00687 - Mechanics of Machines

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education Industry, innovation and infrastructure

Academic Year 2021/2022

Learning outcomes

The course provides the fundamentals for the kinematic, static, and dynamic analysis of mechanical systems of the type commonly found in machinery.

Course contents


Terminology of Mechanism Theory: Definition of machine. Kinematic chains and mechanisms. Kinematic pairs. Mobility analysis. Gruebler criteria.

Kinematics of a rigid body: The relative instantaneous center. Kennedy-Aronhold Theorem. Velocity and acceleration relationships.

Kinematic analysis of mechanisms: The four bar mechanism. The slider-crank mechanism. 2R planar manipulator. Closed-loop and Open-loop mechanisms. Graphical Kinematics: velocities and accelerations. Analytical Kinematics of planar mechanisms.

Machine's Efficiency: Principle of Tribology. Contact forces. Efficiency. Friction. Coulomb friction. Coefficient of friction. Wear. Reye principle. Rolling friction.

Statics and Dynamics: The free-body diagram. Superposition. Graphical force analysis. Analytical Statics.  Calculating Reactions. The Principle of Virtual Work. Kinetic Energy. D'Alembert principle and Inertial forces. Lagrange's equations.

Static analysis of mechanisms: Ideal (workless) constraints. Reaction in ideal mechanisms. Static effects of friction. Slider friction. The inclined plane (ramp). Efficiency of the screw. Friction in hinge joints. Problems.

Gears: Fundamental law of Gearing. Spur Gears and helical gears. Gear Tooth forces. Gear trains. Planetary Gear trains.

Pulleys: fixed and movable pulley; pulley system; block and tackle.

Belt drives: flat belts; trapezoidal belts.

Reciprocating engine dynamics: inertial forces; bearing reactions; balance of slider-crank machines.

Flywheel calculations.

Mechanical vibrations: Single dof model. Free response and forced response of the single dof system. The seismograph and the accelerometer. Vibration isolation.

Balancing of machinery: balance of rigid rotors.



Lezioni di Meccanica Applicata alle Macchine. Prima parte: Fondamenti di Meccanica delle Macchine, ed. Pàtron, Bologna.

2. Callegari M., Fanghella P., Pellicano F., Meccanica Applicata alle Macchine (Seconda Edizione), CittàStudi, 2017.

3. Doughty S., Mechanics of Machines, John-Wiley & Sons, 1988.

4. C. E. Wilson, J. P. Sadler, Kinematics and dynamics of machinery, Prentice Hall, 2003.

5. Copy of the slides.

Teaching methods

The course is based on lectures dealing with the theoretical aspects of the course topics and application examples.

Class attendance, although not mandatory, plays a fundamental role in the learning and evaluation process.

Assessment methods

The exam will be hel by means of the application Esami On Line (EOL).

During the period related to the COVID emergency, the exam will be held in Online mode through the combined use of the On Line Exams (EOL) and Zoom platforms.
General indications are available on https://virtuale.unibo.it.

The final examination is written and consists in solving three problems that aim to ensure the acquisition of knowledge expected by the course program and to assess the achievement of learning objectives:

  • knowledge of the functional principles of machines and mechanisms;
  •  ability to solve simple problems of kinematics, kinetostatic and dynamics of planar mechanisms.

The use of books or notes is not allowed during the exam. Upon the express indication of the examination board, the use of a calculator may be allowed.

The duration of the written test is two hours and is based on three types of questions; each of them is assigned a maximum score of 11.

The ability of the student to solve the proposed problems or articulate and correctly explain the answers to the questions, has a fundamental weight in the attribution of the score.

The exam is passed if the score is at least 6 for each type of questions. If the total score is greater than 30, the final grade will be "30 e lode", to confirm the high level of kowledge achieved in the study.

For students who have " Mechanics of Machines and Materials (Integrated Course)" in their study plan, the overall grade of the Integrated Course will be recorded once both the "Mechanics of materials and structures" examination and the "Mechanics of Machines" examination have been passed. The overall grade will be calculated as the average of the grade obtained in the two individual exams (the evaluation of "30 with honors" obtained in one of the individual exams is equivalent to 31). If this average is greater than or equal to 30, the final grade will be "30 e lode". If the average is a semi-integer number, the final grade will be obtained by rounding up the average.

The order of the two exams is irrelevant. The results of the two exams do not expire.

In accordance with the Art. 16 of the University Didactic Regulations, if a positive grade does not meet the expectations of a student, the latter may ask its cancellation and the repetition of the examination. The instructors of the course comply with the following rules:

  • a student may request the cancellation of a positive grade only within the date of the examination;
  • a cancelled positive grade can in no way be recovered;
  • a student may request the cancellation of a positive grade at most once.


Teaching tools

Blackboard, PC.

On the E-learning Platform (https://virtuale.unibo.it), students may find: slides of the course lectures; exercises and application examples.

Office hours

See the website of Alessandro Rivola