Machine Elements II


The main objectives of Machine Elements II course are:

- To know how to use the graphical and semi-graphical methods, as well as the Cartesian formulation of mechanisms, to determine displacement, velocity, acceleration and forces applied on mechanisms;

- To know how to determine displacement, velocity, acceleration and forces on mechanisms using numerical computer codes (Computer-Aided Engineering), such as SolidWorks, Motion and Simulation.

- To use graphical methods to perform synthesis/design of simple mechanical systems;

- To know how to design axisymmetric pressure vessels submitted to internal and/or external pressure using theoretical equations and the ASME Boiler and Pressure Vessels Code, Section VIII, Division 1.

- To know how to manufacture pressure vessels, including cut, bending and welding of shells. Stress relief treatments, as well as non-destructive testing, will be studied.

- To know how to calculate the hydrostatic pressure test value and the detailed procedures to perform the test.

-  To determine deflections, stresses and strains induced on thin and supported plates using the Navier and the Rayleigh-Ritz methods.

General characterization





Responsible teacher

António José Freire Mourão, Rui Fernando dos Santos Pereira Martins


Weekly - 3

Total - 56

Teaching language



No special requirements are needed.


Schwamb, Merril, James & Doughtie, "Nociones de Mecanismos", Ed. Aguilar S.A. (1985)

Sclater, N., Chironis, N., MECHANISMS AND MECHANICAL DEVICES, SOURCEBOOK, Fourth Edition, McGraw-Hill, 2007

Bednar, Henry H., "Pressure vessel design handbook", Ed. Van Nostrand Reinhold Company (1991)

Ugural, Ansel C., "Stresses in plates and shells", 2a Edição, McGraw-Hill International Editions (1999)

Bibliographical elements furnished by the teacher, namely: slides, exercises, etc

Teaching method

The oral exposition is the teaching method mainly used, associated with sketches, schemes and resumes made by the teacher in the classroom''''s blackboard. The video projector is also used in the classroom. In the practical classes, the teacher solves representative problems to introduce the strategies of resolution of exercises to the students. Then, other exercises are presented and a time period is fixed to its resolution. The teacher will attend any doubts during this period. All exercises are solved in the blackboard and are commented.

The lab/computational work has two main objectives, namely, to compare theoretical with experimental/numerical results and to give the students the possibility to gain some practical experience. The numerical simulations will also allow the students to review some of the subjects taught during the semester.

Evaluation method

The evaluation of students is carried out through a Theoretical and Practical Assessment, which includes two tests, T1 and T2, and a Laboratory or Project Assessment, which includes a practical work, TC.

The final classification, NF, obtained through continuous assessment, will be calculated according to the following formula:

NF = 0.35 x T1 + 0.35 x T2 + 0.3 x TC

where T1 and T2 represent the classifications, rounded to centesimal place, obtained in Tests 1 and 2, respectively, while TC represents the classification, rounded to centesimal place, obtained in the practical work.

The acquisition of frequency, valid for one year, is dependent on obtaining a grade equal or higher than 9.50 (out of 20) in the practical work.

With regard to the Theoretical-Practical evaluation, a weighted average equal to or higher than 9.50 in the two tests is required.

The practical work should be done in groups (maximum number of students / group: 3).

If a student does not reach the minimum score required in the Theoretical-Practical Component Evaluation during the period of continuous assessment, but have obtained frequency, the student may carry out an Exam during Appeal, Special and Extraordinary Seasons.

The exam will be divided in two parts, Exam(T1) and Exam(T2), related with the subjects of the two tests carried out during the continuous assessment period. The calculation of the final classification will be carried out using one of the three following formulas:

NF = 0.35 x Exam(T1) + 0.35 x Exam(T2) + 0.3 x TC

NF = 0.35 x T1 + 0.35 x Exam (T2) +  0.3 x TC

NF = 0.35 x Exam (T1) + 0.35 x T2 + 0.3 x TC

where Exam (T1) and Exam (T2) represent the classifications, rounded to centesimal place, obtained in Exam (tests 1 and 2, respectively), while TC represents the classification, rounded to centesimal place, obtained in the practical work. A weighted average, equal or higher than 9.50, must be obtained in Exam (T1) and Exam (T2), or in T1 and Exam (T2), or in Exam (T1) and T2, in order to get approval.

During the 2nd test (T2) and the Exam (test2), the usage of a formulary, exclusively related to thin plates theory and thin shells theory, is allowed. The formulary must be handwritten.

Subject matter

Mechanism and machine theory: cartesian formulation, graphical and semi-graphical methods for the analysis of displacement, velocity and acceleration of mechanisms. Kinematics and dynamics of machines. Graphical methods for the synthesis of mechanisms with 2 and 3 coordinate positions. Numerical simulation of mechanisms using computer aided engineering software, such as: SolidWorks, CosmosMotion and Simulation/Ansys.

Pressure vessels: design and fabrication of axisymmetric pressure vessels. Introduction to its design through standards, such as ASME Boiler and Pressure Vessels Code, Section VIII, Division 1 and EN 13445 - Unfired pressure vessels.

Theory of thin plates: calculation of deflections, stresses and strains using the Navier and the Rayleigh-Ritz Methods.


Programs where the course is taught: