Teacher

prof. Alessandro GASPARETTO

Credits

6 CFU

Language

Italian

Objectives

This course provides the knowledge necessary to understand the basic principles of mechanics, both in kinematics and in dynamics, with the aim to build mathematical models of planar mechanisms. The course also provides techniques for kinematic, static and dynamic analysis of mechanical systems.

Acquired skills

- Ability to build kinematic and dynamic models of mechanical systems.
- Ability to carry out the kinematic, static and dynamic analysis of a mechanical system, in particular of a planar mechanism.

Lectures and exercises (topics and specific content)

Basic principles for the study of the mechanisms: introduction to the course; examples of design of industrial machines (machine for textile industry, machine for food industry); definition of mechanism, degrees of freedom, planar motion; typology and class of kinematic pairs; examples of mechanisms, four-bar linkage, rod-crank, five-bar linkage; calculation of the number of degrees of freedom for a mechanism; structure equation; kinematic model of a mechanism; example: inserter mechanism for an automatic sewing machine (5 hours).
Kinematic analysis of planar mechanisms: kinematic position analysis of planar mechanisms; position closure equation; calculation of the position of a generic point of the mechanism; application to various mechanisms, rod-crank, four-bar linkage and five-bar linkage with revolute and prismatic pairs; Newton-Raphson method for solving the nonlinear system resulting from the position analysis; mechanisms with several loops, position analysis of the glyph; decomposition of a mechanism in base-mechanisms and Assur groups; typology of Assur group, dyads, triads and tetrads; types of dyads; position analysis of the RRR dyad; position analysis of the RRP dyad; position analysis of the inserter mechanism; kinematic velocity analysis of planar mechanisms; velocity closure equation in matrix form; example: velocity analysis of a four-bar linkage; calculation of the velocity of a generic point of the mechanism;  velocity ratio: definition and properties; exercises on the calculation of velocity ratios for various mechanisms; velocity analysis of the RRR and RRP dyads; velocity analysis of the inserter mechanism; singular configurations of a mechanism; examples: rod-crank mechanism, four-bar linkage, five-bar linkage; kinematic acceleration analysis of planar mechanisms; acceleration closure equation; meaning of the four acceleration components;  acceleration ratio, definition and properties; singularities in the acceleration analysis; acceleration analysis of the RRR and RRP dyads; aceleration analysis of the inserter mechanism; calculation of the inertial loads in the inserter mechanism of a textile machine (27 hours).
Static analysis of planar mechanisms: definition of mechanical equilibrium; conditions of static equilibrium according to the Newtonian approach; example of static analysis of a mechanism with the Newtonian approach; condition of static equilibrium according to the Lagrangian approach; principle of stationary potential and principle of virtual work; static analysis of mechanisms with the Lagrangian method; examples of static analysis of mechanisms with the Lagrangian method (rod-crank, open loop planar manipulator and closed loop planar manipulator); example of kinematic and static analysis of mechanisms with a dedicated software (12 hours).
Dynamic analysis of planar mechanisms: dynamic analysis of mechanisms; moments and products of inertia; the inertia operator and the inertia matrix; axes and principal moments of inertia; examples of moments of inertia for some types of rigid body; dynamics of rigid systems; calculation of the momentum, of the kinetic energy and of the power of the applied forces; cardinal equations for rigid systems; equations of motion for a rigid body that rotates around a fixed axis; definition of the dynamic equilibrium by means of the D'Alembert’s principle; Lagrange equations in the first form; Lagrange equations in the second form; dynamic equilibrium equations for planar mechanisms with the Lagrangian method and with the Newtonian method; example,  otating crank; reduced inertia for a planar mechanism plan with 1 degree of freedom; dynamic analysis of mechanisms using the reduced inertia; examples, four-bar linkage, rod-crank (16 hours).

References

- Appunti delle lezioni
- Dispense sul sito del materiale didattico
- M. Giovagnoni, A. Rossi, Una introduzione allo studio dei meccanismi, Ed. Cortina, Padova

Type of exam

Written and oral

Additional material or information on line