Handbook of machining and metalworking calculations

[...]... 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. .. Companies, Inc Click Here for Terms of Use This page intentionally left blank HANDBOOK OF MACHINING AND METALWORKING CALCULATIONS This page intentionally left blank 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... law of sines to solve the second unknown angle The third angle is 180° − sum of two known angles Then find the other sides using the law of sines or the law of tangents Use the law of cosines for one side and the law of sines for the two angles Use the law of sines to solve the other sides or the law of tangents The third angle is 180° − sum of two known angles Use the law of cosines to solve two of. .. Case 1 Given a, A, and B, angle C may be found from the angle formula; then sides b and c may be found by using the law of sines twice Case 2 Given a, b, and A, angle B may be found by the law of sines, angle C from the angle formula, and side c by the law of sines again Case 3 Given a, b, and C, side c may be found by the law of cosines, and angles A and B may be found by the law of sines used twice;... found by the law of sines used twice; or angle A from the law of sines and angle B from the angle formula Case 4 Given a, b, and c, the angles may all be found by the law of cosines; or angle A may be found from the law of cosines, and angles B and C from the law of sines; or angle A from the law of cosines, angle B from the law of sines, and angle C from the angle formula In all cases, the solutions... secant, and cotangent are the reciprocals of the sine, cosine, and tangent, respectively This fact also must be remembered when performing trigonometric operations Signs and Limits of the Trigonometric Functions The following coordinate chart shows the sign of the function in each quadrant and its numerical limits As an example, the sine of any angle between 0 and 90° will always be positive, and its...PREFACE This handbook contains most of the basic and advanced calculation procedures required for machining and metalworking applications These calculation procedures should be performed on a modern pocket calculator in order to save time and reduce or eliminate errors while improving accuracy Correct bracketing procedures are required when entering equations into the pocket calculator, and it is for... Examples of proper bracketing for entering equations in the pocket calculator are shown in Chap 1 and in Chap 11, where the complex four-bar linkage is analyzed and explained This book is written in a user-friendly format, so that the mathematical equations and examples shown for solutions to machining and metalworking problems are not only highly useful and relatively easy to use, but are also practical and. .. the equations and solving for the unknown quantity using standard algebraic and trigonometric rules and procedures Ratios and Proportions If a/b = c/d, then a+b c+d ᎏ = ᎏ; b d a−b c−d ᎏ=ᎏ b d and a−b c−d ᎏ=ᎏ a+b c+d Quadratic Equations Any quadratic equation may be reduced to the form ax2 + bx + c = 0 The two roots, x1 and x2, equal −b ± ͙ෆෆ b2 − 4ac ᎏᎏ 2a (x1 use +; x2 use −) When a, b, and c are real,... (Complex Equations) The transposition of basic algebraic equations has many uses in the solution of machining and metalworking problems Transposing a complex equation requires considerable skill in mathematics To simplify this procedure, the use of MathCad is invaluable As an example, a basic equation involving trigonometric functions is shown here, in its original and transposed forms The transpositions . class="bi x0 y0 w0 h0" alt="" HANDBOOK OF MACHINING AND METALWORKING CALCULATIONS This page intentionally left blank. HANDBOOK OF MACHINING AND METALWORKING CALCULATIONS Ronald A. Walsh McGRAW-HILL New. 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 subsec- tions of the handbook, all. for Terms of Use. This page intentionally left blank. HANDBOOK OF MACHINING AND METALWORKING CALCULATIONS This page intentionally left blank. CHAPTER 1 MATHEMATICS FOR MACHINISTS AND METALWORKERS This