Handbook of Machining and Metalworking Calculations
With easy-to-use tables, charts, listings, and formulas, this convenient hands-on resource will help you solve virtually any problem involving metalworking and machining tools and applications.
TABLE OF CONTENTS Handbook of Machining and Metalworking Calculations
Chapter 1: Mathematics for Machinists and Metalworkers
This chapter covers all the basic and special mathematical procedures of value to the modern machinist and metalworker. Geometry and plane trigonometry are of prime importance, as are the basic algebraic manipulations. Solutions to many basic and complex machining and metalworking operations would be difficult or impossible without the use of these branches of mathematics. In this chapter and other subsections of the handbook, all the basic and important aspects of these branches of mathematics will be covered in detail. Examples of typical machining and metalworking problems and their solutions are presented throughout this handbook.
1.1 GEOMETRIC PRINCIPLES PLANE GEOMETRY
In any triangle, angle A + angle B + angle C = 180 , and angle A = 180 (angle A + angle B), and so on (see Fig. 1.1). If three sides of one triangle are proportional to the corresponding sides of another triangle, the triangles are similar. Also, if a:b:c = a ? :b ? :c ? , then angle A = angle A ? , angle B = angle B ? , angle C = angle C ? , and a/a ?= b/b ?= c/c ? . Conversely, if the angles of one triangle are equal to the respective angles of another triangle, the triangles are similar and their sides proportional; thus if angle A = angle A ? , angle B = angle B ? ,
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