Triangulation applied to sheet metal pattern cutting

TRIANGULATION APPLIED TO SHEET METAL PATTERN CUTTING

A Comprehensive Treatise for Cutters, Draftsmen, Foremen and Students. Progressing from the simplest phases of the subject to the most complex problems employed in the development of Sheet Metal Patterns. With practical solutions of numerous problems of frequent occurrence in sheet metal shops.

BY F. S. KIDDER

NEW YORK, The Sheet Metal Publication Company, 1917
    

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Triangulation applied to sheet metal pattern cutting
    

CONTENTS

I. Elementary Principles
II. A Simple Transitional Fitting
III. The Oblique Cone
IV. A Transitional Fitting From Rectangular to Round Which Makes an Offset
V. A Twisted Transitional Fitting
VI. The Pattern for the Frustum of an Oblique Cone
VII. A Transitional Fitting From Oblong to Round
VIII. A Two-Pronged Fitting Which Can Be Made in One Piece
IX. Some Principles of Orthographic Projection as Applied to Triangulation
X. The Representation of Objects Upon the Vertical, Horizontal, Profile and Oblique Supplemenary Planes of Projection
XI. The Pattern for a Fitting Whose Ends Are Not in Parallel Planes
XII. The Pattern for a Fitting Whose Ends Are Not in Parallel Planes, Second Demonstration
XIII. A Transitional Elbow From Round to Rectangular
XIV. A Transitional Offset From Round to Rectangular
XV. A Three-Pieced Tapering Elbow
XVI. The Ship's Ventilator
XVII. On the Tapering Elbow to be made in Any Number of Pieces
XVIII. A Transitional Elbow in Rectangular Pipe
XIX. A Transitional Elbow From Round to Elliptical
XX. The Helical Elbow
XXI. When It Is Required That a Round Pipe Should Join the Frustum of an Oblique Cone
XXII. A Branched Fitting Commonly Known as "Breeches"
XXIII. A Simple Two-Pronged Fitting
XXIV. A Two-Pronged Fitting Whose Prongs Are Unequal
XXV. On the Two-Pronged Fitting When It Is Required That the Prongs Radiate at a Given Angle to the Main Stem
XXVI. On a Fitting With Any Number of Prongs
XXVII. The Right or Scalene Cone Considered in Securing the Patterns for a Branched Fitting


PREFACE

The great and increasing demand for irregular forms to be made from sheet metal has made Triangulation an important factor in Sheet Metal Pattern Development. This has induced the writer to lay before the sheet metal worker, a work designed for the purpose of enabling him to acquire a thorough understanding of this branch of Pattern Cutting.

Triangulation has in many instances been a subject of more or less mystery. However, from a study of Geometrical works, we conclude that its secrets have long been known.

Few, if any writers upon Sheet Metal Pattern Development have seen fit to interpret it in a manner which affords the average worker an opportunity of grasping its underlying principles. The universal practice of most writers upon this subject has been to lay before the student worked out examples to be copied, little, or no attempt being made to convey an understanding of the principles employed, which is of the utmost importance.

No amount of time devoted to copying Chinese characters would enable one to understand them, nor will any amount of time consumed in copying pattern demonstrations enable one to understand the use and purpose of lines there found.

In all examples of pattern development lines are presumed to be upon the surface of the object. Upon determining the lengths of said lines, and the distances they are from each other, we are enabled to place them upon the plane of development in their proper lengths and relative positions, thereby securing points through which lines are traced which represent the boundaries of the required pattern.

There is a great sameness in the principles and methods which may be applied to many examples. In other words, if we grasp the reason for, and the use of each and every line in one problem, we are prepared to use those same principles and methods for all.

Forms which must be treated by Triangulation are such that the rectilinear elements of their surfaces are neither parallel or convergent lines. Therefore to determine their lengths we must assume a supplementary plane for each, or employ the right angled triangle. To secure their relative positions, we must presume that the surface of the object is divided into triangles.

Some idea of Orthographic Projection will be of service to the one who aspires to become proficient in this branch of pattern development, although the solving of a great number of the more common problems is but a simple operation.

This work is submitted with every confidence that if attention is devoted to the subject matter enclosed, one will be enabled to more clearly understand the principles involved in Triangulation as Applied to Sheet Metal Pattern Development.


CHAPTER I. - TRIANGULATION - Elementary Principles.

Triangulation is a term which has in recent years been applied to certain operations in Sheet Metal Pattern Development, although said operations have long been explained in works upon Descriptive Geometry, where is found the declaration that the true length of a right line in space may always be found in the hypothenuse of a right angled triangle, whose base is equal in length to the horizontal projection of the line, and whose perpendicular is equal to the difference in length of the vertical projectors from the extremities of that line.

Triangulation as applied to sheet metal pattern development, is the act or process of dividing into triangles, also the results thus secured; specifically, the laying out and accurate measurement of a network of triangles presumed to be upon the surface of the object, and shown upon its geometrical representation which has been correctly delineated.

Triangles with which we deal are considered as plane triangles, although not strictly so, since a plane triangle is presumed to lie in one plane, and is bounded by three right lines. A triangle which is presumed to be a portion of the curved surface of an object will not lie in one plane. In many instances one side at least of said triangle is not a right line but a curved one. Thus many triangles involved in triangulation as applied to sheet metal pattern development are mixtilinear triangles. However, the magnitude of the variation is so small, that it may consistently be considered as a negligible quantity.


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Triangulation applied to sheet metal pattern cutting