Course information

Kinematics of the rigid body: translational motion, rotation around a fixed axis, general plane motion, calculation of velocity and acceleration, instantaneous pole of rotation, rotation around fixed point (spherical motion), angular speed and acceleration, derivative of a vector with respect to a rotating cartesian frame, general space motion, relative motion of point, Euler angles. Dynamics (kinetics) of a rigid body: Euler equations for rigid bodies, angular momentum and inertia tensor, motion equations for rigid body, principle of impulse-momentum, principle of work-energy. Analytical dynamics: Lagrange equations, integrals of motion, Hamilton’s principle. Introduction to the kinematic and dynamic analysis in planar mechanisms, design steps and iterations in mechanisms, constraint requirements, kinematic link-chains-mechanisms and machines, mobility of mechanisms, kinematic inversion, kinematic pairs and joints. Groups of Mechanisms according to their operating principle and application: 4-bar linkage (parallel and non-parallel, drag link, crank and rocker), slider crank mechanism, scotch yoke mechanism, quick return mechanisms, straight line mechanisms, parallel mechanisms (pantograph), toggle mechanisms, Oldham coupling, universal joints (Kardan joints), intermittent motion mechanisms (Geneva wheel-Malta cross), ratchets, elliptic trammel. Kinematic analysis of mechanisms applying vector analysis using the loop closure equation, for position analysis - velocity analysis - acceleration analysis. Application in slider crank mechanism - 4/5-bar mechanism - mechanisms with sliding links - compound mechanisms. Dynamic analysis of mechanisms applying D' Alembert principle (converting dynamic problem to static). Application in slider crank mechanism - 4/5-bar mechanism - mechanisms with sliding links - compound mechanisms. Synthesis of mechanisms: Freudenstein's method and application in 4-bar mechanism. Gyroscopes and Gyroscopic coupling: Calculation of the gyroscopic coupling moment in rotating elements, mechanisms based on gyroscopic phenomena. Flywheels: the problem of instantaneous fluctuation of speed - energy considerations and energy flow in mechanisms (energy balance) - design of flywheels. Design of Cams: Cam profiles and follower motions (linear, harmonic, cycloidal), the challenge for jerk-free motion- cam design using polynomials. Balancing of mechanisms: static and dynamic balancing of mechanisms and of the 'rigid' machine.