Modeling and Simulation of Multibody Systems

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.

What's inside

Learning objectives

Formulate the user and loop constraints existing in your system;
Establish the equations of motion of constrained multibody systems using the coordinate partitioning method;
Build and master a program (in python, matlab or c) to simulate constrained multibody system;

Analyze your multibody system behavior thanks to the suitable numerical method (equilibrium, modal analysis, time integration, inverse models)
In this course devoted to constrained multibody systems, you will learn how to:

Formulate the user and loop constraints existing in your system;
Establish the equations of motion of constrained multibody systems using the coordinate partitioning method;
Build and master a program (in python, matlab or c) to simulate constrained multibody system;
Analyze your multibody system behavior thanks to the suitable numerical method (equilibrium, modal analysis, time integration, inverse models)
In this course devoted to constrained multibody systems, you will learn how to:

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Introduces modeling and simulation of constrained multibody systems, particularly focusing on those found in vehicles, parallel manipulators, and robots

Starts with the basics of Newtonian mechanics and gradually progresses to advanced numerical analyses, including direct and inverse kinematics, equilibrium analysis, modal analysis, direct and inverse dynamics

Leverages the ROBOTRAN symbolic program to automate the generation of equations of motion, allowing learners to focus on the most interesting aspects of the modeling process

Provides learners with the skills to translate real systems into virtual multibody models, select appropriate numerical methods for solving differential equations of motion, and analyze system behavior based on the results

Emphasizes the importance of understanding the kinematic and dynamic constraints existing within multibody systems

Utilizes video clips, written sections, and exercises to facilitate learning

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 II with these activities:

Revisit Newtonian mechanics and linear algebra

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Revisit fundamental concepts to provide a stronger foundation for understanding constrained multibody dynamics.

Browse courses on Newtonian Mechanics

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Review Newton's laws of motion and their application to rigid bodies.
Practice solving linear algebra problems involving matrices and vectors.

Follow tutorials on ROBOTRAN

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Familiarize yourself with the software used in the course to enhance your understanding of multibody modeling techniques.

Browse courses on ROBOTRAN

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Find and access official ROBOTRAN tutorials.
Go through the tutorials step-by-step, trying out the examples provided.
Apply what you learn to model simple multibody systems.

Solve practice problems on constrained multibody dynamics

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Reinforce your understanding of the theoretical concepts by applying them to practical problems.

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Find practice problems from textbooks, online resources, or the course instructor.
Solve the problems using the methods learned in the course.
Check your solutions against provided answers or consult with the instructor for feedback.

Two other activities

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Develop a simulation program for a constrained multibody system

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Apply your knowledge to create a functional program that simulates the behavior of a constrained multibody system.

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Select a multibody system to model and simulate.
Develop a mathematical model of the system using the coordinate partitioning method.
Implement the model in a programming language (e.g., Python, Matlab, C).
Validate the simulation results by comparing them to analytical solutions or experimental data.

Participate in a multibody dynamics competition

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Challenge yourself by applying your skills in a competitive setting, fostering innovation and pushing the boundaries of your knowledge.

Browse courses on Research

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Find and register for a multibody dynamics competition.
Form a team or work individually on a project.
Develop a novel solution to a multibody dynamics problem.
Present your solution to a panel of judges and compete against other teams.

Career center

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

Simulation Engineer

Simulation Engineers use computer-aided techniques to analyze and predict the behavior of complex systems. The course on Modeling and Simulation of Multibody Systems - Part II can help Simulation Engineers gain expertise in modeling and simulating multibody systems, enabling them to work on projects involving robotics, biomechanics, and vehicle dynamics.

See salaries and explore the career path for Simulation Engineer

Research Scientist

Research Scientists are engaged in scientific research and development. The course on Modeling and Simulation of Multibody Systems - Part II can be beneficial for Research Scientists working in fields such as robotics, biomechanics, and vehicle dynamics, as it provides a strong foundation in modeling and simulating complex systems, enabling them to conduct advanced research and develop innovative solutions.

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Robotics Engineer

Robotics Engineers are in high demand in industries like manufacturing, healthcare, and space exploration. A course on Modeling and Simulation of Multibody Systems - Part II can be beneficial as it can provide them with expertise in modeling and simulating complex robotic systems, enabling them to optimize performance and ensure stability.

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Aerospace Engineer

Aerospace Engineers are involved in the design, development, and testing of aircraft and spacecraft. The concepts covered in Modeling and Simulation of Multibody Systems - Part II are directly applicable to Aerospace Engineering, as it provides expertise in modeling and simulating complex aircraft and spacecraft dynamics, which is crucial for ensuring stability, performance, and safety.

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Automotive Engineer

Automotive Engineers focus on designing, developing, and testing vehicles and their components. The concepts learned in the course on Modeling and Simulation of Multibody Systems - Part II are highly relevant to Automotive Engineers, as it provides them with the knowledge to analyze and simulate vehicle dynamics, optimize performance, and improve safety.

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Control Systems Engineer

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Mechanical Engineer

Mechanical Engineers play a pivotal role in various industries, including automotive, aerospace, manufacturing, and robotics. The course can help Mechanical Engineers develop a deep understanding of modeling and simulation techniques which can be applied to design, analyze, and optimize complex mechanical systems.

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Computational Biomechanist

Computational Biomechanists utilize computer simulations to study human movement and predict the behavior of biological systems. The course on Modeling and Simulation of Multibody Systems - Part II can be beneficial as it provides a comprehensive understanding of modeling and simulating musculoskeletal systems, enabling Computational Biomechanists to develop accurate and reliable models for research and clinical applications.

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Systems Engineer

Systems Engineers are responsible for designing, integrating, and evaluating complex systems. The course on Modeling and Simulation of Multibody Systems - Part II can provide Systems Engineers with a solid foundation in modeling and simulating large-scale systems, enabling them to analyze system behavior, optimize performance, and make informed decisions.

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Product Development Engineer

Product Development Engineers are responsible for designing and developing new products. The course on Modeling and Simulation of Multibody Systems - Part II can be valuable for Product Development Engineers, as it provides expertise in modeling and simulating complex mechanical systems, enabling them to optimize product design, improve performance, and ensure reliability.

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Motion Analysis Engineer

Motion Analysis Engineers use specialized techniques to capture and analyze human and animal movement. The concepts covered in the course on Modeling and Simulation of Multibody Systems - Part II can be highly beneficial for Motion Analysis Engineers, as it provides a deeper understanding of the kinematics and dynamics of multibody systems, enabling them to develop more accurate and reliable motion analysis models.

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Biomechanist

A Biomechanist works in improving human health and performance in various domains such as Sports, Rehabilitation, and Ergonomics by using sophisticated technology. Courses like Modeling and Simulation of Multibody Systems - Part II can help a Biomechanist's understanding of deriving and solving equations of motion of the human body for studying human movement, performance, and injury prevention.

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Technical Animator

Technical Animators use computer animation techniques to create realistic simulations of physical systems. The concepts covered in the course on Modeling and Simulation of Multibody Systems - Part II can be extremely valuable for Technical Animators, as it provides a deep understanding of the principles governing the motion of complex systems, enabling them to create more accurate and physically realistic animations.

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Mathematician

Mathematicians develop and analyze mathematical models to solve problems in various fields. The course on Modeling and Simulation of Multibody Systems - Part II may be useful for Mathematicians interested in applying their knowledge to real-world problems. The course provides a framework for formulating and solving complex mathematical models, which can be valuable in fields such as computational mechanics and applied mathematics.

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Consultant

Consultants provide expert advice and guidance to organizations on various business and technical matters. The course on Modeling and Simulation of Multibody Systems - Part II can be useful for Consultants specializing in engineering, manufacturing, or robotics. The course provides a deep understanding of modeling and simulation techniques, which can enable Consultants to effectively evaluate and advise clients on complex technical systems.

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