2020 Machine Dynamics of Rigid Systems

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Academic unit or major
Graduate major in Mechanical Engineering
Takeda Yukio 
Class Format
Media-enhanced courses
Day/Period(Room No.)
Intensive ()  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

The students know the fundamental means for mass balancing and power smoothing of single slider reciprocating machines and other general mechanical systems. The students have the ability to explain and derive the mass forces and mass moments of single and multi-slider reciprocating machines. The students know about the basic relations, resulting in fluctuating angular velocities due to varying mass moments of inertia and varying loads as reduced to a reference shaft. The relations can be derived and explained.

Student learning outcomes

The influencing factors for fluctuating speeds in single and multi-slider reciprocating machines can be described. Based on that, potential means for power smoothing can be derived. Students have the ability to derive the required kinematic and dynamic relations for the machines and mechanisms under investigation. Moreover, balancing of machines and mechanisms with high mass forces can be performed, including design issues and mathematical derivations. From the dynamic analyses, students learn to develop practical and innovative instructions for mass balancing and power smoothing. To sum up, student gain fundamental knowledge that can be applied to related industrial challenges (including special machine construction and specifications) in the field of design improvement by means of mass balancing and power smoothing.


planar kinematics and dynamics of rigid bodies, dynamic force and motion analysis of planar mechanisms with rigid links, mass balancing for reciprocating machines, power smoothing in mechanisms and slider reciprocating machines, equations of motion

Competencies that will be developed

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

Class flow

The lectures are given by a guest lecturer, Prof. Mathias Huesing, RWTH Aachen University together with the corresponding instructor, Prof. Yukio Takeda.
Students are required to self-study the contents prior to the class using the supplementary material. Based on this, homework problem is given and then, evaluation is done at the final presentation.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction Plane slider-crank mechanism Dynamically equivalent system for the connecting rod
Class 2 Kinematics of the slider-crank mechanism Inertia forces (shaking forces) Effect of inertia forces acting on the frame
Class 3 Effect of inertia forces acting on the frame and basics of balancing of inertia forces/ of shaking forces The Basics: Balancing of inertia forces / of shaking forces Complete balancing of inertia forces (shaking forces) Balancing by countermass at the crank (1st harmonic)
Class 4 Complete balancing of 1st and 2nd harmonic Experiment: Measurement of shaking forces and balancing of single cylinder engine Inertia / shaking torques (especially frame torque)
Class 5 Multi Slider Reciprocating Machines Design: different structures Determine inertia forces by analytical approach Determine inertia forces by graphical approach Balancing of inertia forces
Class 6 Determination of shaking moments of multi-cylinder engines Balancing of shaking moments of multi-cylinder engines Power balancing: introduction and outlook Kinetic energy Potential energy Solutions of the equation of motion
Class 7 Presentation of homework Application of the content of the lecture in research and applications


Original hand-outs are provided.

Reference books, course materials, etc.

References are uploaded in OCW-i.

Assessment criteria and methods

Learning achievement is evaluated at the final presentation.

Related courses

  • MEC.D201 : Mechanical Vibrations
  • MEC.I211 : Robot Kinematics

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


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