Description:

Development Process of Simulation, Matrix Formulation of Kinematics, Different Coordinates for Description of Multibody Systems, Solution of Kinematical Loops, Numerical Methods for Solution of Multibody Kinematics, Kinematical Synthesis of Multibody Systems, Dynamics of Multibody Systems by Lagrange Equations of Mixed Type, Numerical Methods of DAE Solution, Advanced formulation of equations of motion of multibody systems
Practice of multibody modelling

Contents:

1 - Development Process of Simulation Model
Ideal objects of engineering sciences. Conceptual model, physical model, simulation model
2 - Matrix Formulation of Kinematics
Matrix of directional cosines, transformation, velocity and acceleration matrices. Basic motions, basic transformation matrices. Method of basic matrices
3 - Different Coordinates for Description of Multibody Systems
Independent and dependent, relative, Cartesian and physical coordinates. Euler angles, Cardan angles, Euler parameters. Kinematical description of open kinematic chain
4 - Solution of Kinematical Loops
Kinematical solution of kinematical loops by method of closed loop, method of disconnected loop, method of removed body, method of natural coordinates, method of compartments (physical coordinates)
5 - Numerical Methods for Solution of Multibody Kinematics
Position, velocity and acceleration problems. Solution of over- and under-constrained system of linear and nonlinear algebraic equations. Special and singular cases of multibody systems
6 - Kinematical Synthesis of Multibody Systems
Engineering design process, formulation of kinematical synthesis, solving procedures, optimization. Synthesis of vehicle suspensions
7 - Dynamics of Multibody Systems by Lagrange Equations of Mixed Type
Lagrange equations of mixed type, assembly of particular expressions. Multibody dynamic formalism by physical coordinates. Interpretation of Lagrange multipliers. Force elements for vehicle modelling
8 - Numerical Methods of DAE Solution
Numerical problems of solution of differential-algebraic equations (DAE). Solution in indepenedent and dependent coordinates, Baumgarte stabilization, coordinate partitioning, projection into independent coordinates
9 - Advanced formulation of equations of motion of multibody systems
Equivalence of Newton-Euler and Lagrange equations. Equations of motion of small vibrations. Dynamics of flexible multibody systems.
10 - Practice of multibody modelling
Multibody modelling for different multibody dynamic formalisms. Example of modelling in Simpack. Modelling of vehicle suspension, modelling of vehicle dynamics

Recommended literature:

1. Lecturing material and hand-outs
2. Stejskal, V., Valasek, M.: Kinematics and Dynamics of Machinery, Marcel Dekker, New York 1996 (basis textbook)

Keywords:

Kinematics, Dynamics, Multibody Systems, Lagrange Equations of Mixed Type, Modelling

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar