84229 - Mechanics of Machines for Automation M

Learning outcomes

The course aims at strengthening the knowledge on the modelling of mechanisms for automatic machines. Topics that are covered include: kinematics and dynamics of multibody systems with spatial motion and multiple degrees of freedom; dynamics of motor-transmission-load systems; mechanical vibrations of spring-mass-damper systems with multiple degrees of freedom. At the end of the course, the student possesses advanced notions and methodologies for the analysis and design of automatic machines.

Course contents

3D Rigid Body Kinematics: Finite motion

• Coordinate transformations,
• Rotation matrices,
• Homogeneous transformations.

3D Rigid Body Kinematics: Infinitesimal motion

• Angular velocity and angular acceleration,
• Vector derivatives in different reference frames,
• Instantaneous kinematics of rigid body systems.

Kinematics applications:

• Planar four bar-linkage mechanism,
• Planar five-bar linkage mechanism,
• 3R spherical linkage mechanism and gyroscope.

3D Rigid Body Dynamics: Forces and moments

• Gravity forces, elastic forces,
• Contact friction forces,
• Impulsive forces,
• Resultant force and moment.

3D Rigid Body Dynamics: Momentum and inertia forces

• Linear and angular momentum,
• Inertia matrix and inertia forces.

3D Rigid Body Dynamics: Laws of motion

• Dynamic equilibrium of a rigid body,
• Dynamic equilibrium of a multi-body system.

3D Rigid Body Dynamics: Kinetic energy

• Kinetic energy of a rigid body and of a multi-body system,
• Kinetic energy and the work of inertia forces.

3D Rigid Body Dynamics: Virtual work principle

• Work of external forces,
• Conservative and non conservative forces,
• Principle of virtual work.

3D Rigid Body Dynamics: Lagrange equations

• Lagrange equations of holonomic systems,
• Lagrange equations for constrained systems.

Dynamics applications:

• Lumped-parameter model of a 1-DOF mechanical transmission,
• Planar four-bar linkage mechanism,
• Planar five-bar linkage mechanism,
• 3R spherical mechanism and gyroscope.

Motor-load coupling:

• Characteristic curves of actuators and loads,
• Criteria for the choice/verification of actuator size,
• Effect of transmission ratio and flywheels,
• Choice of actuator and transmission ratio for static loads,
• Choice of actuator and transmission ratio for dynamic loads,
• Choice of actuator and flywheel for intermittent-motion machines.

Mechanical vibrations of 1-DOF spring-mass-damper systems:

• Recall on free vibrations and extension to systems with coulombic friction,
• Recall on the forced vibration response to harmonic forces (with complex number notation) and extension to impulsive, step, periodic and general excitation forces (via the convolution integral),
• Estimation methods for the calculation of system damping coefficient,
• Energetic (Rayleigh’s) methods for the approximate analysis of vibrations.

Vibration of 1-DOF system applications:

• Vibrations isolation,
• Vibration of a system excited from the base,
• Vibration model of a translation stage with screw-nut transmission,
• Vibration of a system with harmonic excitation due to imbalances,
• Whirling of rotating shafts (Jeffcott rotor),
• Energy absorption from an oscillating system,
• Vibrations of systems having a spring with no negligible mass,
• Approximate vibration response of beams.

Mechanical vibrations of n-DOF spring-mass-damper systems:

• Orthogonality of vibration modes and Expansion theorem for the decoupling of motion equations,
• Rigid body modes,
• Approximate approaches for the study of damped systems,
• Rayleigh-Ritz method for the approximate analysis of system lower modes.

Vibration of n-DOF system applications:

• Vibration reducing devices: vibration absorber, tuned mass damper,
• Vibration model of a shaft with multiple disks,
• Vibration model of a motorcycle,
• Vibration model of a cam-lever-valve system.

Readings/Bibliography

• H. Baruh, Applied Dynamics, 2015, CRC Press.
• S. Rao, Mechanical Vibrations, 2010, Prentice Hall.
• G.Legnani, M.Tiboni, R.Adamini, D.Tosi, Meccanica degli Azionamenti, 2016, Esculapio.

Teaching methods

The course is based on lectures, during which the arguments of the program will be covered, and on exercises hours, which will present application examples related to the themes discussed during lectures.

Assessment methods

Written examination.

Teaching tools

Movies of automatic machines, PC, projector.

Lecture notes, presentations and other teaching materials will be available on IOL

Office hours

See the website of Rocco Vertechy

See the website of Michele Conconi