Rigid body dynamics algorithms

Rigid Body Dynamics Algorithms presents the subject of computational rigid-body dynamics through the medium of spatial 6D vector notation. It explains how to model a rigid-body system and how to analyze it, and it presents the most comprehensive collection of the best rigid-body dynamics algorithms to be found in a single source. The use of spatial vector notation greatly reduces the volume of algebra which allows systems to be described using fewer equations and fewer quantities. It also allows problems to be solved in fewer steps, and solutions to be expressed more succinctly. In addition algorithms are explained simply and clearly, and are expressed in a compact form. The use of spatial vector notation facilitates the implementation of dynamics algorithms on a computer: shorter, simpler code that is easier to write, understand and debug, with no loss of efficiency. Unique features include: • A comprehensive collection of the best rigid-body dynamics algorithms • Use of spatial (6D) vectors to greatly reduce the volume of algebra, to simplify the treatment of the subject, and to simplify the computer code that implements the algorithms • Algorithms expressed both mathematically and in pseudocode for easy translation into computer programs • Source code for many algorithms available on the internet Rigid Body Dynamics Algorithms is aimed at readers who already have some elementary knowledge of rigid-body dynamics, and are interested in calculating the dynamics of a rigid-body system. This book serves as an algorithms recipe book as well as a guide to the analysis and deeper understanding of rigid-body systems. The purpose of this book is to present computationally efficient algorithms for calculating the dynamics of robot mechanisms represented as systems of rigid bodies. The efficiency is achieved by the use of recursive formulations of the equations of motion, i.e. formulations in which the equations of motion are expressed implicitly in terms of recurrence relations between the quantities describing the system. The use of recursive formulations in dynamics is fairly new, 50 the principles of their operation and reasons for their efficiency are explained. Three main algorithms are described: the recursIve Newton-Euler formulation for inverse dynamics (the calculation of the forces given the accelerations), and the composite-rigid-body and articulated-body methods for forward dynamics (the calculation of the accelerations given the forces). These algorithms are initially described in terms of an un-branched, open­ loop kinematic chain -- a typical serial robot mechanism. This is done to keep the descriptions of the algorithms simple, and is in line with descriptions appearing in the literature. Once the basic algorithms have been introduced, the restrictions on the mechanism are lifted and the algorithms are extended to cope with kinematic trees and loops, and general constraints at the joints. The problem of simulating the effect of contact between a robot and its environment is also considered. Some consideration is given to the details and practical problems of implementing these algori?hms on a computer. Rigid Body Dynamics Presents The Subject Of Computational Rigid-body Dynamics Through The Medium Of Spatial 6d Vector Notation. It Explains How To Model A Rigid-body System And How To Analyze It, And It Presents The Most Comprehensive Collection Of The Best Rigid-body Dynamics Algorithms To Be Found In A Single Source. The Use Of Spatial Vector Notation Greatly Reduces The Volume Of Algebra Which Allows Systems To Be Described Using Fewer Equations And Fewer Quantities. It Also Allows Problems To Be Solved In Fewer Steps, And Solutions To Be Expressed More Succinctly. In Addition Algorithms Are Explained Simply And Clearly, And Are Expressed In A Compact Form. The Use Of Spatial Vector Notation Facilitates The Implementation Of Dynamics Algorithms On A Computer: Shorter, Simpler Code That Is Easier To Write, Understand And Debug, With No Loss Of Efficiency. Rigid Body Dynamics Algorithms Is Aimed At Readers Who Already Have Some Elementary Knowledge Of Rigid-body Dynamics, And Are Interested In Calculating The Dynamics Of A Rigid-body System. This Book Serves As An Algorithms Recipe Book As Well As A Guide To The Analysis And Deeper Understanding Of Rigid-body Systems.--book Jacket. ''Robot Dynamics Algorithms, Second Edition'' presents the subject of computational rigid-body dynamics through the medium of spatial (6D) vector notation. It explains how to model a rigid-body system and how to analyze it. The book is a comprehensive collection of the best rigid-body dynamics algorithms in a single source. This second edition includes nearly twice the content of the previous edition with algorithms shown explicitly in pseudocode and laid out in tables for easy implementation. It also has more algorithms than the previous edition including algorithms that exploit sparse matrices and ones for kinematic loops. New material on the mathematics of spatial (6D) vectors and how to analyze rigid-body systems using spatial vectors is covered. Finally there is an entire chapter devoted to how to build computer-oriented models of rigid-body systems.This book is for engineers with knowledge of rigid-body dynamics who are interested in calculating the dynamics of a rigid-body system. It is both an algorithms recipe book as well as a guide to the analysis and deeper understanding of rigid-body systems.