In the name of GOD

Sharif University of Technology

Department of Aerospace Engineering

Computational MultiBody Dynamics

Aero 45-946

Instructor:

Hassan Haddadpour

Haddadpour@sharif.edu

Course Objectives:

In this course we will cover a systematic approach to the generation and solution of equations of motion for mechanical systems consisting of multiple interconnected rigid bodies, the so-called multibody systems. The emphasis is on the computer formulation and solution of the governing equations of motion, using a Cartesian coordinate approach (like Working Model, DADS, ADAMS, …).

Prerequisites by Topic:

1. An understanding of dynamics.
2. An understanding of mathematics

Syllabus:

1. Introduction

· Computer Aided Design

· Conventional Methods of Kinematics and Dynamics Analysis

· Objective of Computational Kinematics and Dynamics

2. Vector, Matrices, and Differential Calculus

· Geometric Vector

· Matrix Algebra

· Algebraic Vectors

· Transformation of Coordinates

· Vector and Matrix Differentiation

· Velocity and Acceleration of a Point Fixed in a Moving Frame 

3. Planer Kinematics
• Basic Concepts in Kinematics
• Constraints between Pair of Bodies
• Revolute, Translation, and Composite joints, Gears and Cam-Followers
• Driving Constraints
• Position, Velocity, and Acceleration Analysis
• Singular Configurations
4. Numerical Methods in Kinematics

· Organization of Computations

· Evaluation of Constraint Equations and Jacobian

· Assembly of a System

· Linear Equation Solution and Matrix Factorization

· Newton-Raphson Method for Nonlinear Equations

· Redundant Constraints Detection and Elimination

5. Dynamics of Planner Systems
• Equations of Motion of a Planar Rigid Body
• Virtual Work and Generalized Force
• Equation of Motion of Constrained Planner systems
• Inverse Dynamics of Kinematically Driven Systems
• Forward Dynamics
• Equilibrium Conditions
• Constraints Reaction Forces
6. Numerical Methods in Dynamics

· Organization of Computations

• Solution of Mixed Differential-Algebraic Equations of Motion
• Algorithms for Solving Differential-Algebraic Equations
• Numerical Integration of First Order Initial Value Problems

Course Outcomes:

Students who successfully complete the course will demonstrate the following outcomes.

1. Analyze multibody kinematics and dynamics using computational methods.
2. Become familiar with generalized coordinates, constraint vectors and differential-algebraic equations.
3. Improve knowledge of applied numerical methods in mechanisms analysis.
4. Achieve a working understanding of these issues applied to various mechanical systems.
5. Improve knowledge in working with commercial software such as Working Model, DADS, ADAMS, ….

Grading:

Homework Sets: 20 %

Midterm Exam: 20 %

Project: 40 %

Final Exam: 20 %

Text:

The two main references are:

• P. E. Nikravesh Computer-Aided Analysis of Mechanical Systems Prentice-Hall, 1988 (also translated in Persian). 
• Haug, E.J., Computer Aided Kinematics and Dynamics of Mechanical Systems, Part I: Basic Methods, Allyn & Bacon, Boston, 1989.