$24.00

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Screw Theory in Robotics

An Illustrated and Practicable Introduction to Modern Mechanics

- Available for pre-order. Item will ship after November 24, 2021

## Preview

## Book Description

Screw theory is an effective and efficient method used in robotics applications. This book demonstrates how to implement screw theory, explaining the key fundamentals and real-world applications using a practical and visual approach.

An essential tool for those involved in the development of robotics implementations, the book uses case studies to analyse mechatronics. Screw theory offers a significant opportunity to interpret mechanics at a high level, facilitating contemporary geometric techniques in solving common robotics issues. Using these solutions results in an optimised performance in comparison to algebraic and numerical options. Demonstrating techniques such as 6D vector notation and the Product of Exponentials (POE), the use of screw theory notation reduces the need for complex algebra, which results in simpler code, which is easier to write, comprehend and debug. The book provides exercises and simulations to demonstrate this, with new formulas and algorithms presented to aid the reader in accelerating their learning. Through walking the user through the fundamentals of screw theory and providing a complete set of examples for the most common robot manipulator architecture, it delivers an excellent foundation through which to comprehend screw theory developments.

The visual approach of the book means it can be used as a self-learning tool for professionals alongside students. It will be of interest to those studying robotics, mechanics, mechanical engineering and electrical engineering.

## Table of Contents

Preface Acknowledgments List of Acronyms and Abbreviations 1. Introduction 1.1 Motivation 1.2 About this Book 1.3 Preview 1.4 Audience 1.5 Further Reading 2. Mathematical Tools 2.1 Rigid Body Motion 2.2 Homogeneous Representation 2.2.1 Exercise: Homogeneous Rotation 2.2.2 Exercise: Homogeneous Rotation plus Translation 2.3 Exponential Representation 2.3.1 Exercise: Exponential Rotation 2.3.2 Exercise: Exponential Rotation plus Translation 2.4 Summary 3. Forward Kinematics 3.1 Problem Statement in Robotics 3.2 Denavit-Hartenberg Convention 3.2.1 Puma robots (e.g., ABB IRB120) 3.3 Product of Exponentials Formulation 3.3.1 General Solution to Forward Kinematics 3.3.2 Puma robots (e.g., ABB IRB120) 3.3.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 3.3.4 Bending backwards robots (e.g., ABB IRB1600) 3.3.5 Gantry robots (e.g., ABB IRB6620LX) 3.3.6 Scara robots (e.g., ABB IRB910SC) 3.3.7 Collaborative robots (e.g., UNIVERSAL UR16e) 3.3.8 Redundant robots (e.g., KUKA IIWA) 3.3.9 Many DoF robots (e.g., RH0 UC3M Humanoid) 3.4 Summary 4. Inverse Kinematics 4.1 Problem Statement in Robotics and Analytical Difficulty 4.2 Numeric vs. Geometric Solutions 4.2.1 Puma robot Inverse Kinematics algorithms 4.3 Canonical subproblems for Inverse Kinematics 4.3.1 Paden-Kahan subproblem One (PK1) – one rotation 4.3.2 Paden-Kahan subproblem Two (PK2) – two crossing rotations 4.3.3 Paden-Kahan subproblem Three (PK3) – rotation to a distance 4.3.4 Pardos-Gotor subproblem One (PG1) – one translation 4.3.5 Pardos-Gotor subproblem Two (PG2) – two crossing translations 4.3.6 Pardos-Gotor subproblem Three (PG3) – translation to a distance 4.3.7 Pardos-Gotor subproblem Four (PG4) – two parallel rotations 4.3.8 Pardos-Gotor subproblem Five (PG5) – rotation of a line or plane 4.3.9 Pardos-Gotor subproblem Six (PG6) – two skewed rotations 4.3.10 Pardos-Gotor subproblem Seven (PG7) – three rotations to a point 4.3.11 Pardos-Gotor subproblem Eight (PG8) – three rotations to a pose 4.4 Product of Exponentials Approach 4.4.1 General Solution to Inverse Kinematics 4.4.2 Puma robots (e.g., ABB IRB120) 4.4.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 4.4.4 Bending backwards robots (e.g., ABB IRB1600) 4.4.5 Gantry robots (e.g., ABB IRB6620LX) 4.4.6 Scara robots (e.g., ABB IRB910SC) 4.4.7 Collaborative robots (e.g., UNIVERSAL UR16e) 4.4.8 Redundant robots (e.g., KUKA IIWA) 4.4.9 Many DoF robots (e.g., RH0 UC3M Humanoid) 4.5 Summary 5. Differential Kinematics 5.1 Problem Statement in Robotics 5.2 The Analytic Jacobian 5.2.1 Scara robot (e.g., ABB IRB910SC) 5.2.2 Puma robot (e.g., ABB IRB120) 5.3 The Geometric Jacobian 5.3.1 General solution to Differential Kinematics 5.3.2 Puma robots (e.g., ABB IRB120) 5.3.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 5.3.4 Bending backwards robots (e.g., ABB IRB1600) 5.3.5 Gantry robots (e.g., ABB IRB6620LX) 5.3.6 Scara robots (e.g., ABB IRB910SC) 5.3.7 Collaborative robots (e.g., UNIVERSAL UR16e) 5.3.8 Redundant robots (e.g., KUKA IIWA) 5.4 Summary 6. Inverse Dynamics 6.1 Problem Statement in Robotics 6.2 The Lagrange Characterization 6.2.1 General Non-recursive Solution to Inverse Dynamics 6.2.2 Puma robots (e.g., ABB IRB120) 6.2.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 6.2 4 Bending backwards robots (e.g., ABB IRB1600) 6.2.5 Gantry robots (e.g., ABB IRB6620LX) 6.2.6 Scara robots (e.g., ABB IRB910SC) 6.2.7 Collaborative robots (e.g., UNIVERSAL UR16e) 6.2.8 Redundant robots (e.g., KUKA IIWA) 6.3 Robot Dynamics Control 6.4 Spatial Vector Algebra 6.5 The Newton-Euler Equations 6.5.1 General Recursive Solution to Inverse Dynamics RNEA with POE 6.5.2 Puma robots (e.g., ABB IRB120) 6.5.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 6.5 4 Bending backwards robots (e.g., ABB IRB1600) 6.5.5 Gantry robots (e.g., ABB IRB6620LX) 6.5.6 Scara robots (e.g., ABB IRB910SC) 6.5.7 Collaborative robots (e.g., UNIVERSAL UR16e) 6.5.8 Redundant robots (e.g., KUKA IIWA) 6.6 Summary 7. Trajectory Generation 7.1 Concepts and Definitions 7.2 Trajectory Planning 7.2.1 General Solution to Trajectory Generation 7.2.2 Puma robots (e.g., ABB IRB120) 7.2.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 7.2 4 Bending backwards robots (e.g., ABB IRB1600) 7.2.5 Gantry robots (e.g., ABB IRB6620LX) 7.2.6 Scara robots (e.g., ABB IRB910SC) 7.2.7 Collaborative robots (e.g., UNIVERSAL UR16e) 7.2.8 Redundant robots (e.g., KUKA IIWA) 7.3 Summary 8. Robotics Simulation 8.1 Robotics Simulation 8.2 Screw Theory Toolbox for Robotics (ST24R) 8.3 Forward Kinematics Simulations 8.3.1 General Solution to Forward Kinematics Simulation 8.3.2 Puma robots (e.g., ABB IRB120) 8.3.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 8.3 4 Bending backwards robots (e.g., ABB IRB1600) 8.3.5 Gantry robots (e.g., ABB IRB6620LX) 8.3.6 Scara robots (e.g., ABB IRB910SC) 8.3.7 Collaborative robots (e.g., UNIVERSAL UR16e) 8.3.8 Redundant robots (e.g., KUKA IIWA) 8.4 Inverse Kinematics Simulations 8.4.1 General Solution to Inverse Kinematics Simulation 8.4.2 Puma robots (e.g., ABB IRB120) 8.4.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 8.4 4 Bending backwards robots (e.g., ABB IRB1600) 8.4.5 Gantry robots (e.g., ABB IRB6620LX) 8.4.6 Scara robots (e.g., ABB IRB910SC) 8.4.7 Collaborative robots (e.g., UNIVERSAL UR16e) 8.4.8 Redundant robots (e.g., KUKA IIWA) 8.5 Differential Kinematics Simulations 8.5.1 General Solution to Differential Kinematics Simulation 8.3.2 Puma robots (e.g., ABB IRB120) 8.5.3 Puma robots(e.g., ABB IRB120) "Tool-Up" 8.5.4 Bending backwards robots (e.g., ABB IRB1600) 8.5.5 Gantry robots (e.g., ABB IRB6620LX) 8.5.6 Scara robots (e.g., ABB IRB910SC) 8.5.7 Collaborative robots (e.g., UNIVERSAL UR16e) 8.5.8 Redundant robots (e.g., KUKA IIWA) 8.6 Inverse Dynamics Simulations 8.6.1 General Solution to Inverse Dynamics Simulation 8.6.2 Puma robots (e.g., ABB IRB120) 8.6.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 8.6 4 Bending backwards robots (e.g., ABB IRB1600) 8.6.5 Gantry robots (e.g., ABB IRB6620LX) 8.6.6 Scara robots (e.g., ABB IRB910SC) 8.6.7 Collaborative robots (e.g., UNIVERSAL UR16e) 8.6.8 Redundant robots (e.g., KUKA IIWA) 8.7 Summary 9. Conclusions 9.1 Summary 9.1.1 Introduction 9.1.2 Mathematical Tools 9.1.3 Forward Kinematics 9.1.4 Inverse Kinematics 9.1.5 Differential Kinematics 9.1.6 Inverse Dynamics 9.1.7 Trajectory Generation 9.1.8 Robotics Simulation 9.2 Future Prospects Bibliography & References Epilogue

## Author(s)

### Biography

Dr. Jose M. Pardos-Gotor is Associate Professor at University Carlos III of Madrid. He also works for the multinational Enel group and has developed projects in Europe and Latin America in Change Management, Sustainability, Innovation, R&D, Commodity Markets & Trading, Energy Management, and Power Generation. He teaches and researches production systems, industrial automation, and robotics.