A mechanical engineer has the capacity of designing machines and solving several mechanical problems. To do so, an engineer must have a deep theoretical and practical knowledge. In particular, he/she must be able to explain the relation between structural topology, geometry, forces and motion of mechanisms and machines. All these concepts are the target of study of the subject Mechanism Theory and Mechanical Vibrations.



The aim of this subject is to teach students how to solve common problems in Mechanism Kinematics, as well as understanding the approaches in Machine Dynamics for solid or deformable bodies. Besides, the basic concepts of mechanical design are explained so that the students are introduced to the synthesis of mechanisms in charge of carrying out specific mechanical functions.



The knowledge acquired in this subject are of great relevance in the professional world of an engineer, covering several fields such as vibration analysis of automotive suspension systems, vibration modes testing in structural models, design and development of mechanisms and industrial robots destined to aeronautical aplications, motor vehicles manufacturing, object manipulation (Pick&Place applications), flight simulatior, etc.

The main goal of this subject consists in acquiring:



- M03E3: Knowledge and abilities for computing, designing and testing machines.



The learning outcome of the subject according to the oficial memory is: Analysis and design of mechanisms and machine elements. This global result has been broken down into the following results for a better understanding of the objectives of the subject:



- Understand the structures of both planar and spatial mechanisms; that is, the elements and kinematics pairs forming the mechanism, the number of degrees of freedom and the concept of kinematic chain.



- Learn the fundamental theorems of planar motion, which complement the concepts already illustrated in prior subjects as Mechanics and Applied Mechanics, to achieve the theoretical basis for the analysis and dimensional synthesis of mechanisms.



- Achieve the ability to perform kinematic analysis of planar and spatial mechanisms basing on the analytic and matrix-based procedures respectively. Study of rotation capacity, singular position analysis and quality indicators related to motion and force transmission of mechanisms.



- Use the classical methods for planar mechanism dimensional synthesis: function generation synthesis, trajectory-based synthesis and rigid solid guidance synthesis. Design of mechanisms intended for specific applications.



- Perform direct and inverse dynamic analysis of planar mechanisms (rigid solid hypothesis) basing on the principles studied in Applied Mechanics and specific procedures for desmodromic mechanisms.



- Perform the dynamic analysis of deformable solids of one or more degrees of freedom. Characterizing the systems subjected to mechanical vibrations taking into consideration different types of excitations such as impulse-based input, ramp-based input, step-based input, harmonic input or general type input.



- Achieve the ability to analyze vibratory systems with various degrees of freedom. Understand the concepts of vibration modes, natural frequencies and natural coordinates. Solve the systems subjected to free or forced vibrations.



- Obtain the knowledge related to the experimental vibrations measurement, describing the components forming the same. Achieve the capacity to test and justify the results obtained from the experimental analysis.

Part A: MECHANISM KINEMATICS



CHAPTER I: BASIC CONCEPTS ON MECHANISMS AND THEIR DESIGN

1.1. Basic concepts regarding mechanisms, machines and their design.

1.2. Classification of elements and kinematic joints.

1.3. Kinematic chains, mechanisms and inversions.

1.4. Grübler and Malishev criteria. Limitations.

1.5. Methods for structural synthesis of mechanisms.



CHAPTER II: PLANAR MOTION GEOMETRY

2.1. Planar motion of a rigid body. Acceleration and velocity fields.

2.2. Aronhold-Kennedy Theorem or Three centers Theorem.

2.3. Hartmann's Theorem. Euler-Savary Formula.

2.4. Bobillier's Theorem.

2.5. Conjugate profiles, Generalisation of the Euler-Savary Formula.

2.6. Main circles: inflections, Bresse and return circles.



CHAPTER III: KINEMATIC ANALYSIS OF PLANAR LINKAGES

3.1. Introduction: general problems of mechanisms kinematics.

3.2. Position analysis resolution. Rotability analysis.

3.3. Quality indicators: transmission angle and mechanical advantage.

3.4. Analytical methods for kinematic analysis.



CHAPTER IV: DIMENSIONAL SYNTHESIS OF PLANAR LINKAGES

4.1. Function generation synthesis.

4.2. Trajectory generation synthesis.

4.3. Rigid body guidance synthesis.



CHAPTER V: KINEMATICS ANALYSIS OF SPATIAL ROBOTS

5.1. Representation of an object location: transformation matrices.

5.2. Matrix-based method.

5.3. Position analysis of spatial mechanisms.

5.4. Accelerations and velocities analysis.





Part B: MACHINE DYNAMICS



CHAPTER I: MECHANISM DYNAMICS (rigid body dynamics)

1.1. Introduction to Machine Dynamics.

1.2. Inverse dynamic problem.

1.3. Direct dynamic problem.

1.4. Flywheels.

1.6. Machine balancing



CHAPTER II: THEORY OF VIBRATIONS (deformable body dynamics)

2.1. Introduction to Theory of Vibrations.

2.2. Modelization of mechanical systems.

2.3. Single degree of freedom systems I: free vibrations.

2.4. Single degree of freedom systems II: harmonic vibrations.

2.5. Single degree of freedom systems III: convolution integral.

2.6. Single degree of freedom systems IV: Fourier transformation.

2.7. Single degree of freedom systems V: vibrations isolation.

2.8. Multi-degree of freedom systems I: free vibrations.

2.9. Multi-degree of freedom systems II: forced vibrations.

2.10. Introduction to experimental measurement of vibrations.

The teaching program of the subject is composed of theoretical lectures, practical lessons, seminars, practical lectures and labs.



The practical lectures reinforce and complement the knowledge acquired from the theoretical lectures and seminars, and constitute an essential part of the learning process. Practical lectures consist in using computational simulation software and experimental analysis systems to solve some practical cases of mechanical systems' analysis and design. In the first term, Part A, two practical lectures (each of 2,5 hours) using specific software are given. In the second term, Part B, one practical lecture of 2,5 hours is given in the mechanical lab.



These lectures are given in the computer rooms of the University, and in the labs belonging to Department of Mechanical Engineering.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 95
  • Realization of Practical Work (exercises, cases or problems) (%): 5

According to the regulations of the University of the Basque Country, a continuous evaluation has been established, which consists in:



- Practicals in mechanical labs and laboratories. In order to pass the practicals the student must attend to all of them and present the corresponding report, adequately completed, in the established date.



- An exam related to the first part of the subject; Mechanisms Kinematics. To pass the exam the student must get a mark equal or higher than 5. Passing this exam implies that the student is released of the corresponding part of the subject during the current academic course.



- A final exam.





The final written exam will consist of two tests both in the ordinary and extraordinary calls: Written test on Kinematics of Mechanisms and a written test on Dynamics of Machines.



In each call, a student will only have to take the test/tests that they have not previously passed in the current academic year. Each test will be considered passed when a score equal to or greater than 5 out of 10 has been obtained.





* Practical work: passing the practical work implies attendance and active participation in the three practices, as well as the delivery and positive assessment of the corresponding reports, duly completed and delivered within the indicated period.



For those students who opt for the final evaluation system and for students who have not obtained positive grades in the practical works in the extraordinary call, the part corresponding to the note of the practical works will be evaluated by means of a work to be delivered before the date of the exam and whose theme will be defined throughout the course.



Obtaining the final grade for the subject both in the ordinary and extraordinary calls:



The final grade for the course will be calculated as follows, provided that at least 4 out of 10 have been obtained in each written test (Written test on Kinematics of Mechanisms and a written test on Dynamics of Machines):

o 95% Final written exam (average of the two tests).

o 5% note of the practical works.





Conditions to pass the subject:



Pass the written exam and obtain a final grade of the subject equal to or greater than 5.



Students who do not meet any of the requirements to pass the subject will have a maximum grade of 4 out of 10.





Attendance to exams:

In the face of any circumstance that does not allow the student to attend the exam, this fact will be regulated according to the current regulations of the UPV/EHU.



Claim of exams:

The marks are published in Egela and, in the case of the final exams, they are simultaneously published in GAUR system.

Once the marks have been published, the students who want to claim the exam have to indicate it in the established period of time. The claims of the students that do not indicate it, or that despite of indicating they do not come in the corresponding revision day at established timetable, will not be heeded. All this is done with the purpose of dedicating the necessary time to the revision process, and giving an equitable and fair solution to each claim.



Resignation:

As it is specified in the "Normativa Evaluación de Enseñanzas de Grado" any student that wants to resign from the continuous evaluation in order to do the final evaluation, then he/she has to present the resignation document to the teachers in charge of the subject in the period of 18 weeks counting from the starting of the course, according to the academic calendar of the faculty. The final evaluation implies a unique final exam which is the 100% of the final grade.

According to the regulations of the University of the Basque Country, a continuous evaluation has been established, which consists in:



- Practicals in mechanical labs and laboratories. In order to pass the practicals the student must attend to all of them and present the corresponding report, adequately completed, in the established date.



- An exam related to the first part of the subject; Mechanisms Kinematics. To pass the exam the student must get a mark equal or higher than 5. Passing this exam implies that the student is released of the corresponding part of the subject during the current academic course.



- A final exam.





The final written exam will consist of two tests both in the ordinary and extraordinary calls: Written test on Kinematics of Mechanisms and a written test on Dynamics of Machines.



In each call, a student will only have to take the test/tests that they have not previously passed in the current academic year. Each test will be considered passed when a score equal to or greater than 5 out of 10 has been obtained.





* Practical work: passing the practical work implies attendance and active participation in the three practices, as well as the delivery and positive assessment of the corresponding reports, duly completed and delivered within the indicated period.



For those students who opt for the final evaluation system and for students who have not obtained positive grades in the practical works in the extraordinary call, the part corresponding to the note of the practical works will be evaluated by means of a work to be delivered before the date of the exam and whose theme will be defined throughout the course.



Obtaining the final grade for the subject both in the ordinary and extraordinary calls:



The final grade for the course will be calculated as follows, provided that at least 4 out of 10 have been obtained in each written test (Written test on Kinematics of Mechanisms and a written test on Dynamics of Machines):

o 95% Final written exam (average of the two tests).

o 5% note of the practical works.





Conditions to pass the subject:



Pass the written exam and obtain a final grade of the subject equal to or greater than 5.



Students who do not meet any of the requirements to pass the subject will have a maximum grade of 4 out of 10.





Attendance to exams:

In the face of any circumstance that does not allow the student to attend the exam, this fact will be regulated according to the current regulations of the UPV/EHU.



Claim of exams:

The marks are published in Egela and, in the case of the final exams, they are simultaneously published in GAUR system.

Once the marks have been published, the students who want to claim the exam have to indicate it in the established period of time. The claims of the students that do not indicate it, or that despite of indicating they do not come in the corresponding revision day at established timetable, will not be heeded. All this is done with the purpose of dedicating the necessary time to the revision process, and giving an equitable and fair solution to each claim.



Resignation:

As it is specified in the "Normativa Evaluación de Enseñanzas de Grado" any student that wants to resign from the continuous evaluation in order to do the final evaluation, then he/she has to present the resignation document to the teachers in charge of the subject in the period of 18 weeks counting from the starting of the course, according to the academic calendar of the faculty. The final evaluation implies a unique final exam which is the 100% of the final grade.

The work material of the subject that is available to the students, directly given by the teachers, is the following:

- The Student Guide of the subject.

- Guides for the preparation and accomplishment of the practical lectures of the subject.

- Simulation software for the computer-based practical lectures:

GIM, software for kinematic analysis and simulation of planar mechanisms (COMPMECH Research Group: Hernández, A.; Altuzarra, O.; Pinto, Ch.; Petuya, V.; Amezua, E.; Macho, E; Corral, J.; Diez, M.; Urízar, M.; Herrero, S.; Campa, F.J.)

User guide of GIM software (COMPMECH Research Group) Available in electronic format in Egela web site.

- ABB IRB 120 Robot.

- ADEPT Cobra e-vario 600 Robot.

- Parallel robot Physik Instrumente H-840.

- FANUC S-10 Robot.

- Work material for the lab lecture:

Experimental system of one degree of freedom for the measurement of transmissibility.

Digital signal analyser DI 2200, accelerometers, bending beam models and simplified building models, excitation table, signal generator and stroboscope.

Basic bibliography

The teachers will use the following reading material to teach the subject:



- Hernández, A.; CINEMÁTICA DE MECANISMOS. ANÁLISIS Y DISEÑO. ISBN: 84-7738-224-0. Ed. Síntesis, 2004.

Available at the publications' department of the University- Sección de publicaciones Escuela de Ingeniería de Bilbao, and in the bookshoop Bilbao Herriak (Licenciado Poza, 11), and Casa del Libro (Alameda Urquijo, 9).



- Hernández, A.; Aguirrebeitia, J.; Petuya, V.; Pinto, Ch.; DINÁMICA DE MÁQUINAS. ISBN: 978-84-9171-271-8. Editorial Síntesis, 2019. Publications' department of the University- Sección de publicaciones Escuela de Ingeniería de Bilbao



- Agirrebeitia, J.; Hernández, A.; Pinto, Ch.; Petuya, V.; BIBRAZIOEN TEORIA, OINARRIZKO JAKINGARRIAK. ISBN 84-95809-17-6. Publications' department of the University- Sección de publicaciones Escuela de Ingenierías de Bilbao, 2004.



- Compilation of exams. In Egela website.

In-depth bibliography

The students that are interested in studying some concepts in greater depth, have many books, journals, regulations and catalogs available at the university library and at the department of Mechanical Engineering. It is recommended to previously ask for advice to the teacher so that the student gets to know the best choice. A representative bibliography is the following:

- Uicker, J.J. (Jr.); Pennock, G.R.; Shigley, J.E. Theory of Machines and Mechanisms. Oxford University Press, 2003.
- Erdman, A. G.; Sandor, G. N.; Mechanism Design. Analysis and Synthesis. Prentice-Hall, 1997.
- Norton, R. L.; Diseño de Maquinaria, 1995.
- Waldron, K.J; Kinzel, G.L; Kinematics, Dynamics and Design of Machinery. John Wiley & Sons Inc, 1999.
- Shabana, A. A.; Theory of Vibration. An introduction. Springer, 1996.

Journals

- Mechanism and Machine Theory.
- Journal of Mechanisms and Robotics.
- IEEE Transactions on Robotics.
- Advanced Robotics.
- Robotica.
- Computer Applications in Engineering Education.
- Journal of Mechanical Design.

Web addresses

www.ehu.eus/compmech/software/
www.thinkmotion.eu
www.dmg-lib.org
http://kmoddl.library.cornell.edu
www.technologystudent.com
www.howstuffworks.com
www.biblioteka.ehu.eus