Abstract:

This paper presents an experience about the didactical approach that we have adopted for teaching to BSc students of the School of Engineering at the University of Bergamo a rather complex subject, such as the kinematic analysis of planar mechanisms.

Planar mechanisms, cam and linkages, are typically used to transform the input motion from a mover into the desired output motion of the follower, or to constrain a rigid body to follow a specific path. The kinematic analysis of such systems is not trivial and requires both intuition and method.

Since a lot of years, mechanisms are taught in the "general" course of “Mechanical Systems Engineering”, delivered within the bachelor degree of Mechanical Engineering during the fifth semester, and in the course of “Theoretical and Applied Mechanics” offered both to undergraduate students of “Management Engineering” (sixth semester, elective) and “Technology Engineering for Health” (fourth semester, compulsory).

The kinematic analysis methods span from graphical to analytical approaches. Analytical approaches, based on complex numbers or matrix formulation, are essential to deal with the more challenging problem of mechanisms synthesis and optimization, not addressed in the above-mentioned courses, since it is a topic covered in the Master Degree of Mechanical Engineering.

In order to help students to improve their mechanical sensibility and to develop geometric insight, we are used to teach this topic using both the traditional graphical methods and the analytical approach.
From an educational point of view each of these approaches has pros and cons.

Graphical methods are simpler to use and require less effort when a kinematic analysis in a given configuration of the mechanism is required. Moreover, these methods can be easily implemented on a computer using the sketching mode of any commercial parametric CAD to obtain quantitative results. However, they require a good intuition and some practice in different cases.

Analytical methods, based either on matrix formulation or on complex numbers, are less suited to hand computation, but the procedure can be easily implemented in a software code allowing students to be introduced to numerical simulation. Less intuition is required, but mechanical sensitivity can be recovered only after the examination of several graphs produced by the simulation.

The advantage of the proposed mixed didactic approach to the kinematic analysis of mechanism is that the students can both perform the analysis with a program developed by themselves and acquire intuition about mechanism behaviour. Moreover, the graphical method can be used as a check for the correctness of the simulation in a small sample of configurations.

Students, when inquired, show to appreciate this approach and are found with a good background in Master Degree courses.

Keywords:

Mechanism kinematic analysis, graphical methods, analytical approaches, teaching experience.