Rational Kinematics

ISBN-13: 9781461284000 / Angielski / Miękka / 2011 / 121 str.

Jorge Angeles

Opis

The purpose of this book is to present kinematics of rigid bodies and systems in an axiomatic framework, stressing invariant relations. The audience addressed is engineers, mathematicians and computer scientists working in research and development that involves rigid-body motions. The areas of application are robotics, mechanism design, spacecraft dynamics, computer graphics, solid modelling, finite elements, etc. The most important features of the book are its axiomatic approaches on invariant principles, thus departing from a common but obscure practice of studying general principles based on component-form relations. The book fills the gap between rigid-body kinematics and the theory of kinematic chains, including results published for the first time. The reader can derive the following benefits from this book: a sound theoretical formulation of rigid-body kinematics following an axiomatic presentation, i.e., definitions, theorems and corollaries are given in logical order, the necessary proofs being included after each theorem and corollary. Invariant relations between the time rates of change of the rotation invariants and angular velocity and acceleration are derived. These can be useful to those writing computational algorithms for the simulation, control and graphic display of motions of mechanical systems in a great variety of fields.

Spis treści

1 Preliminary Notions.- 1.1 Introduction.- 1.2 On Notation and Basic Definitions.- 1.3 Further Definitions.- 1.4 Invariance.- 1.5 Generalized Inverses.- 2 Displacement of a Rigid Body.- 2.1 Introduction.- 2.2 Rotation of a Rigid Body About a Fixed Point.- 2.3 The Theorem of Euler.- 2.4 The Rotation Tensor.- 2.5 General Motion of a Rigid Body. The Pose and the Screw of a Rigid Body.- 2.6 Theorems About the General Motion of a Rigid Body.- 2.7 Compatibility Equations.- 3 Velocity Analysis of Rigid-Body Motions.- 3.1 Introduction.- 3.2 Motion of a Rigid Body About a Fixed Point.- 3.3 General Instantaneous Motion of a Rigid Body. The Twist of a Rigid Body.- 3.4 Further Results on the Velocity Distribution Throughout a Rigid Body.- 3.5 Compatibility Equations.- 4 Acceleration Analysis of Rigid-Body Motions.- 4.1 Introduction.- 4.2 Acceleration Field of a Body Moving About a Fixed Point.- 4.3 Acceleration Field of a Rigid Body Under General Motion.- 4.4 Change of Observer. Coriolis’ Theorem.- 4.5 Determination of Angular Acceleration. Compatibility Equations.- 5 Kinematic Chains.- 5.1 Introduction.- 5.2 Kinematic Pairs. Classification.- 5.3 Simple Kinematic Chains. Degree of Freedom by Groups of Motion.- 5.4 The Twist of a Link and the Jacobian of a Simple Kinematic Chain.- 5.4.1 Example 1.- 5.4.2 Example 2.- 5.5 The Condition Number of a Kinematic Chain. Isotropy.- 5.6 Complex Kinematic Chains. An Overview.- 5.7 The Jacobian of a Multiple-Closed-Loop Kinematic Chain. Degree of Freedom.- 5.8 Holonomic and Nonholonomic Constraints.- 5.9 Analysis of Kinematic Chains.- 5.10 Synthesis of Kinematic Chains.- 5.10.1 The Function-Generation Synthesis Problem.- 5.10.2 Kinematic Synthesis for Rigid-Body Guidance.- 5.10.3 Kinematic Synthesis for Path Generation.- References.