Screw theory and its application to spatial robot manipulators / Carl D. Crane, Michael Griffis, Joseph Duffy.

Format:

Book

Author/Creator:

Crane, Carl D. (Carl David), 1956- author.

Griffis, Michael, author.

Duffy, Joseph, 1937-2002, author.

Language:

English

Subjects (All):

Screws, Theory of.

Machinery, Kinematics of.

Robots.

Physical Description:

1 online resource (xiii, 206 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2022.

Summary:

Discover a fresh take on classical screw theory and understand the geometry embedded within robots and mechanisms with this essential text. The book begins with a geometrical study of points, lines, and planes and slowly takes the reader toward a mastery of screw theory with some cutting-edge results, all while using only basic linear algebra and ordinary vectors. It features a discussion of the geometry of parallel and serial robot manipulators, in addition to the reciprocity of screws and a singularity study. All 41 essential screw systems are unveiled, establishing the possible freedom twists and constraint wrenches for a kinematic joint. Familiarizing the reader with screw geometry in order to study the statics and kinematics of robots and mechanisms, this is a perfect resource for engineers and graduate students.

Contents:

Cover

Half-title

Title page

Copyright information

Contents

Preface

1 Geometry of Points, Lines, and Planes

1.1 Introduction

1.2 The Position Vector of a Point

1.3 The Equation of a Plane

1.3.1 Sample Problem

1.3.2 Sample Problem

1.4 Projection of a Point onto a Plane

1.5 The Equation of a Line

1.5.1 Sample Problem

1.6 Two Planes Determine a Line

1.7 The Pencil of Planes through a Line

1.7.1 The Plane Defined by a Line and a Point

1.7.2 The Plane That Contains a Line and Is Parallel to a Second Line

1.7.3 The Plane Defined by a Pair of Parallel Lines

1.8 A Line and a Plane Determine a Point

1.9 Determination of the Point on a Line That Is Closest to a Given Point

1.10 The Mutual Moment of Two Lines

1.10.1 Numerical Example

1.11 Determination of the Unique Perpendicular Line to Two Given Lines

1.12 A Pair of Intersecting Lines

1.12.1 Approach 1

1.12.2 Approach 2

1.13 Summary

1.14 Problems

2 Coordinate Transformations and Manipulator Kinematics

2.1 Introduction

2.2 Relative Pose of Two Coordinate Systems

2.3 Transformations of Points

2.4 Inverse of a Transform

2.5 Standard Transformations

2.6 General Transformations

2.6.1 Determination of Equivalent Rotation Matrix

2.6.2 Determination of Axis and Angle of Rotation

2.7 Transformation of Direction Vectors

2.8 Transformation of Lines

2.9 Transformations of Planes

2.10 Spatial Links and Joints

2.10.1 Spatial Link

2.10.2 Revolute Joint (R)

2.10.3 Prismatic Joint (P)

2.10.4 Cylindrical Joint (C)

2.10.5 Screw Joint (H)

2.10.6 Higher Order Joints

2.11 Labeling of a Kinematic Chain

2.11.1 Step 1: Label the Joint Axis Vectors

2.11.2 Step 2: Label the Link Vectors

2.11.3 Step 3: Label the Joint Angles and Twist Angles.

2.11.4 Step 4: Label the Offset and Link Lengths

2.11.5 Step 5: Compilation of Mechanism Parameters

2.12 Standard Link Coordinate Systems

2.13 Summary

2.14 Problems

3 Statics of a Rigid Body

3.1 Introduction

3.2 The Coordinates of a Force

3.3 The Coordinates of a Couple

3.4 Translation of a Force: Equivalent Force/Couple Combination

3.5 A Dyname and a Wrench

3.5.1 Sample Problem

3.6 Transformation of Screw Coordinates

3.6.1 Sample Problem

3.7 Forward and Reverse Static Analysis of In-Parallel Platform Devices

3.8 Forward and Reverse Static Analysis of a Serial Manipulator

3.8.1 Sample Problem

3.8.2 Sample Problem

3.9 The Resultant of a Pair of Wrenches Acting Upon a Rigid Body

3.10 The Cylindroid

3.11 Circular Representation of the Cylindroid

3.12 Motor Product

3.13 Problems

4 Velocity Analysis

4.1 Introduction

4.2 Time Derivative of a Vector

4.2.1 Case 1: Points A and B Embedded in Body 0

4.2.2 Case 2: Point A Embedded in Body 0 and Point B Embedded in Body 1

4.2.3 Case 3: Points A and B Embedded in Body 1

4.2.4 Case 4: Point A Embedded in Body 1 and Point B Embedded in Body 2

4.2.5 Case 5: Derivatives of a Vector with Respect to Two Coordinate Systems

4.3 Definition of Velocity State

4.4 Screw Interpretation of Velocity State

4.4.1 Example Problem 1

4.4.2 Example Problem 2

4.4.3 Example Problem 3

4.4.4 Example Problem 4

4.5 Serial Chain of Three Rigid Bodies

4.6 Serial Chain of Multiple Rigid Bodies

4.7 Forward and Reverse Velocity Analyses for Serial Manipulators

4.7.1 Example Problem

4.7.2 Example Problem

4.8 Problems

5 Reciprocal Screws

5.1 Introduction

5.2 Definition of Reciprocal Screws

5.3 Reciprocal Product

5.3.1 Axes of the Two Screws Intersect

5.3.2 Axes Are Perpendicular

5.3.3 Axes Are Parallel.

5.3.4 Body Constrained in Translation

5.4 Reciprocal Screw Systems

5.4.1 A Single Screw: One Degree of Freedom

5.4.2 Two Screws: Two Degrees of Freedom

5.4.3 Three Screws: Three Degrees of Freedom

5.4.4 Four Screws: Four Degrees of Freedom

5.4.5 Five Screws: Five Degrees of Freedom

5.4.6 Six Screws: Six Degrees of Freedom

5.4.7 Example Problem 1

5.4.8 Example Problem 2

5.4.9 Example Problem 3

5.4.10 Example Problem 4

5.4.11 Example Problem 5

5.5 Velocity Analysis of Serial Manipulators Using Reciprocal Screws

5.5.1 Example Problem

5.6 Forward and Reverse Velocity Analysis for Parallel Mechanisms

5.6.1 Reverse Velocity Analysis

5.6.2 Forward Velocity Analysis

5.6.3 Example Problem

5.7 Problems

6 Singularity Analysis of Serial Chains

6.1 Introduction

6.2 Singular Configurations

6.3 Symbolic Expansion of Screw Coordinates

6.4 Selection of Coordinate System

6.5 Example Problems

6.5.1 Cincinnati Milacron T3-776 Manipulator

6.5.2 G.E. P60 Manipulator

6.6 Problems

7 Acceleration Analysis of Serially Connected Rigid Bodies

7.1 Introduction

7.2 General Case of Two Bodies

7.3 General Case of Three Bodies

7.4 General Case of Four Bodies

7.5 General Case of n Bodies

7.6 Two Bodies Connected by a Screw Joint

7.7 Two Bodies Connected by a Revolute Joint

7.8 Two Bodies Connected by a Prismatic Joint

7.9 Forward Acceleration Analysis for Serial Manipulators

7.9.1 Sample Problem

7.10 Reverse Acceleration Analysis for Serial Manipulators

7.10.1 Sample Problem

7.11 Problems

Appendix A Derivation of Cylindroid Equations

Bibliography

Index.

Notes:

Title from publisher's bibliographic system (viewed on 12 Sep 2022).

Includes bibliographical references and index.

Other Format:

Print version: Crane, Carl D., III Screw Theory and Its Application to Spatial Robot Manipulators

ISBN:

1-139-01921-X

1-009-30176-4