Planar Multibody Dynamics: Formulation. Programming with MATLAB® and Applications – Parviz E. Nikravesh – 2nd Edition

Preface
Acknowledgments
Author
1. Introduction
1.1 Multibody Mechanical Systems1
1.2 Types of Analyses
1.3 Methods of Formulation
1.4 Computer Programs
2. Preliminaries
2.1 Reference Axes
2.2 Scalars and Vectors
2.2.1 Arrays
2.3 Matrices
2.3.1 Matrix Operations
2.3.2 Linear Algebraic Equations
2.4 Vector, Array, and Matrix Differentiation
2.4.1 Time Derivatives
2.4.2 Partial Derivatives
2.5 Equations and Expressions
2.5.1 Compact and Expanded Forms
2.6 Problems
3. Fundamentals of Planar Kinematics
3.1 A Particle
3.1.1 Kinematics of a Particle
3.2 Kinematics of a Rigid Body
3.2.1 Coordinates of a Body
3.2.2 Velocity of a Body
3.2.3 Acceleration of a Body
3.3 Definitions
3.3.1 Array of Coordinates
3.3.2 Degrees of Freedom
3.3.3 Constraint Equations
3.3.4 Kinematic Joints
3.4 Problems
4. Fundamentals of Planar Dynamics
4.1 Newton’s Laws of Motion
4.2 Particle Dynamics
4.2.1 Dynamics of a System of Particles
4.3 Rigid body Dynamics
4.3.1 Moment of a Force and Torque
4.3.2 Centroidal Equations of Motion
4.3.3 Noncentroidal Equations of Motion
4.4 Multibody Dynamics
4.4.1 Applied Forces
4.4.2 Reaction Forces
4.5 Friction Force
4.5.1 Wheel and Tire
4.5.2 Motor and Driver
4.6 Work and Energy
4.7 Problems
References
5. Vector Kinematics
5.1 Use of Vectors
5.1.1 Unit Vectors
5.1.2 Types of Vectors
5.2 Open-Chain Systems
5.3 Closed-Chain Systems
5.3.1 Slider-Crank Mechanism
5.3.2 Four-Bar Mechanism
5.3.3 Six-Bar Quick-Return Mechanism
5.3.4 Six-Bar Dwell Mechanism
5.3.5 Complete Kinematic Analysis
5.4 Problems
6. Free-Body Diagram
6.1 FBD Examples
6.1.1 Two-Body System (Unconstrained)
6.1.2 Two-Body System (Constrained)
6.1.3 Sliding Pendulum
6.1.4 Slider-Crank Mechanism
6.1.5 Four-Bar Mechanism
6.2 Equations of Motion
6.3 Force Analysis
6.3.1 Slider-Crank Mechanism
6.3.2 Four-Bar Mechanism
6.3.3 Generalization of Force Analysis
6.4 Problems
7. Body-Coordinate Formulation
7.1 General Procedure
7.2 Kinematic Joints
7.2.1 Revolute (Pin) Joint
7.2.2 Translational (Sliding) Joint
7.2.3 Revolute–Revolute Joint
7.2.4 Revolute–Translational Joint
7.2.5 Rigid Joint
7.2.6 Simple Constraints
7.2.7 Circular Disc
7.2.8 Driver Constraints
7.2.9 System Jacobian
7.3 Unconstrained Equations of Motion
7.4 Constrained Equations of Motion
7.4.1 Reaction Forces and Lagrange Multipliers
7.5 Total Energy
7.6 Problems
8. Body-Coordinate Simulation Program
8.1 Application Examples
8.1.1 Double A-Arm Suspension
8.1.2 MacPherson Suspension
8.1.3 Cart
8.1.4 Conveyor Belt and Friction
8.1.5 Rod Impacting Ground
8.2 Problems
9. Joint-Coordinate Formulation
9.1 Definitions
9.1.1 Joint Coordinate and Joint Reference Point
9.1.2 Recursive Kinematics
9.2 Open-Chain Systems
9.2.1 Absolute Angle
9.2.2 Equations of Motion
9.3 Closed-Chain Systems
9.3.1 Cut-Joint Constraints
9.3.2 Equations of Motion
9.3.3 Jacobian Matrix
9.3.4 Initial Conditions
9.3.5 Reaction Forces
9.3.6 Driver Constraint
9.4 A MATLAB Program
9.5 Problems
10. Point-Coordinate Formulation
10.1 Classical Method
10.2 Primary and Stationary Points
10.3 Constraints
10.3.1 Length Constraint
10.3.2 Angle Constraints
10.3.3 Simple Constraints
10.4 Secondary Points
10.5 Equations of Motion
10.6 Force and Torque Distribution
10.7 Mass Distribution
10.8 Mass Condensation
10.8.1 Two Primary Points
10.8.2 Three Primary Points
10.9 Force and Mass Addition
10.10 Problems
11. Contact and Impact
11.1 Piecewise Analysis
11.1.1 Momentum
11.1.2 Impact of Particles
11.1.3 Unconstrained Bodies
11.1.4 Constrained Bodies
11.1.5 Impact with Friction
11.2 Continuous Analysis
11.2.1 A Body Contacting a Rigid Surface
11.2.2 Two-Body Contact
11.3 Problems
References
12. Kinematics and Inverse Dynamics
12.1 Kinematic Analysis
12.1.1 Solution Procedures
12.1.2 Nonlinear Algebraic Equations
12.1.3 A Program for Four-Bar Kinematics
12.2 Inverse Dynamic Analysis
12.2.1 A Program for Four-Bar Inverse Dynamics
12.2.2 Application in Robotics
12.3 Problems
Reference
13. Forward Dynamics
13.1 Unconstrained Formulation
13.1.1 Initial Value Problem
13.1.2 Runge–Kutta Algorithm
13.1.3 Integration Time-Step Size
13.1.4 General Procedure
13.2 Constrained Formulation
13.2.1 Initial Conditions
13.2.2 General Integration Procedure
13.3 Constraint Violation
13.3.1 Constraint Violation Stabilization Method
13.3.2 Coordinate Partitioning Method
13.3.3 Penalty Method
13.3.4 Joint-Coordinate Method
13.3.5 Momentum Method
13.4 Contact and Impact
13.5 Adding or Deleting Constraints
13.6 Combined Analyses
13.7 Problems
References
14. Complementary Analyses
14.1 Static Analysis
14.2 Static Equilibrium
14.3 Initial Condition Correction
14.4 Redundant Constraints
14.5 Friction
14.6 Deformable Body
14.7 Problems
15. Application Examples
15.1 Film-Strip Advancer
15.2 Web-Cutter Mechanism
15.3 Six-Bar Quick-Return Mechanism
15.4 Six-Bar Dwell Mechanism
15.5 Windshield Wiper Mechanism
15.6 Double A-Arm Suspension
15.7 MacPherson Strut Suspension
15.8 Half-Car
15.9 Mountain Bike
15.10 Motorcycle
15.11 Dump Truck
15.12 Creeping Robot
15.13 Sled Test and Belted Dummy
15.14 Head and Neck
15.15 Elliptical Exercise Machine
15.16 Swing
15.17 Satellite Panels
Appendix A: L-U Factorization
Appendix B: Dynamic Analysis Program: Body Coordinates (DAP_BC)
Appendix C: Dynamic Analysis Program: Joint Coordinates (DAP_JC)
Index