We may earn an affiliate commission when you visit our partners.
Course image
Maxime Raison and Paul Fisette

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.

Read more

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:

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

Save this course

Save Modeling and Simulation of Multibody Systems - Part II to your list so you can find it easily later:
Save

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
Revisit fundamental concepts to provide a stronger foundation for understanding constrained multibody dynamics.
Browse courses on Newtonian Mechanics
Show steps
  • 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
Familiarize yourself with the software used in the course to enhance your understanding of multibody modeling techniques.
Browse courses on ROBOTRAN
Show steps
  • 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
Reinforce your understanding of the theoretical concepts by applying them to practical problems.
Show steps
  • 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
Expand to see all activities and additional details
Show all five activities
Develop a simulation program for a constrained multibody system
Apply your knowledge to create a functional program that simulates the behavior of a constrained multibody system.
Show steps
  • 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
Challenge yourself by applying your skills in a competitive setting, fostering innovation and pushing the boundaries of your knowledge.
Browse courses on Research
Show steps
  • 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.
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.
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.
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.
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.
Control Systems Engineer
Control Systems Engineers specialize in designing and implementing systems that control and regulate physical processes. The knowledge gained from the course on Modeling and Simulation of Multibody Systems - Part II can be valuable for Control Systems Engineers as it provides a strong foundation in modeling and simulating dynamic systems, enabling them to develop and fine-tune control algorithms that ensure stability and optimal performance.
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.
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.
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.
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.
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.
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.
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.
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.
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.

Reading list

We've selected ten books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Modeling and Simulation of Multibody Systems - Part II.
This classic textbook provides a comprehensive overview of the theory of elasticity, with a focus on topics such as stress, strain, and deformation. It valuable resource for students and professionals who want to gain a deeper understanding of the mechanical behavior of materials.
This textbook provides a comprehensive overview of the mechanics of materials, with a focus on topics such as stress, strain, and deformation. It valuable resource for students and professionals who want to gain a deeper understanding of the mechanical behavior of materials.
This textbook provides a comprehensive overview of plasticity theory, with a focus on topics such as yield criteria, flow rules, and hardening laws. It valuable resource for students and professionals who want to gain a deeper understanding of the mechanical behavior of materials.
This textbook provides a comprehensive overview of fracture mechanics, with a focus on topics such as crack initiation and propagation. It valuable resource for students and professionals who want to gain a deeper understanding of the failure of materials.
This textbook provides a comprehensive overview of heat transfer, with a focus on topics such as conduction, convection, and radiation. It valuable resource for students and professionals who want to gain a deeper understanding of the transfer of heat.
This textbook provides a comprehensive overview of thermodynamics, with a focus on topics such as the first law of thermodynamics, the second law of thermodynamics, and the third law of thermodynamics. It valuable resource for students and professionals who want to gain a deeper understanding of the fundamental principles of thermodynamics.
This textbook provides a comprehensive overview of fluid mechanics, with a focus on topics such as fluid statics, fluid dynamics, and fluid machinery. It valuable resource for students and professionals who want to gain a deeper understanding of the behavior of fluids.
This textbook provides a comprehensive overview of electronics, with a focus on topics such as diodes, transistors, and amplifiers. It valuable resource for students and professionals who want to gain a deeper understanding of the behavior of electronic circuits.
This classic textbook provides a comprehensive overview of advanced mathematics, including topics such as calculus, linear algebra, and differential equations. It is an essential resource for students and professionals who need a strong foundation in mathematics for engineering applications.
This textbook provides a comprehensive overview of operating systems, with a focus on topics such as processes, threads, and memory management. It valuable resource for students and professionals who want to gain a deeper understanding of the design and implementation of operating systems.

Share

Help others find this course page by sharing it with your friends and followers:

Similar courses

Here are nine courses similar to Modeling and Simulation of Multibody Systems - Part II.
Modeling and Simulation of Multibody Systems - Part I
Most relevant
Automated Reasoning: Symbolic Model Checking
Most relevant
Machine Dynamics with MATLAB
Most relevant
Simulating a Quadcopter's Flight
Advanced Engineering Systems in Motion: Dynamics of Three...
Automobile Engineering: Vehicle dynamics for Beginners
Applied Control Systems 3: UAV drone (3D Dynamics &...
Analytical Mechanics for Spacecraft Dynamics
Model-Based Automotive Systems Engineering
Our mission

OpenCourser helps millions of learners each year. People visit us to learn workspace skills, ace their exams, and nurture their curiosity.

Our extensive catalog contains over 50,000 courses and twice as many books. Browse by search, by topic, or even by career interests. We'll match you to the right resources quickly.

Find this site helpful? Tell a friend about us.

Affiliate disclosure

We're supported by our community of learners. When you purchase or subscribe to courses and programs or purchase books, we may earn a commission from our partners.

Your purchases help us maintain our catalog and keep our servers humming without ads.

Thank you for supporting OpenCourser.

© 2016 - 2024 OpenCourser