the mathematical point. In this volume the order of presentation is reversed and th(^ reader IS asked to consider first some concrete object, a box, for instance, the study of which furnishes material of use in the later discussion of its bounding surfaces and lines. The '' Theory of " Engineering Drawing is divided into four IV PREFACE parts. Part I treats of oblique projection, orthographic projec- tion, and a special case of the latter, axonometric projection. The student is advised to give special attention to the classification at the end of this section, because it gives a complete outline of the entire subject. Part II contains a variety of problems of such nature as to be easily understood by those whose training has not extended to the more highly speciahzed branches of com- mercial or engineering practice. Part III considers convergent projective line drawing, more familiar under the name of perspec- tive. Part IV has to do \vith the pictorial effects of illumination, since a knowledge of shades and shadows is frequently required in the preparation of complicated drawings. No claim is made to originality of subject matter, but it is not possible to acknowledge indebtedness to individual writers, for the topics discussed have been widely studied, and an historical review is here out of place. The author wishes, however, to express his sense of obligation to Professor WiUiam J. Berry of the Depart- ment of Mathematics in the Polytechnic Institute of Brooklyn for his criticism of Chapters IX and X, and other assistance, and to Professor Ernest J. Streubel of the Department of English for his untiring efforts in preparing the manuscript for the press. A. A. A. Polytechnic Institute of Brooklyn, October, 1912. PREFACE TO THE SECOND EDITION In this edition the author has limited the revision to the cor- rection of minor errors. These have been suggested by various readers, to whom thanks are hereby given. A. A. A. Polytechnic Institute of Brooklyn, February, 1915. CONTENTS PART I THE PRINCIPLES OF PARALLEL PROJECTING-LINE DRAWING CHAPTER I INTRODUCTORY AKT. PAGE 101. Nature of drawing 3 102. Science and art of drawing 4 103. Magnitude of objects 4 104. Commercial application of drawing 4 CHAPTER II OBLIQUE PROJECTION 201. Nature of obKque projection 6 202. Oblique projection of lines parallel to the plane of projection 7 203. Oblique projection considered as a shadow 8 204. Obhque projection of Hues perpendicular to the plane of projection . 9 205. Obhque projection of the combination of parallel and perpendicular lines to the plane of projection 10 206. Obhque projection of circles 11 207. Obhque projection of inclined lines and angles 12 208. Representation of visible and invisible lines 13 209. Drawings to scale 14 210. Examples of oblique projection 14 211. Distortion of obhque projection 20 212. Commercial application of obhque projection 21 CHAPTER III ORTHOGRAPHIC PROJECTION 301. Nature of orthographic projection 2.") 302. Theory of orthographic j)rojection 20 303. Revolution of the horizontal phuie 27 V vi . CONTENTS ART. PAGE 304. Position of the eye 27 305. Relation of size of object to size of projection 28 306. Location of object with respect to the planes of projection 28 307. Location of projections with respect to each other 29 308. Dimensions on a projection 29 309. Comparison between oblique and orthographic projection 29 310. Orthographic projection considered as a shadow 30 311. Profile plane 30 312. Location of profiles 31 313. Section plane 33 314. Supplementary plane 34 315. Angles of projection 36 316. Location of observer in constructing projections 36 317. Application of angles of projections to drawing 37 318. Commercial application of orthographic projection 38 CHAPTER IV AXONOMETRIC PROJECTION 401. Nature of isometric projections 45 402. Theory of isometric projection 46 403. Isometric projection and isometric drawing 47 404. Direction of axes 48 405. Isometric projection of circles 48 406. Isometric projection of incHned fines and angles 49 407. Isometric graduation of a circle 49 408. Examples of isometric drawing 51 409. Dimetric projection and dimetric drawing 54 410. Trimetric projection and trimetric drawing 55 411. Axonometric projection and axonometric drawing 56 412. Commercial application of axonometric projection 56 413. Classification of projections 57 PART II GEOMETRICAL PROBLEMS IN ORTHOGRAPHIC PROJECTION CHAPTER V REPRESENTATION OF LINES AND POINTS 501. Introductory 61 502. Representation of the fine 62 503. Line fixed in space by its projections 64 504. Orthographic representation of a fine 65 505. Transfer of diagrams from orthographic to obUque projection, 66 CONTENTS vii ART. PAGE 506. Piercing points of lines on the principal planes. > 66 507. Nomenclature of projections 68 508. Representation of points 68 509. Points lying in the principal planes 69 510. Mechanical representation of the principal planes 69 511. Lines parallel to the planes of projection 70 512. Lines lying in the planes of projection 71 513. Lines perpendicular to the planes of projection 72 514. Lines in all angles 72 515. Lines with coincident projections 74 516. Points in all angles 75 517. Points with coincident projections 75 518. Lines in profile planes 75 CHAPTER VI REPRESENTATION OF PLANES 601. Traces of planes parallel to the principal planes 80 602. Traces of planes parallel to the ground line 80 603. Traces of planes perpendicular to one of the principal planes 82 604. Traces of planes perpendicular to both principal planes 83 605. Traces of planes inclined to both principal planes 83 606. Traces of planes intersecting the ground Hne 84 607. Plane fixed in space by its traces 84 608. Transfer of diagrams from orthographic to obHque projection 84 609. Traces of planes in all angles 86 610. Projecting plane of fines 86 CHAPTER VII ELEMENTARY CONSIDERATIONS OF LINES AND PLANES 701. Projection of lines parallel in space 89 702. Projection of lines intersecting in space 89 703. Projection of lines not intersecting in space 90 704. Projection of lines in obfique planes 91 705. Projection of lines parallel to the principal planes and lying in an oblique plane 92 706. Projection of lines perpendicular to given planes 95 707. Revolution of a point about a fine 96 CHAPTER VIII PROBLEMS INVOLVING THE POINT, THE LINE, AND THE PLANE 801. Introductory 99 802. Solution of problems 99 803. Problem 1. To draw a fine through a given point paraUel to a given lino 100 viii CONTENTS ART. PAGE 804, Problem 2. To draw a line intersecting a given line at a given point . 100 S05. Problem 3. To find where a given line pierces the principal planes 101 806. Problem 4. To pass an obhque plane through a given obhque hne. 102 807. Special cases of the preceding problem 102 808. Problem 5. To i)ass an obhque plane through a given point 103 809. Problem 6. To find the intersection of two planes, oblique to each other and to the principal planes 104 810. Special case of the preceding problem 104 811. Problem 7. To find the corresponding projection of a given point lying in a given obhque plane, when one of its projections is given 104 812. Special case of the preceding problem 105 813. Problem 8. To draw a plane which contains a given point and is paraUel to a given plane 106 814. Problem 9. To draw a line perpendicular to a given plane through a given point 107 815. Special case of the precechng problem 108 816. Problem 10. To draw a plane through a given point perpendicular to a given line 108 817.