Kinematics, Dynamics, and Design of Machinery

Kinematics, Dynamics, and Design of Machinery, Third Edition, presents a fresh approach to kinematic design and analysis and is an ideal textbook for senior undergraduates and graduates in mechanical, automotive and production engineering * Presents the traditional approach to the design and analysis of kinematic problems and shows how GCP can be used to solve the same problems more simply * Provides a new and simpler approach to cam design * Includes an increased number of exercise problems * Accompanied by a website hosting a solutions manual, teaching slides and MATLAB(R) programs

PREFACE

1 INTRODUCTION

1.1 Historic Perspective

1.2 Kinematics

1.3 Design: Analysis and Synthesis

1.4 Mechanisms

1.5 Planar Linkages

1.6 Visualization

1.7 Constraint Analysis

1.8 Constraint Analysis of Spatial Linkages

1.9 Idle Degrees of Freedom

1.10 Overconstrained Linkages

1.11 Uses of the Mobility Criterion

1.12 Kinematic Inversion

1.13 Reference Frames

1.14 Motion Limits

1.15 Slider-Crank Linkages

1.16 Coupler-Driven Linkages

1.17 Motion Limits for Slider-Crank Mechanisms

1.18 Interference

1.19 Practical Design Considerations

1.19.1 Revolute Joints

1.19.2 Prismatic Joints

1.19.3 Higher Pairs

1.19.4 Cams versus Linkages

References

Problems

2 TECHNIQUES IN GRAPHICAL CONSTRAINT PROGRAMMING

2.1 Introduction

2.2 Geometric Constraint Programming

2.3 Constraints and Program Structure

2.3.1 Required Constraints

2.3.2 Other Constraint Options

2.3.3 Annotations

2.3.4 Use of Drawing Layers

2.3.5 Limitations of GCP

2.4 Initial Setup for a GCP Session

2.4.1 The Effect of Typical Constraints

2.4.2 Unintended Constraints

2.4.3 Layers, Line Type, and Line Color

2.5 Drawing a Basic Linkage Using GCP

2.5.1 Drawing a Four-Bar Linkage Using GCP

2.5.2 Including Ground Pivots and Bushings

2.5.3 Drawing a Slider-Crank Linkage

2.6 Troubleshooting Graphical Programs Developed Using GCP

References

Problems

3 PLANAR LINKAGE DESIGN

3.1 Introduction

3.2 Two-Position Double Rocker Design

3.2.1 Graphical Solution Procedure

3.2.2 Solution Using Graphical Constraint Programming

3.2.3 Numerical Solution Procedure

3.3 Synthesis of Crank-Rocker Linkages for Specified-Rocker Amplitude

3.3.1 The Rocker Amplitude Problem: Graphical Approach

3.3.2 Alternative Graphical Design Procedure Based on Specification of A*B*

3.3.3 Use of GCP To Design Crank-Rocker and Crank-Shaper Mechanisms

3.4 Motion Generation

3.4.1 Introduction

3.4.2 Two Positions

3.4.3 Three Positions with Selected Moving Pivots

3.4.4 Synthesis of a Crank with Chosen Fixed Pivots

3.4.5 Design of Slider Cranks and Elliptic Trammel

3.4.6 Order Problem and Change of Branch

3.4.7 Using GCP for Rigid-Body Guidance

3.5 Path Synthesis

3.5.1 Design of Six-Bar Linkages Using Coupler Curves

3.5.2 Motion Generation for Parallel Motion Using Coupler Curve

3.5.3 Cognate Linkages

3.5.4 Using GCP for Path Synthesis

References

Problems

4 GRAPHICAL POSITION, VELOCITY AND ACCELERATION ANALYSIS FOR MECHANISMS WITH REVOLUTE JOINTS AND FIXED SLIDES

4.1 Introduction

4.2 Graphical Position Analysis

4.3 Planar Velocity Polygons

4.4 Graphical Acceleration Analysis

4.5 Graphical Analysis of a Four-Bar Mechanism

4.6 Graphical Analysis of a Slider-Crank Mechanism

4.7 The Velocity Image Theorem

4.8 The Acceleration Image

4.9  Solution by Graphical Constraint Programming

4.9.1 Introduction

4.9.2 Scaling Properties of Velocity Polygons

4.9.3 Using GCP To Analyze Linkages That Cannot Be Analyzed by Classical Means

References

Problems

5 LINKAGES WITH ROLLING AND SLIDING CONTACTS, AND JOINTS ON MOVING SLIDERS

5.1 Introduction

5.2 Reference Frames

5.3 General Velocity and Acceleration Equations

5.3.1 Velocity Equations

5.3.2 Acceleration Equations

5.3.3 “Chain Rule for Positions, Velocities, and Accelerations

5.4 Special Cases for the Velocity and Acceleration Equations

5.4.1 Two Points Fixed in a Moving Body

5.4.2 Two Points Are Instantaneously Coincident

5.4.3 Two Are Instantaneously Coincident and In Rolling Contact

5.5 Linkages with Rotating Sliding Joints

5.6 Rolling Contact

5.6.1 Basic Kinematic Relationships for Rolling Contact

5.6.2 Modeling Rolling contact using a Virtual Linkage

5.7 Cam Contact

5.7.1 Direct Approach to the Analysis of Cam Contact

5.7.2 Analysis of Cam Contact Using Equivalent Linkages

5.8 General Coincident Points

5.8.1 Velocity Analyses Involving General Coincident Points

5.8.2 Acceleration Analyses Involving General Coincident Points

5.9 Solution by Graphical Constraint Programming

Problems

6 INSTANT CENTERS OF VELOCITY

6.1 Introduction

6.2 Definition

6.3 Existence Proof

6.4 Location of an Instant Center from the Directions of Two Velocities

6.5 Instant center at a Revolute Joint

6.6 Instant Center of a Curved Slider

6.7 Instant Center of a Prismatic Joint

6.8 Instant Center of a Rolling Contact Pair

6.9 Instant Center of a General Cam-Pair Contact

6.10 Centrodes

6.11 The Kennedy-Aronholdt Theorem

6.12 Circle Diagram as a Strategy for Finding Instant Centers

6.13 Using Instant Centers, the Rotating Radius Method

6.14 Finding Instant Centers Using GCP

References

Problems

7 COMPUTATIONAL ANALYSIS OF LINKAGES

7.1 Introduction

7.2 Position, Velocity, and Acceleration Presentations

7.2.1 Position Representation

7.2.2 Velocity Representation

7.2.3 Acceleration Representation

7.2.4 Special Cases

7.2.5 Mechanisms To Be Considered

7.3 Analytical Closure Equations for Four-Bar Linkages

7.3.1 Solution of Closure Equation for Four-Bar Linkages when Link 2 Is the Driver

7.3.2 Analysis When the Coupler (Link 3) Is the Driving Link

7.3.3 Velocity Equations for Four-Bar Linkages

7.3.4 Acceleration Equations for Four-Bar Linkages

7.4 Analytical Equations for a Rigid Body after the Kinematic Properties of Two Points Are Known

7.5 Analytical Equations for Slider-Crank Mechanisms

7.5.1 Solution to Position Equations When  Is Input

7.5.2 Solution to Position Equations When r Is Input

7.5.3 Solution to Position Equations When  Is Input

7.5.4 Velocity Equations for Slider-Crank Mechanism

7.5.5 Acceleration Equations for Slider-Crank Mechanism

7.6 Other 4-Bar Mechanisms with Revolute and Prismatic Joints

7.6.1 Slider-Crank Inversion

7.6.2 A RPRP Mechanism

7.6.3 A RRPP Mechanism

7.6.4 Elliptic Trammel

7.6.5 Oldham Mechanism

7.7 Closure or Loop Equation Approach for Compound Mechanisms

7.7.1 Handling Points Not on the Vector Loops

7.7.2 Solving the Position Equations

7.8 Closure Equations for Mechanisms with Higher Pairs

7.9 Notational Differences: Vectors and Complex Numbers

Problems

8 SPECIAL MECHANISMS

8.1 Special Planar Mechanisms

8.1.1 Introduction

8.1.2 Straight Line and Circle Mechanisms

8.1.3 Pantographs

8.2 Spherical Mechanisms

8.2.1 Introduction

8.2.2 Gimbals

8.2.3 Universal Joints

8.3 Constant Velocity Couplings

8.3.1 Geometric Requirements of Constant Velocity Couplings

8.3.2 Practical Constant Velocity Couplings

8.4 Automotive Steering and Suspension Mechanisms

8.4.1 Introduction

8.4.2 Steering Mechanisms

8.4.3 Suspension Mechanisms

8.5 Indexing Mechanisms

8.5.1 Geneva Mechanisms

References

Problems

9 SPATIAL LINKAGE ANALYSIS

9.1 Spatial Mechanisms

9.1.1 Introduction 497

9.1.2 Velocity and Acceleration Relationships

9.2 Robotic Mechanisms

9.3 Direct Position Kinematics of Serial Chains

9.3.1 Introduction

9.3.2 Concatenation of Transformations

9.3.3 Homogeneous Transformations

9.4 Inverse Position Kinematics

9.5 Rate Kinematics

9.5.1 Introduction

9.5.2 Direct Rate Kinematics

9.5.3 Inverse Velocity Problem

9.6 Closed Loop Linkages

9.7 Lower Pair Joints

9.8 Motion Platforms

9.8.1 Mechanisms Actuated in Parallel

9.8.2 The Stewart-Gough Platform

9.8.3 The 3-2-1 Platform

References

Problems

10 PROFILE CAM DESIGN

10.1 Introduction

10.2 Cam-Follower Systems40

10.3 Synthesis of Motion Programs

10.4 Analysis of Different Types of Follower Displacement Functions

10.4.1 Uniform Motion

10.4.2 Parabolic Motion

10.4.3 Harmonic Follower-Displacement Programs

10.4.4 Cycloidal Follower-Displacement Programs

10.4.5 General Polynomial Follower-Displacement Programs

10.5 Determining the Cam Profile

10.5.1 Graphical Cam Profile Layout

10.5.2 Analytical Determination of Cam Profile

References

Problems

11 SPUR GEARS

11.1 Introduction

11.2 Spur Gears

11.3 Condition for Constant-Velocity Ratio

11.4 Involutes

11.5 Gear Terminology and Standards

11.5.1 Terminology

11.5.2 Standards

11.6 Contact Ratio

11.7 Involutometry

11.8 Internal Gears

11.9 Gear Manufacturing

11.10 Interference and Undercutting

11.11 Nonstandard Gearing

11.12 Cartesian Coordinates of an Involute Tooth Generated with a Rack

11.12.1  Coordinate Systems

11.12.2  Gear Equations

References

Problems

12 HELICAL, BEVEL, AND WORM GEARS

12.1 Helical Gears

12.1.1 Helical Gear Terminology

12.1.2 Helical Gear Manufacturing

12.1.3 Minimum Tooth Number to Avoid Undercutting

12.1.4 Helical Gears with Parallel Shafts

12.1.5 Crossed Helical Gears

12.2 Worm Gears

12.2.1 Worm Gear Nomenclature

12.3 Involute Bevel Gears

12.3.1 Tredgold’s Approximation for Bevel Gears

12.3.2 Additional Nomenclature for Bevel Gears

12.3.3 Crown Bevel Gears and Face Gears

12.3.4 Miter Gear

12.3.5 Angular Bevel Gears

12.3.6 Zerol Bevel Gears

12.3.7 Spiral Bevel Gears

12.3.8 Hypoid Gears

References

Problems

13 GEAR TRAINS

13.1 Gear Trains

13.2 Direction of Rotation

13.3 Simple Gear Trains

13.2.1 Simple Reversing Mechanism

13.4 Compound Gear Trains

13.4.1 Concentric Gear Trains

13.5 Planetary Gear Trains

13.5.1 Planetary Gear Nomenclature

13.5.2 Analysis of Planetary Gear Trains Using Equations

13.5.3 Analysis of Planetary Gear Trains Using Tabular Method

13.6 Harmonic Speed Reducers

References

Problems

14 STATIC FORCE ANALYSIS OF MECHANISMS

14.1 Introduction

14.2 Forces, Moments, and Couples

14.3 Static Equilibrium

14.4 Free-Body Diagrams

14.5 Solution of Static Equilibrium Problems

14.6 Transmission Angle in a Four-Bar Linkage

14.7 Friction Considerations

14.7.1 Friction in Cam Contact

14.7.2 Friction in Slider Joints

14.7.3 Friction in Revolute Joints

14.8 In-Plane and Out-of-Plane Force Systems

14.9 Conservation of Energy and Power

14.10 Virtual Work

14.11 Gear Loads

14.11.1  Spur Gears

14.11.2  Helical Gears

14.11.3  Worm Gears

14.11.4  Straight Bevel Gears

Problems

15 DYNAMIC FORCE ANALYSIS

15.1 Introduction

15.2 Particle Kinetics

15.2.1 Dynamic Equilibrium of Systems of Particles

15.2.2 Conservation of Energy

15.2.3 Conservation of Momentum

15.3 Dynamic Equilibrium of Systems of Rigid Bodies

15.4 Flywheels

Problems

16 STATIC AND DYNAMIC BALANCING

16.1 Introduction

16.2 Single Plane (Static) Balancing

16.3 Multi-plane (Dynamic) Balancing

16.4 Balancing Reciprocating Masses

16.4.1 Expression for Lumped Mass Distribution

16.4.2 Balancing a Slider-Crank Mechanism

16.5 Expressions for Inertial Forces

16.6 Balancing Multi-Cylinder Machines

16.6.1 Balancing a Three-Cylinder In-Line Engine

16.6.2 Balancing an Eight Cylinder V Engine

16.7 Static Balancing of Mechanisms

16.7.1 Gravity Balancing of Planar Mechanisms: Examples

16.7.2 Gravity Balancing Orthosis (GBO)

16.8 Reactionless Mechanisms

References

Problems

17 INTEGRATION OF DIGITALLY CONTROLLED ACTUATORS

17.1 Introduction

17.2 Computer Control of Linkage Motion

17.3 The Basics of Feedback Control

17.4 Actuator Selection and Types

17.4.1 Electrical Actuation

17.4.2 Hydraulic Actuation

17.4.3 Pneumatic Actuation

17.5 Hands-on Design Laboratory

17.5.1 Examples of Class Projects

References

Problems

INDEX