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Theory of Machines and Mechanisms

Fourth Edition

John Uicker, Gordon Pennock, and Joseph Shigley

Publication Date - February 2010

ISBN: 9780195371239

928 pages
8 x 10 inches

In Stock

Retail Price to Students: $170.95

A classic text on the theory of mechanisms and kinematics, now updated with Working Model and MATLAB resources


Theory of Machines and Mechanisms provides a text for the complete study of displacements, velocities, accelerations, and static and dynamic forces required for the proper design of mechanical linkages, cams, and geared systems. The authors present the background, notation, and nomenclature essential for students to understand the various independent technical approaches that exist in the field of mechanisms, kinematics, and dynamics.

Now fully revised in its fourth edition, this text is ideal for senior undergraduate or graduate students in mechanical engineering who are taking a course in kinematics and/or machine dynamics.

New to this Edition

  • Includes more worked examples throughout, and many new and updated end-of-chapter homework problems
  • Coverage of helical gears, bevel gears, worms, and worm gears is now integrated into a single chapter
  • Material on planar and spatial dynamic force analysis is now integrateded into a single chapter
  • A completely new chapter has been added on multi-degree-of-freedom planar linkage analysis
  • The chapter on kinematic synthesis has been markedly expanded, and now includes three and four accuracy position graphical methods
  • The chapter on static force analysis has been expanded to included coverage of buckling of axially-loaded two-force members under compression


  • Offers balanced coverage of all topics by both graphic and analytic methods
  • Covers all major analytic approaches
  • Includes the method of kinematic coefficients-which clearly separates kinematic (geometric) effects from those depending on operating speed or other dynamic effects-and also integrates the coverage of linkages, cams, and geared systems
  • Provides high-accuracy graphical solutions to exercises, by use of CAD software

About the Author(s)

John J. Uicker, Jr., is Professor Emeritus of Mechanical Engineering at the University of Wisconsin-Madison.

Gordon R. Pennock is Associate Professor of Mechanical Engineering at Purdue University.

The late Joseph E. Shigley was Professor Emeritus of Mechanical Engineering at the University of Michigan.

Previous Publication Date(s)

January 2003
November 1994
June 1980

Table of Contents

    About the Authors

    Part 1 Kinematics and Mechanisms
    1 The World of Mechanisms
    1.1 Introduction
    1.2 Analysis and Synthesis
    1.3 The Science of Mechanics
    1.4 Terminology, Definitions, and Assumptions
    1.5 Planar, Spherical, and Spatial Mechanisms
    1.6 Mobility
    1.7 Classification of Mechanisms
    1.8 Kinematic Inversion
    1.9 Grashof's Law
    1.10 Mechanical Advantage

    2 Position and Displacement
    2.1 Locus of a Moving Point
    2.2 Position of a Point
    2.3 Position Difference Between Two Points
    2.4 Apparent Position of a Point
    2.5 Absolute Position of a Point
    2.6 The Loop-Closure Equation
    2.7 Graphic Position Analysis
    2.8 Algebraic Position Analysis
    2.9 Complex-Algebra Solutions of Planar Vector Equations
    2.10 Complex Polar Algebra
    2.11 The Chace Solutions to Planar Vector Equations
    2.12 Position Analysis Techniques
    2.13 Coupler-Curve Generation
    2.14 Displacement of a Moving Point
    2.15 Displacement Difference Between Two Points
    2.16 Rotation and Translation
    2.17 Apparent Displacement
    2.18 Absolute Displacement
    2.19 Apparent Angular Displacement

    3 Velocity
    3.1 Definition of Velocity
    3.2 Rotation of a Rigid Body
    3.3 Velocity Difference Between Points of a Rigid Body
    3.4 Graphic Methods; Velocity Polygons
    3.5 Apparent Velocity of a Point in a Moving Coordinate System
    3.6 Apparent Angular Velocity
    3.7 Direct Contact and Rolling Contact
    3.8 Systematic Strategy for Velocity Analysis
    3.9 Analytic Methods
    3.10 Complex-Algebra Methods
    3.11 The Vector Method
    3.12 The Method of Kinematic Coefficients
    3.13 Instantaneous Center of Velocity
    3.14 The Aronhold-Kennedy Theorem of Three Centers
    3.15 Locating Instant Centers of Velocity
    3.16 Velocity Analysis Using Instant Centers
    3.17 The Angular Velocity Ratio Theorem
    3.18 Relationships Between First-Order Kinematic Coefficients and Instant Centers
    3.19 Freudenstein's Theorem
    3.20 Indices of Merit; Mechanical Advantage
    3.21 Centrodes

    4 Acceleration
    4.1 Definition of Acceleration
    4.2 Angular Acceleration
    4.3 Acceleration Difference Between Points of a Rigid Body
    4.4 Acceleration Polygons
    4.5 Apparent Acceleration of a Point in a Moving Coordinate System
    4.6 Apparent Angular Acceleration
    4.7 Direct Contact and Rolling Contact
    4.8 Systematic Strategy for Acceleration Analysis
    4.9 Analytic Methods
    4.10 Complex-Algebra Methods
    4.11 The Chace Solutions
    4.12 The Method of Kinematic Coefficients
    4.13 The Euler-Savary Equation
    4.14 The Bobillier Constructions
    4.15 The Instant Center of Acceleration
    4.16 The Bresse Circle (or de La Hire Circle)
    4.17 Radius of Curvature of Point Trajectory Using Kinematic Coefficients
    4.18 The Cubic of Stationary Curvature

    5 Multi-Degree-of-Freedom Planar Linkages
    5.1 Introduction
    5.2 Position Analysis; Algebraic Solution
    5.3 Graphic Methods; Velocity Polygons
    5.4 Instant Centers of Velocity
    5.5 First-Order Kinematic Coefficients
    5.6 The Method of Superposition
    5.7 Graphic Method; Acceleration Polygons
    5.8 Second-Order Kinematic Coefficients
    5.9 Path Curvature of a Coupler Point
    5.10 The Finite Difference Method

    Part 2 Design of Mechanisms

    6 Cam Design
    6.1 Introduction
    6.2 Classification of Cams and Followers
    6.3 Displacement Diagrams
    6.4 Graphical Layout of Cam Profiles
    6.5 Kinematic Coefficients of the Follower Motion
    6.6 High-Speed Cams
    6.7 Standard Cam Motions
    6.8 Matching Derivatives of Displacement Diagrams
    6.9 Plate Cam with Reciprocating Flat-Face Follower
    6.10 Plate Cam with Reciprocating Roller Follower

    7 Spur Gears
    7.1 Terminology and Definitions
    7.2 Fundamental Law of Toothed Gearing
    7.3 Involute Properties
    7.4 Interchangeable Gears; AGMA Standards
    7.5 Fundamentals of Gear-Tooth Action
    7.6 The Manufacture of Gear Teeth
    7.7 Interference and Undercutting
    7.8 Contact Ratio
    7.9 Varying the Center Distance
    7.10 Involutometry
    7.11 Nonstandard Gear Teeth

    8 Helical Gears, Bevel Gears, Worms and Worm Gears
    8.1 Parallel-Axis Helical Gears
    8.2 Helical Gear Tooth Relations
    8.3 Helical Gear Tooth Proportions
    8.4 Contact of Helical Gear Teeth
    8.5 Replacing Spur Gears with Helical Gears
    8.6 Herringbone Gears
    8.7 Crossed-Axis Helical Gears
    8.8 Straight-Tooth Bevel Gears
    8.9 Tooth Proportions for Bevel Gears
    8.10 Crown and Face Gears
    8.11 Spiral Bevel Gears
    8.12 Hypoid Gears
    8.13 Worms and Worm Gears

    9 Mechanism Trains
    9.1 Parallel-Axis Gear Trains
    9.2 Examples of Gear Trains
    9.3 Determining Tooth Numbers
    9.4 Epicyclic Gear Trains
    9.5 Bevel Gear Epicyclic Trains
    9.6 Analysis of Epicyclic Gear Trains by Formula
    9.7 Tabular Analysis of Epicyclic Gear Trains
    9.8 Summers and Differentials
    9.9 All Wheel Drive Train

    10 Synthesis of Linkages
    10.1 Type, Number, and Dimensional Synthesis
    10.2 Function Generation, Path Generation, and Body Guidance
    10.3 Two Finitely Separated Positions of a Rigid Body (N = 2)
    10.4 Three Finitely Separated Positions of a Rigid Body (N = 3)
    10.5 Four Finitely Separated Positions of a Rigid Body (N = 4)
    10.6 Five Finitely Separated Positions of a Rigid Body (N = 5)
    10.7 Precision Positions; Structural Error; Chebychev Spacing
    10.8 The Overlay Method
    10.9 Coupler-Curve Synthesis
    10.10 Cognate Linkages; The Roberts-Chebychev Theorem
    10.11 Freudenstein's Equation
    10.12 Analytic Synthesis Using Complex Algebra
    10.13 Synthesis of Dwell Mechanisms
    10.14 Intermittent Rotary Motion

    11 Spatial Mechanisms
    11.1 Introduction
    11.2 Exceptions to the Mobility of Mechanisms
    11.3 The Spatial Position-Analysis Problem
    11.4 Spatial Velocity and Acceleration Analyses
    11.5 Euler Angles
    11.6 The Denavit-Hartenberg Parameters
    11.7 Transformation-Matrix Position Analysis
    11.8 Matrix Velocity and Acceleration Analyses
    11.9 Generalized Mechanism Analysis Computer Programs

    12 Robotics
    12.1 Introduction
    12.2 Topological Arrangements of Robotic Arms
    12.3 Forward Kinematics
    12.4 Inverse Position Analysis
    12.5 Inverse Velocity and Acceleration Analyses
    12.6 Robot Actuator Force Analysis

    Part 3 Dynamics of Machines

    13 Static Force Analysis
    13.1 Introduction
    13.2 Newton's Laws
    13.3 Systems of Units
    13.4 Applied and Constraint Forces
    13.5 Free-Body Diagrams
    13.6 Conditions for Equilibrium
    13.7 Two- and Three-Force Members
    13.8 Four-Force Members
    13.9 Friction-Force Models
    13.10 Static Force Analysis with Friction
    13.11 Spur- and Helical-Gear Force Analysis
    13.12 Straight-Tooth-Bevel-Gear Force Analysis
    13.13 The Method of Virtual Work
    13.14 Euler Column Formula
    13.15 The Critical Unit Load
    13.16 Critical Unit Load and the Slenderness Ratio
    13.17 The Johnson Parabolic Equation

    14 Dynamic Force Analysis
    14.1 Introduction
    14.2 Centroid and Center of Mass
    14.3 Mass Moments and Products of Inertia
    14.4 Inertia Forces and D'Alembert's Principle
    14.5 The Principle of Superposition
    14.6 Planar Rotation about a Fixed Center
    14.7 Shaking Forces and Moments
    14.8 Complex Algebra Approach
    14.9 Equation of Motion From Power Equation
    14.10 Measuring Mass Moment of Inertia
    14.11 Transformation of Inertia Axes
    14.12 Euler's Equations of Motion
    14.13 Impulse and Momentum
    14.14 Angular Impulse and Angular Momentum

    15 Vibration Analysis
    15.1 Differential Equations of Motion
    15.2 A Vertical Model
    15.3 Solution of the Differential Equation
    15.4 Step Input Forcing
    15.5 Phase-Plane Representation
    15.6 Phase-Plane Analysis
    15.7 Transient Disturbances
    15.8 Free Vibration with Viscous Damping
    15.9 Damping Obtained by Experiment
    15.10 Phase-Plane Representation of Damped Vibration
    15.11 Response to Periodic Forcing
    15.12 Harmonic Forcing
    15.13 Forcing Caused by Unbalance
    15.14 Relative Motion
    15.15 Isolation
    15.16 Rayleigh's Method
    15.17 First and Second Critical Speeds of a Shaft
    15.18 Torsional Systems

    16 Dynamics of Reciprocating Engines
    16.1 Engine Types
    16.2 Indicator Diagrams
    16.3 Dynamic Analysis-General
    16.4 Gas Forces
    16.5 Equivalent Masses
    16.6 Inertia Forces
    16.7 Bearing Loads in a Single-Cylinder Engine
    16.8 Crankshaft Torque
    16.9 Shaking Forces of Engines
    16.10 Computation Hints
    17 Balancing
    17.1 Static Unbalance
    17.2 Equations of Motion
    17.3 Static Balancing Machines
    17.4 Dynamic Unbalance
    17.5 Analysis of Unbalance
    17.6 Dynamic Balancing
    17.7 Balancing Machines
    17.8 Field Balancing with a Programmable Calculator
    17.9 Balancing a Single-Cylinder Engine
    17.10 Balancing Multi-Cylinder Engines
    17.11 Analytical Technique for Balancing Multi-Cylinder Engines
    17.12 Balancing Linkages
    17.13 Balancing of Machines

    18 Cam Dynamics
    18.1 Rigid- and Elastic-Body Cam Systems
    18.2 Analysis of an Eccentric Cam
    18.3 Effect of Sliding Friction
    18.4 Analysis of Disk Cam with Reciprocating Roller Follower
    18.5 Analysis of Elastic Cam Systems
    18.6 Unbalance, Spring Surge, and Windup

    19 Flywheels, Governors, and Gyroscopes
    19.1 Dynamic Theory of Flywheels
    19.2 Integration Technique
    19.3 Multi-Cylinder Engine Torque Summation
    19.4 Classification of Governors
    19.5 Centrifugal Governors
    19.6 Inertia Governors
    19.7 Mechanical Control Systems
    19.8 Standard Input Functions
    19.9 Solution of Linear Differential Equations
    19.10 Analysis of Proportional-Error Feedback Systems
    19.11 Introduction to Gyroscopes
    19.12 The Motion of a Gyroscope
    19.13 Steady or Regular Precession
    19.14 Forced Precession

    Appendix A: Tables
    Table 1 Standard SI Prefixes
    Table 2 Conversion from US Customary Units to SI Units
    Table 3 Conversion from SI Units to US Customary Units
    Table 4 Properties of Areas
    Table 5 Mass Moments of Inertia
    Table 6 Involute Function
    Appendix B: Answers to Selected Problems

Teaching Resources

* In-text CD includes Working Model animations of many figures from the text to help students visualize and comprehend their movement

* A companion website for instructors (www.oup.com/us/uicker) provides additional information and resources, including PowerPoint-based slides of figures from the text

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