Modeling and Simulation of Multibody Systems
Offered By: Université catholique de Louvain via edX
Course Description
Overview
What is the similarity between a car suspension, a robot, a railway vehicle and a human body? They are all complex mechanical systems composed of rigid bodies moving through articulated joints and submitted to forces and torques. Their study is the basis of the scientific field called multibody dynamics.
Whether you are an engineer designing a vehicle, a technician building a robot or setting up a prothesis, or a physiotherapist studying a human body motion, you might need to model and analyze the behavior of such multibody systems. You will learn that skill through this program.
Although an advanced program, your learning will be very progressive. It starts from the basic principles of Newtonian mechanics and then proposes to solve everyday applications of increasing complexity, using the free symbolic software Robotran (www.robotran.be) that generates the nonlinear equations in C, Python or MATLAB language.
The advantage of the symbolic generation is to be able to deal with realistic three-dimensional applications without having to generate the nonlinear equations of motion yourself, by hand or with a commercial numerical software.
The program successively covers the following topics:
- Recall and notations of Newtonian mechanics
- Principles of the multibody formalism
- Introduction to symbolic modeling (with Robotran)
- Numerical simulation of simple cases
- Modeling of external and internal forces
- Treatment of kinematic constraints
- Analysis techniques: direct/inverse kinematics, inverse dynamics, time integration, equilibrium and modal analysis.
Both courses combine videos, exercises, projects, continuous assessment and final exams so that you’ll gain maximum practice and deep learning in multibody system dynamics.
Syllabus
Course 1: Modeling and Simulation of Multibody Systems - Part I
Vehicles, bicycles, cranes, human body and robots are multibody systems. Learn how to model them and compute their kinematic and dynamic characteristics, such as velocities, accelerations and forces.
Course 2: Modeling and Simulation of Multibody Systems - Part II
90% of daily life multibody systems contain loops of bodies, e.g. vehicle or bike suspensions, parallel manipulators or robots, and musculoskeletal systems. They can also include joint constraints. In this second course about multibody systems, learn how to model them and how to deal with more advanced numerical analyses.
Courses
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This course aims at acquainting you with the modeling and simulation of complex articulated mechanical systems, denoted as multibody systems, such as vehicles, merry-go-rounds, motorbikes, cranes, human bodies, suspensions, robot manipulators, mechanical transmissions, etc.
This course is based on (1) video clips focusing on the main theoretical background and concepts, (2) well-illustrated written sections giving more details about the mathematical formulation, and (3) questions, exercises and modeling projects.
Despite the intrinsic complexity of such systems in terms of morphology and motions, basic skills in Newtonian mechanics, linear algebra and numerical methods are sufficient to model them, provided that the endless and tedious computation related to their internal kinematics and dynamics are at our disposal. This is the purpose of the symbolic program ROBOTRAN*, which can be used with this course and can automatically generate the full set of equations of motion of MBS, in a symbolic manner, i.e. exactly as if you were writing them by hand, whatever the size and the morphological complexity of the application. Hence, this course will instead teach you how to intervene upstream and downstream this generation step.
Upstream the latter, you will learn how to translate a real system, e.g. a car suspension, into a virtual multibody model comprising bodies, joints, internal or external forces and torques and imposed motion… with a level of refinement that will be dictated by the original issue. For example, what is the minimum tire ground force when the car suspension is excited by a shaker?
Downstream the symbolic generation, your intervention will consist in:
- Completing the symbolic model with features that are specific to your system, e.g. a tire force model or the tuning of a motion controller, among other things;
- Implementing under the form of a program (in Python, Matlab, or C) a time simulation to solve the differential equations of motion, given the original question: e.g. find the transient motion of the system submitted to forces and torques and compute a specific force time history or the maximal acceleration of a particular point.
- Selecting the most suitable results, including self-explanatory - and sometimes funny - video animations of your multibody system in motion.
In sum, this course, based on the use of the ROBOTRAN* symbolic generator, will allow you to focus on the most interesting aspects of the multibody modeling process, by entirely mastering your computer model from the input data to the results, instead of using a black-box multibody software that clearly goes against the educational objective of this course.
Enjoy Multibody Dynamics!
*Note: The course was built to teach modeling and simulation of multibody systems, and not to teach any specific software. However, we suggest that you use the symbolic ROBOTRAN program to model and study the various multibody systems proposed in this course.
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This course aims at acquainting you with the modeling and simulation of constrained multibody systems, and especially mechanical systems with kinematic loops, such as real vehicle or bicycle suspensions, parallel manipulators or robots, musculoskeletal systems, etc.
You will also learn to deal with more advanced numerical analyses:
• Direct kinematics;
• Inverse kinematics;
• Equilibrium;
• Modal analysis;
• Direct Dynamics;
• Inverse Dynamics.This course is based on (1) video clips focusing on the main theoretical background and concepts, (2) well-illustrated written sections given more details about the mathematical formulation, and (3) questions, exercises and modeling projects.
Despite the intrinsic complexity of such systems in terms of morphology and motions, basic skills in Newtonian mechanics, linear algebra and numerical methods are sufficient to model them, provided that the endless and tedious computation related to their internal kinematics and dynamics are at our disposal. This is the purpose of the symbolic program ROBOTRAN, which can be used with this course and can automatically generate the full set of equations of motion of a constrained MBS, in a symbolic manner, i.e. exactly as if you were writing them by hand, whatever the size and their morphological complexity of the application. Hence, this course will instead teach you how to intervene upstream and downstream this generation step.
Upstream the latter, you will learn how to translate a real system, e.g. a car suspension, into a virtual multibody model comprising algebraic constraints between joints, kinematic loops, etc.
Downstream the symbolic generation, your intervention will consist in:
• Completing the symbolic model with features that are specific for your system, e.g. a tire force model or the tuning of a motion controller, among other things;
• Selecting and implementing under the form of a program (in Python, Matlab, or C) the suitable numerical method to solve the differential equations of motion, given the original question; (1) an equilibrium solution can give you the static forces and the system deflection, (2) a time simulation can compute any transient motion of the system submitted to forces and torques, (3) a modal analysis will provide you with the eigenmodes that inform you about the system stability and damping characteristics, (4) an inverse dynamics study can provide you with the necessary forces and torques for any prescribed motion of the system, (5) etc.
• Selecting the most suitable results, including self-explanatory - and sometimes funny - video animations of your multibody system in motion.
In sum, this course, based on the use of the ROBOTRAN* symbolic generator, will allow you to focus on the most interesting aspects of the multibody modeling process, by entirely mastering your computer model from the input data to the results, instead of using a black-box multibody program that clearly goes against the educational objective of such a course.
Enjoy Multibody Dynamics!
*Note: The course was built to teach modeling and simulation of multibody systems, and not to teach any specific software. However, we suggest that you use the symbolic ROBOTRAN program to model and study the various multibody systems proposed in this course.
Taught by
Paul Fisette and Maxime Raison
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