Design Engineer's Reference Guide : Mathematics, Mechanics, and Thermodynamics book cover
1st Edition

Design Engineer's Reference Guide
Mathematics, Mechanics, and Thermodynamics

ISBN 9781138073722
Published March 29, 2017 by CRC Press
357 Pages 239 B/W Illustrations

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Book Description

Author Keith L. Richards believes that design engineers spend only a small fraction of time actually designing and drawing, and the remainder of their time finding relevant design information for a specific method or problem. He draws on his own experience as a mechanical engineering designer to offer assistance to other practicing and student engineers facing the same struggle. Design Engineer's Reference Guide: Mathematics, Mechanics, and Thermodynamics provides engineers with a roadmap for navigating through common situations or dilemmas.

This book starts off by introducing reference information on the coverage of differential and integral calculus, Laplace’s transforms, determinants, and matrices. It provides a numerical analysis on numerical methods of integration, Newton–Raphson’s methods, the Jacobi iterative method, and the Gauss–Seidel method. It also contains reference information, as well as examples and illustrations that reinforce the topics of most chapter subjects.

A companion to the Design Engineer's Handbook and Design Engineer's Case Studies and Examples, this textbook covers a range of basic engineering concepts and common applications including:

• Mathematics

• Numerical analysis

• Statics and kinematics

• Mechanical vibrations

• Control system modeling

• Basic thermodynamics

• Fluid mechanics and linkages

An entry-level text for students needing to understand the underlying principles before progressing to a more advanced level, Design Engineer's Reference Guide: Mathematics, Mechanics, and Thermodynamics is also a basic reference for mechanical, manufacturing, and design engineers.

Table of Contents



Hyperbolic Functions

Solution of the Quadratic Equation

Solution of Simultaneous Equations (Two Unknowns)

Laws of Exponents


Real Root of the Equation f(x) = 0 Using the Newton–Raphson Method



Differential Calculus

Integral Calculus

Laplace Transforms

Parallel Axis Theorem

Complex Numbers




Determinant Order

Properties of the Determinant

Minors and Cofactors


Introduction to Numerical Methods


Numerical Methods for Integration

Evaluation of Errors

Round-Off and Truncation Errors

Errors Arising from Differentiation

Integration Errors


Newton–Raphson Method

Iterative Methods for Solving Linear Equations

Non-Linear Equations

Properties of Sections and Figures

Centroid Cx, Cy, Cz

Moment of Inertia/Second Moment of Area

Polar Moment of Inertia of a Plane Area


Force, Mass and Moments


Vectors and Vector Analysis




Newton’s Laws of Motion (Constant Acceleration)

Rectilinear Motions

Circular Motion

Absolute and Relative Motion

Rotating Unit Vector

Vector of Point in a Rotating Reference Frame

Velocity of a Point in a Moving Reference Frame

Acceleration of a Particle

Kinematics of Rigid Bodies in One Plane

Instantaneous Centre of Rotation

Kinematics of Rigid Bodies in Three Dimensions


Translation Motion

Rotation About a Fixed Axis

Rotation About a Fixed Point

General Motion

Mechanical Vibrations


Single Degree of Freedom: Free Vibrations

Damped Vibrations

Single Degree of Freedom: Forced Vibrations

Natural Frequency of Beams and Shafts

Forced Vibrations

Introduction to Control Systems Modelling


Engineering System Models

Block Diagram and Transfer Function Manipulations



Thermodynamic Basics


Basic Thermodynamics

Conservation of Energy

Fluid Mechanics

Fluid Properties

Fluid Flow

Continuity Equation


Dimension Analysis

Fluid Drag

Properties of Water

Channel Flow

Orifice Plate

Fluid Machines

Introduction to Linkages


Brief History

Kinematic Definitions

Kinematic Pairs

Planar, Spherical and Spatial Mechanisms


Chebyshev–Gruber–Kutzbach Criterion

Grashof’s Law

Four–Bar Linkage

Mechanical Advantage of a Four-Bar Linkage

Freudenstein’s Equation

Drawing Velocity Vectors for Linkages

Drawing Acceleration Vectors for Linkages


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Keith Richards is a retired mechanical design engineer who has worked in the industry for over 55 years. Initially he served an engineering apprenticeship with B.S.A. Tools, a company that manufactured a wide range of machine tools. On leaving B.S.A., he served as a freelance engineering designer in a wide range of industries that also included aluminum rolling mill design, industrial fork lift trucks, and the Hutton tension leg platform, an offshore oil production platform. In later years, Richards was involved in the aerospace industry working on projects covering aircraft undercarriages, environmental control systems for the military and commercial aircraft.


"Designers usually need a quick reference/validation for proposed design. This second volume will, like the first, provide a good, basic collection of math, mechanics and foundational topics they need for project work. Good resource for interdisciplinary design terms."
––Ronald L. Huston, Mechanical Engineering, University of Cincinnati, Ohio, USA

"It would appear that the book addresses a large part of what mechanical design engineers need for their day-to-day work… I like the practical treatment of the subject. Key points are explained simply and clearly. There are many worked examples to illustrate the application of the theory. The book would be suitable for engineers wishing to refresh their knowledge of the topics covered."
––Duc Pham, University of Birmingham, UK