Preface
The fundamental principles of descriptive geometry are few and comparatively simple and practically the same as they were fifty years ago. But engineers today are much more aware of the extreme value and usefulness of these principles for solving problems arising in their work. The chief objective of the author in offering this text to the profession is to place the major emphasis on the application of these principles, as stated in the title Applied Descriptive Geometry.
The method followed is to start the student out with simple three-view orthographic projection. He is also required to draw other objects, for which he will see that it is necessary to know how to draw any kind of an auxiliary view. After he has become thoroughly familiar with the methods of drawing an object in any view desired, the ordinary point-line-plane problems are introduced and are solved by the same orthographic methods. No mention is made of quadrants or angles of projection; the solutions are all obtained by the change-of-position or draftsman's method. A chapter is then presented giving the revolution method for solving many of the same problems. The following chapter, which the author believes to be unique in its application of the same principles to the graphical solution of noncoplanar structural and vector problems, will have the student keenly interested. The usual problems on curved lines and surfaces are introduced with particular emphasis placed on cone and cylinder problems because they occur most frequently in engineering practice.
The last two chapters are devoted entirely to problems. Chapter 8 gives about 400 practice problems arranged in 61 groups. As each principle is introduced in the text, reference is made to one of these groups with corresponding practice problems. These are given without data, for working freehand on the blackboard or at home, and the author intends them to be checked for method only.
Chapter 9 is the main part of the text, since it furnishes the opportunity to apply the principles in a practical way. These problems are carefully laid out ready to assign to a class. They have all been tested, and many of them will force the student to do some clear thinking.
These solutions should be carefully checked by an instructor for correctness and clearness of work. The problems should furnish the basis for many new ones that may be taken from the experience of any wide-awake instructor. By altering the data slightly, they will be found to be sufficient for several years' use. Draftsmen who have had many years practical experience have studied this text and have shown an enthusiastic interest in the method and the problems.
Every year of teaching produces new and better ideas, either as a result of personal experience or as a result of suggestions from the many users of this text. In this fourth edition an attempt has been made to include most of these suggestions, which the author greatly appreciates.
To the text proper have been added a section on visualization and reading of drawings, one on the mathematical solution of graphical problems, one on a plane perpendicular to a line, one on fault problems, one on shades and shadows, one on restricted revolution, and one on a new noncoplanar stress method. None of these sections are intended to cover the subject completely. But it is hoped that they will show the large number of applications possible and that they may stimulate others to delve further into any of these fields. The keynote of the entire book is application.
Chapter 9, which contains problems mostly from industry, has been enlarged. Many new and interesting problems have been added, and for some of the old problems the data have been changed to renew them.
It has been found that our students complete about 30 per cent more problems by using the Warner and Douglass ProblemBook which accompanies this text. The revised edition includes many additional problems partially laid out to save student time.
The author wishes to express his appreciation to his colleagues and to the many teachers and engineers in industry who have used this text for so many years and who have been a source of encouragement and inspiration. May they find this fourth edition more complete, more helpful, and more useful.
Frank M. Warner