2020 Multibody Systems

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Academic unit or major
Graduate major in Mechanical Engineering
Okuma Masaaki  Furuya Hiroshi 
Class Format
Media-enhanced courses
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Course description and aims

All machines are "Systems" which inevitably consists of multi number of mechanical parts relatively linked and connected. That is, "Multibody Systems." The relative motion of the mechanical parts creates the motion and function of machines. This course is to lecture the motion, mechanics and control of the systems as follows:
1. Multi particle systems
2. Rigid body link systems
3. Dynamics and inverse dynamics
The aim of this course is to give students enough ability to solve the mechanics of multibody systems by means of not only lecturing but also offering some excercises using computational analysis.

Student learning outcomes

At the end of this course, students' will be able to:
1) express and transform the coordinate systems mathematically
2) analyze the kinematics and dynamics of multi particle and body link systems
3) analyze the synthesis of ribid body systems' kinematics
4) understand the basic analysis of flexible multi body systems


Rigid link system, Kinematics, Dynamics, Control, Robot

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

This course mainly consists of lecturing. In addition, exercise and homework (report) are provided appropriately for students' good understanding.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Basic expression of kinematics Understand the method to express kinematics.
Class 2 Transformation between coordinate systems Understand how to transform from a coordinate system to another.
Class 3 Expression of velocity, acceleration and angular velocity Understand and derive the velocity, acceleration and angular velocity mathematically.
Class 4 Kinematics and dynamics of particle motion Understand and analyze the motion of particle.
Class 5 Kinmematics and dynamics of multi-particle connected systems Understand multi-particle connected systems
Class 6 Expression of generalized coordinates of rigid body link systems Express rigid body link systems in generalized coordinate system.
Class 7 Moment of inertia regarding rigid body link systems Understand the analysis of the moment of inertia.
Class 8 Dynamics of rigid body link systems Understand basic dynamic analysis of rigid body link systems.
Class 9 Dynamic analysis of rigid body link systems Understand the methods of dynamic analysis.
Class 10 Inverse dynamics of rigid body link systems Understand the inverse dynamics.
Class 11 Path control and planning of rigid body link systems Understand the theory of path control and planning.
Class 12 Linear control of rigid body link systems Understand linear control theory.
Class 13 Nonlinear control of rigid body link systems Understand nonlinear control theory.
Class 14 Dynamics of flexible multi body link systems Understand flexible link systems.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


Several materials are proveded by lecturers

Reference books, course materials, etc.

Thomas R. Kane, David A. Levinson著 Dynamics - Theory and Applications
John J. Craig著 Introduction to Robotics: Mechanics and Control
Ahmed A. Shabana著 Dynamics of Multibody Systems

Assessment criteria and methods

Students' achievement scores are determined by final examination (about 60%) plus exercise and reports (about 40%).

Related courses

  • LAS.M102 : Linear Algebra I / Recitation
  • LAS.M106 : Linear Algebra II
  • LAS.P101 : Fundamentals of Mechanics 1
  • LAS.P102 : Fundamentals of Mechanics 2
  • MEC.A201 : Engineering Mechanics
  • MEC.B214 : Vector Analysis
  • ZUL.A201 : Motion and Vibration Control
  • MEC.I333 : Robot Dynamics and Control
  • SCE.S203 : Kinematics and Dynamics of Robotic systems
  • MEC.I211 : Robot Kinematics

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Successful completion of learning the undergraduate level subjects listed the related courses above.


It is required to bring a note PC in which Matlab has been installed.
Due to the consideration of COVID-19 crisis, this course is provided in 3Q in 2020 and only master students in mechanical engineering course are permitted to take.

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