Università degli Studi di Roma "Tor Vergata"

KINEMATICS Rigid body motion and Rivals theorems. Relative motion and Coriolis theorem. Instant center of rotation and Chasles theorem. Velocity vector field. Fixed and moving centrodes. Application: Cardan mechanism. Curvature analysis and Euler-Savary equation. Inflection circle and return circle. Aronhold theorems. Acceleration pole and Bresse circle. Acceleration vector field. Lower and higher kinematic pairs. Kinematic chains and derived mechanisms. Grübler’s formula. Kinematic inversion. Four-bar linkages and Grashof law. Slider-crank/rocker mechanisms. Double sliders mechanisms. Aronhold-Kennedy theorem. Collineation axis and Bobillier theorem. Loop closure equation method: four-bar and slider-crank analysis. Kinematic analysis of planar mechanisms. Introduction to the kinematic synthesis of planar mechanisms (graphical methods): rigid body guidance (two and three positions), straight path generators, function generators. Conjugate profiles and Euler-Savary equation. Gear transmissions. Transmission ratio, interference, minimum number of teeth, continuity of motion, contact ratio, sliding velocity. Kinematic analysis of epicyclic gear trains based on graph theory. Cardan joint. MECHANICAL VIBRATIONS Free and forced response of one degree-of-freedom mass spring-damper model. Amplification factor. Vibration of 1 d.o.f. system with moving base. Coefficients of transmissibility of forces and displacements. Logarithmic decrement. Average dissipated power. Two degrees-of-freedom systems: Equations of motion. Dynamic dampers. Fourier series. Free response of n degrees of freedom undamped system. Natural frequencies and vibration modes. Orthogonality of vibration modes. Decoupling of equations. Critical speed of shafts. Frequency equation. Dunkerley equation. Rayleigh method. DYNAMICS Equivalent systems of forces. The equations of Statics. Static analysis of a slider-crank. The Principle of Virtual Work and its application to statics. Resultant of inertia forces. The Lagrange-d'Alembert principle. Application of virtual work principle to the solution of dynamics problems. Energy balance equation. Mechanical efficiency. Static and dynamics analysis of slider-crank and four-bar linkages. Applications of the Principle of Virtual Work. Numerical integrations of equations of motion: methods of Euler, Heun, Runge.

1. R. Norton, Design of Machinery: An Introduction To The Synthesis and Analysis of Mechanisms and Machines,. 2. J. Denavit, R.S. Hartenberg, Kinematic Synthesis of Linkages (pdf available online) 3. Rao, S.S, Mechanical Vibrations, Wiley & Sons

KINEMATICS Rigid body motion and Rivals theorems. Relative motion and Coriolis theorem. Instant center of rotation and Chasles theorem. Velocity vector field. Fixed and moving centrodes. Application: Cardan mechanism. Curvature analysis and Euler-Savary equation. Inflection circle and return circle. Aronhold theorems. Acceleration pole and Bresse circle. Acceleration vector field. Lower and higher kinematic pairs. Kinematic chains and derived mechanisms. Grübler’s formula. Kinematic inversion. Four-bar linkages and Grashof law. Slider-crank/rocker mechanisms. Double sliders mechanisms. Aronhold-Kennedy theorem. Collineation axis and Bobillier theorem. Loop closure equation method: four-bar and slider-crank analysis. Kinematic analysis of planar mechanisms. Introduction to the kinematic synthesis of planar mechanisms (graphical methods): rigid body guidance (two and three positions), straight path generators, function generators. Conjugate profiles and Euler-Savary equation. Gear transmissions. Transmission ratio, interference, minimum number of teeth, continuity of motion, contact ratio, sliding velocity. Kinematic analysis of epicyclic gear trains based on graph theory. Cardan joint. MECHANICAL VIBRATIONS Free and forced response of one degree-of-freedom mass spring-damper model. Amplification factor. Vibration of 1 d.o.f. system with moving base. Coefficients of transmissibility of forces and displacements. Logarithmic decrement. Average dissipated power. Two degrees-of-freedom systems: Equations of motion. Dynamic dampers. Fourier series. Free response of n degrees of freedom undamped system. Natural frequencies and vibration modes. Orthogonality of vibration modes. Decoupling of equations. Critical speed of shafts. Frequency equation. Dunkerley equation. Rayleigh method. DYNAMICS Equivalent systems of forces. The equations of Statics. Static analysis of a slider-crank. The Principle of Virtual Work and its application to statics. Resultant of inertia forces. The Lagrange-d'Alembert principle. Application of virtual work principle to the solution of dynamics problems. Energy balance equation. Mechanical efficiency. Static and dynamics analysis of slider-crank and four-bar linkages. Applications of the Principle of Virtual Work. Numerical integrations of equations of motion: methods of Euler, Heun, Runge.

1. R. Norton, Design of Machinery: An Introduction To The Synthesis and Analysis of Mechanisms and Machines,. 2. J. Denavit, R.S. Hartenberg, Kinematic Synthesis of Linkages (pdf available online) 3. Rao, S.S, Mechanical Vibrations, Wiley & Sons