2016 Advanced Mechanical Elements

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Academic unit or major
Graduate major in Mechanical Engineering
Iwatsuki Nobuyuki 
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Course description and aims

The course offers the knowledge on kinematic and dynamic analysis of planar and spatial link mechanisms and methods to control redundant and over/underactuated mechanisms.
The characteristic of motion mechanisms affects the performance of advanced mechanical systems such as robots, which students learn in Mechanical Engineering Course. It is thus required to quantitatively evaluate the characteristic and to design and control mechanisms based on the evaluation critera. For this purpose, students will understand how to analyze the kinematics and dynamics of planar and spatial closed-loop link mechanisms by utilyzing the systematic kinematic analysis method and will experience to apply them to kinematic and dynamic analyses and motion control of redundant mechanisms, overactuated mechanisms of which actuator inputs are more than mobility of mechanism and underactuated mechanisms constrained by elastic elements.

Student learning outcomes

By the end of this course, students will be able to:
1. Explain mobility of mechanism and relation between input/output motion of mechanism
2. Analyze displacement, velocity and acceleration of planar/spatial closed-loop link mechanism with the systematic kinematic analysis method
3.Analyze the dynamics of planar/spatial closed-loop link mechanism utilizing the systematic kinematic analysis method
4.Explain the optimum motion control of redundant link mechanisms
5.Explain motion control of overactuated or underactuated mechanism with elastic elements


Close-loop link mechanism, kinematics, dynamics, systematic kinematic analysis, motion control, optimum control, redundancy, overactuated mechanism, underactuated mechanism, wire-driven mechanism

Competencies that will be developed

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

Important issues are summaried at the end of lecture every week. Sample softwares to analyze mechanisms, which are explained in this lecuture, will be offered to students, and students are expected to try to analyze various mechanisms with the softwares by themselves so as to understand what they learn.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Kinematic analysis of planar link mechanism with the systematic kinematic analysis method - Displacement, velocity and acceleration analyses of planar closed-loop link mechanism with the systematic kinematic analysis method - Understanding of geometric and differential equations of planar link chains
Class 2 Kinematic analysis of spatial link mechanism with the systematic kinematic analysis method - Expansion of the systematic kinematic analysis method to spatial mechanisms - Understanding of three-dimensional angular motion and vector expression of spatial motion
Class 3 Dynamic analysis of planar/spatial link mechanisms - Driving force and joint force analysis using the systematic kinematic analysis - Derivation of equation of motion of each link
Class 4 Evaluation of motion performance of link mechanisms with redundancy - Quantitative criteria for subtask of redundant link mechanisms - Understanding of input/output velocity rerlation and manipulability measure
Class 5 Motion control of redundant link mechanisms - Optimum motion control to utilize redundancy - Understanding of objective function and optimization method
Class 6 Kinematic analysis and motion control of overactuated mechanisms - Motion control of overactuated mechanisms using relaxation with elastic elements - Understanding of input/output equation taking acount of elastic elements
Class 7 Kinematic analysis and motion control of underactuated mechanisms with elastic elements - Motion control of underactuated mechanisms constrained by elastic elements - Understanding of kinematic analysis with virtual external force
Class 8 Kinematic analysis and motion control of underactuated wire-driven mechanisms - Motion control of wire-driven underactuated mechanisms under gravitational force - Understanding of kinematic analysis to minimize potential energy


None required.

Reference books, course materials, etc.

Several handouts will be often distributed. The following textbook is recommended as a reference book:
JSME Textbook series 'Kinematics od Machinery', edited by the Japan Society of Mechanical Engineers (2007).

Assessment criteria and methods

Students' knowledge of kinematic and dynamic analyses of planar/spatial closed-loop link mechanisms with the systematic kinematic analysis method and their application to analyses and motion controls of redundant and under/overactuated mechanisms is accessed via submitted reports on seceral issues(100%).

Related courses

  • MEC.H532 : Kinematic Analysis and Synthesis of Robots
  • MEC.H531 : Robot Control System Design

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

Students must have successfully completed 'Mechanical elements and draftings(MEC.H201 )' or have equivalnet knowledge.

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Nobuyuki Iwatsuki: nob[at]mep.titech.ac.jp, 03-5734-2538

Office hours

Contact by e-mail in advance to schedule an appointment.

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