Modeling and Simulation of Multibody Systems

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.

What's inside

Learning objectives

Translate a real mechanical system into a multibody model;
Complete your model with features and sub-models that are specific to your application;
Build and master a program (in python, matlab or c) to time simulate the system;

Produce the expected results.
In this course devoted to tree-like multibody systems, you will learn how to:

Translate a real mechanical system into a multibody model;
Complete your model with features and sub-models that are specific to your application;
Build and master a program (in python, matlab or c) to time simulate the system;
Produce the expected results.
In this course devoted to tree-like multibody systems, you will learn how to:

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Delves into multibody system modeling and simulation, which is widely used in industry

Teaches how to build dynamic multibody simulations using symbolic software

Develops foundational skills in multibody modeling and simulation

Taught by Paul Fisette and Maxime Raison, who are recognized for their work in multibody dynamics

Uses ROBOTRAN, an industry-standard symbolic program for modeling multibody systems

Covers both theoretical and practical aspects of multibody dynamics

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Modeling and Simulation of Multibody Systems - Part I with these activities:

Review the basics of Newtonian mechanics, linear algebra, and numerical methods

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Strengthens your foundational knowledge, which is crucial for understanding the complexities of multibody systems.

Browse courses on Newtonian Mechanics

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Review your notes or textbooks on Newtonian mechanics
Solve practice problems related to kinematics and dynamics
Review the concepts of linear algebra, including vectors, matrices, and transformations
Practice solving systems of linear equations and performing matrix operations
Familiarize yourself with numerical methods for solving differential equations and other mathematical problems

Find a mentor or tutor who can provide guidance on multibody dynamics

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Finding a mentor or tutor can provide personalized guidance and support throughout the course.

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Reach out to professors, researchers, or industry professionals who have expertise in multibody dynamics.
Explain your learning goals and ask for their guidance.

Follow online tutorials about ROBOTRAN

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Provides guided practice in using ROBOTRAN, reinforcing your understanding of the material.

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Search for online tutorials on ROBOTRAN
Select a tutorial that aligns with your learning goals
Follow the tutorial step-by-step, implementing the concepts in ROBOTRAN
Seek assistance from the tutorial's author or online forums if needed

Nine other activities

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Follow tutorials on using ROBOTRAN

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Following tutorials on using ROBOTRAN will provide hands-on experience with the software used in the course.

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Find online tutorials or documentation for ROBOTRAN.
Follow the tutorials step-by-step, creating and simulating simple multibody systems.

Create a simple multibody model using ROBOTRAN

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Boosts your proficiency in using ROBOTRAN to construct multibody models, which is foundational to the course's focus on multibody dynamics.

Browse courses on ROBOTRAN

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Learn the basics of ROBOTRAN modeling
Identify a simple mechanical system, such as a pendulum or a lever
Translate the system into a ROBOTRAN model using appropriate bodies, joints, forces, and constraints
Simulate the model and analyze the results

Join a study group and collaborate on solving example problems

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Fosters collaborative learning and reinforces your understanding of multibody dynamics concepts.

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Find a study group or create your own
Select example problems related to the course material
Work together to solve the problems, discussing different approaches and solutions
Present your solutions to the group and receive feedback

Solve practice problems on multibody dynamics

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Solving practice problems will reinforce the concepts learned in the course and improve problem-solving skills.

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Find practice problems in textbooks, online resources, or from the instructor.
Solve the problems using the concepts and techniques learned in the course.

Solve practice problems on multibody system dynamics

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Enhances your problem-solving skills and deepens your understanding of the course material.

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Find a collection of practice problems or create your own
Solve the problems using the concepts and techniques covered in the course
Compare your solutions to the provided solutions or discuss them with your peers

Create a presentation on a multibody dynamics topic

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Creating a presentation on a multibody dynamics topic will allow students to synthesize their knowledge and communicate it effectively.

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Choose a specific topic related to multibody dynamics.
Research the topic and gather information from textbooks, journal articles, and other sources.
Create slides that outline the main points of the presentation.
Practice presenting the material in front of a mirror or with a friend or family member.

Contribute to an open-source project related to multibody dynamics

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Provides exposure to real-world applications of multibody dynamics and enhances your problem-solving and collaboration skills.

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Identify an open-source project related to multibody dynamics, such as OpenSim or Bullet Physics
Review the project's documentation and familiarize yourself with its codebase
Find an area where you can contribute, such as bug fixes, feature enhancements, or documentation improvements
Submit your contributions to the project and engage with the community

Build a simple multibody model and simulate it using ROBOTRAN

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Building and simulating a multibody model will provide hands-on experience with the concepts and techniques learned in the course.

Browse courses on ROBOTRAN

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Identify a simple multibody system, such as a pendulum or a four-bar linkage.
Create a model of the system in ROBOTRAN, including bodies, joints, and forces.
Simulate the model and analyze the results.

Build a physical model of a multibody system and demonstrate its motion

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Provides a hands-on experience in designing and analyzing multibody systems, solidifying your understanding.

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Select a simple multibody system, such as a pendulum or a slider-crank mechanism
Design and build a physical model of the system using materials like cardboard, wood, or metal
Test the model and collect data on its motion
Compare the experimental results to the analytical or simulated results obtained using ROBOTRAN
Present your findings in a report or presentation

Career center

Learners who complete Modeling and Simulation of Multibody Systems - Part I will develop knowledge and skills that may be useful to these careers:

Aerospace Engineer

Aerospace Engineers design, build, and maintain aircraft and spacecraft. These professionals need a strong understanding of the physical principles that govern the behavior of aircraft and spacecraft. Modeling and Simulation of Multibody Systems - Part I can help Aerospace Engineers develop this understanding. This course covers topics such as kinematics, dynamics, and vibrations, which are essential for designing and analyzing aircraft and spacecraft.

See salaries and explore the career path for Aerospace Engineer

Simulation Engineer

Simulation Engineers use computer models to simulate the behavior of systems. These professionals need a strong understanding of the physical principles that govern the behavior of systems. Modeling and Simulation of Multibody Systems - Part I can help Simulation Engineers develop this understanding. This course covers topics such as systems modeling, simulation, and analysis, which are essential for developing and using computer models.

See salaries and explore the career path for Simulation Engineer

Mechanical Engineer

Mechanical Engineers design, build, and maintain machines, engines, and other mechanical devices. These professionals need a strong understanding of the physical principles that govern the behavior of mechanical systems. Modeling and Simulation of Multibody Systems - Part I can help Mechanical Engineers develop this understanding. This course covers topics such as kinematics, dynamics, and vibrations, which are essential for designing and analyzing mechanical systems.

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Robotics Engineer

Robotics Engineers design, build, and maintain robots. These professionals need a strong understanding of the physical principles that govern the behavior of robots. Modeling and Simulation of Multibody Systems - Part I can help Robotics Engineers develop this understanding. This course covers topics such as kinematics, dynamics, and control, which are essential for designing and analyzing robots.

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Automotive Engineer

Automotive Engineers design, build, and maintain vehicles. These professionals need a strong understanding of the physical principles that govern the behavior of vehicles. Modeling and Simulation of Multibody Systems - Part I can help Automotive Engineers develop this understanding. This course covers topics such as kinematics, dynamics, and vibrations, which are essential for designing and analyzing vehicles.

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Motion Control Engineer

Motion Control Engineers design and implement control systems for machines and robots. These professionals need a strong understanding of the physical principles that govern the behavior of mechanical systems. Modeling and Simulation of Multibody Systems - Part I can help Motion Control Engineers develop this understanding. This course covers topics such as kinematics, dynamics, and control, which are essential for designing and implementing control systems for machines and robots.

See salaries and explore the career path for Motion Control Engineer

Biomedical Engineer

Biomedical Engineers design and develop medical devices and equipment. These professionals need a strong understanding of the physical principles that govern the behavior of the human body. Modeling and Simulation of Multibody Systems - Part I can help Biomedical Engineers develop this understanding. This course covers topics such as kinematics, dynamics, and vibrations, which are essential for designing and analyzing the motion of the human body.

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Systems Engineer

Systems Engineers design, build, and maintain complex systems. These professionals need a strong understanding of the physical principles that govern the behavior of systems. Modeling and Simulation of Multibody Systems - Part I can help Systems Engineers develop this understanding. This course covers topics such as systems modeling, simulation, and analysis, which are essential for designing and analyzing complex systems.

See salaries and explore the career path for Systems Engineer

Product Design Engineer

Product Design Engineers design and develop new products. These professionals need a strong understanding of the physical principles that govern the behavior of products. Modeling and Simulation of Multibody Systems - Part I may be useful because it can help Product Design Engineers understand the physical interactions between different components of a product. This course can help Product Design Engineers design products that are safe, efficient, and reliable.

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Electrical Engineer

Electrical Engineers design, build, and maintain electrical systems. These professionals need a strong understanding of the physical principles that govern the behavior of electrical systems. Modeling and Simulation of Multibody Systems - Part I may be useful because it can help Electrical Engineers understand the physical interactions between different components of an electrical system. This course can help Electrical Engineers design electrical systems that are safe and efficient.

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Software Engineer

Software Engineers design, develop, and maintain software systems. These professionals need a strong understanding of the physical principles that govern the behavior of computer systems. Modeling and Simulation of Multibody Systems - Part I may be useful because it can help Software Engineers understand the physical interactions between different components of a computer system. This course can help Software Engineers design software systems that are safe and efficient.

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Chemical Engineer

Chemical Engineers design, build, and maintain chemical plants. These professionals need a strong understanding of the physical principles that govern the behavior of chemical processes. Modeling and Simulation of Multibody Systems - Part I may be useful because it can help Chemical Engineers understand the physical interactions between different components of a chemical plant. This course can help Chemical Engineers design chemical plants that are safe and efficient.

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Industrial Engineer

Industrial Engineers plan and optimize the processes and systems of a production facility. These professionals design ways to use people, materials, and equipment to improve efficiency, productivity, and quality. Modeling and Simulation of Multibody Systems - Part I may be useful because it can help Industrial Engineers understand the physical interactions between different components of a production system. This course can help Industrial Engineers optimize the design and layout of production facilities.

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Data Scientist

Data Scientists use data to solve problems and make decisions. These professionals need a strong understanding of the physical principles that govern the behavior of data. Modeling and Simulation of Multibody Systems - Part I may be useful because it can help Data Scientists understand the physical interactions between different components of a data set. This course can help Data Scientists design data models that are accurate and reliable.

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Civil Engineer

Civil Engineers design and build infrastructure projects, such as bridges, buildings, and roads. These professionals need a strong understanding of the physical principles that govern the behavior of structures. Modeling and Simulation of Multibody Systems - Part I may be useful because it can help Civil Engineers understand the physical interactions between different components of a structure. This course can help Civil Engineers design structures that are safe and reliable.

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