78818 - Mechanics Of Machines for Automation M 2

Learning outcomes

The course deals with advanced topics for the functional analysis and synthesis of mechanisms for automatic machines.

The student will learn the methods to study the direct and inverse dynamics of mechanisms, with both rigid and elastic elements, and interacting with their electrical actuation system.

The course is organized in four blocks:

1. Dynamics of Cyclic Machines with Rigid Links: advanced topics with a focus on the multidomain analysis of the dynamic interaction between mechanisms and electrical actuators.
2. Mechanics of Materials and Components: topic recall and advanced problems.
3. Dynamics of Mechanisms with Elastic Links.
4. Vibration of Machines with Elastic Transmission Mechanisms.
   
   
   

 

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.

Introduction to the multi-body software MSC ADAMS

• Review of multi-body system analysis,
• Modelling and analysis of a rigid-body spatial mechanism (serial robot),
• Introduction to multibody analysis with flexible bodies,
• Control system: introduction to mechatronics.

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

Lecture notes, compendium of exercises.

Office hours

See the website of Rocco Vertechy