Mechanical Engineering

COURSE SYLLABUS APPLIED MECHANICS FOR MACHINES Prof. Antonio Carcaterra Contents Course Objectives Kinematics and Dynamics of Rigid Body Systems Force Analysis in Machine Components Mechanical Components: Rigid friction wheels Gears Rolling of deformable wheels and tire theory Gear reducer dynamics Planetary gear systems Cams Electric and thermal engines Brakes Propellers Power Transmission Systems: (Engines and brakes, stepped gearboxes, continuously variable transmissions, electromechanical power combiners, CVTs) Mechanics of Devices and Actuators Applications: Cars, motorcycles, drones Course Tools MATLAB and SIMULINK Rigid body kinematics Rigid body dynamics (Newton-Euler) System dynamics (Newton-Euler vs. Lagrangian approach) Multibody system dynamics (Lagrangian method + Lagrange multipliers) Exam Format Analysis and modeling of a complex mechanical device SECTION 1: KINEMATICS OF A PARTICLE 1.1 Kinematics of a material point SECTION 2: RIGID BODY KINEMATICS 2.1 Rotation matrix 2.2 Properties of the rotation matrix 2.3 Rotation about a fixed axis 2.4 Composition of rotations 2.5 Rotation matrix via Cardan angles 2.6 Roto-translations 2.7 Velocity and acceleration distribution 2.8 Planar motions 2.9 Reference frame transformation for operators SECTION 3: APPLIED KINEMATICS PROBLEMS 3.1 Robotic arm (rotation operator method) 3.2 Wheel (rotation operator method) 3.3 Planetary gear train (rotation operator method) 3.4 Engine crank mechanism analysis: Rotation operator method Loop-closure equations Velocity and acceleration polygons 3.5 Vehicle suspension (loop-closure equations) 3.6 Oscillating glyph drive mechanism SECTION 4: DYNAMICS OF RIGID BODIES AND RIGID BODY SYSTEMS 4.1 Review of particle dynamics 4.2 Rigid body dynamics 4.3 First cardinal equation (linear momentum) 4.4 Second cardinal equation (angular momentum) 4.4.1 Inertia matrix 4.4.2 Expression of angular momentum using inertia tensor 4.5 Summary of rigid body dynamics 4.6 Euler’s equations 4.7 Power balance equation 4.8 Lagrangian equations for complex mechanical systems 4.9 Case study: Quadrotor drone dynamics in 3D space SECTION 5: GEARS 5.1 Friction wheels and gears 5.2 Involute curve and its properties 5.3 Geometric parameters of gears 5.4 Gear kinematics 5.5 Force analysis in gear systems SECTION 6: ELEMENTS OF POWER TRANSMISSION DESIGN 6.1 Objectives of power transmission 6.2 Shaft torsional sizing 6.3 Shaft bending verification 6.4 Gear tooth sizing 6.5 Bearing selection SECTION 7: APPLIED MECHANICS PROBLEMS Problem 1: Motorcycle dynamics (Case 1) a) Acceleration profile b) Maximum climbable slope c) Force calculations Problem 2: Truck dynamics Problem 3: Motorcycle dynamics (Case 2) Problem 4: Amusement park ride mechanism a) Motor torque calculation b) Reaction forces at the base Problem 5: Aircraft propulsion system a) System motion equations b) Force calculation in the gearbox Problem 6: Motion conversion device a) System motion equations b) Motor torque calculation c) Force analysis on guides Problem 7: Pneumatic device Problem 8: Sports car dynamics Problem 9: Aircraft dynamics Problem 10: Pneumatic system with planetary gear train Problem 11: Centrifugal clutch speed governor a) Lagrange equation formulation b) Stationary solution and limiting speed Problem 12: Dynamics of a reciprocating internal combustion engine a) Physical modeling and mathematical formulation b) Crank mechanism kinematics c) Crank mechanism dynamics d) Observations on the nature of the resulting equations

Fisica I, Meccanica razionale, Disegno di macchine

A.Carcaterra, MECCANICA APPLICATA ALLE MACCHINE, Edition 2022-2023 –LECTURE NOTES

The evaluation method is based on a written and an oral test.

The course is based on classroom lectures in which all theoretical argument are presented. The course is completed by lessons for the development of exercises based also on the use of the computer