Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

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Aim of the course is the analysis of the dynamics of systems consisting in articulated rigid bodies, and its use in human movement describing the specificities of these concepts in biomechanics. In particular, focus is on the inertial body parameters estimations, and on the computation of joint moments using an inverse dynamics approach. Musculoskeletal modeling is also presented

By this mandatory course, the students learn how to establish the laws of motion linking the movement of a multi-body system (the musculoskeletal system) and the causes of this movement (mechanical actions). They are able to choose and apply the relevant methods to quantify the joints loads in different situations, from the determination of body segment inertial parameters to the calculation of the joints net moments. The examples are mostly in the domain of human movement analysis (sport gestures, ) . The students are aware of measurement errors and to the main hypotheses to assume to establish the movement equations, so that they keep a critical mind when they have to interpret their results for example in a clinical context.

Capabilities of: synthesis, autonomy and clarity. Read a document, understand an interlocutor expressing himself, and speak in English. Work in an international context.

. Dynamics of a material point a. Some basic concepts (reference frame, mass, linear momentum, angular momentum) b. Newtons first law of inertia c. Newtons second law or Fundamental Principle of Dynamics d. Newtons third law or Action-Reaction law e. Some classical forces (gravitational force, friction force, spring force) II. Work, kinetic energy, kinetic moment and related theorems a. Work and Power b. Kinetic energy and work-energy theorem c. Conservative forces and potential energy d. Conservation of total energy e. Angular momentum theorem III. Kinetics of a rigid body a. Introduction b. Mass distribution c. Centre of mass d. Kinetic energy associated to the movement of a solid e. Kinetic vectorial quantities associated to the movement of a solid f. Koenigs theorems for the kinetic energy and the angular momentum g. Kinetics of the specific movement of a solid around a fixed point h. Matrix of the inertia tensor in any direct orthonormal basis i. Application of the Koenigs theorems for kinetic calculations j. Time derivative of the linear and angular momentums k. Application in human movement : Inertial body segment parameters evaluation IV. Rigid multi-body dynamics a. Introduction b. Fundamental Principle of Dynamics c. Kinetic energy theorem d. Energy conservation theorem e. Joint modelling f. Application in human movement i. External forces measurement devices ii. Inverse dynamics method to compute net joint moments V. Lagranges equations of motion a. Generalized coordinates and kinematical constraints b. Generalized forces and virtual work c. Lagranges equations of motion VI. Musculoskeletal modelling a. Musculo-skeletal models i. Muscle contraction dynamics model ii. Muscle-tendon dynamics model iii. Skeletal dynamics model b. Prediction of mucle-tendon and joint reaction forces i. Static optimization ii. EMG to force iii. Forward dynamics assisted data tracking The course notes will be available for students in PDF format. New concepts will be regularly applied on exercises, mostly related to human movement.

The assessment of student learning consists of a two written tests, composed of two or three exercises on topics covered in the course, to be completed in 120 minutes.

To successfully pass the examination, the student must demonstrate to have well understood the concepts presented in the course and that he/she is able to apply these concepts in typical concrete situations.

A score between zero and thirty is assigned for each written test. The overall grade is the average of the scores obtained in the two tests, with rounding to the entire excess.

The student must achieve at least the sufficiency, equal to 18/30, in the overall grade. The highest rating is achieved by demonstrating a thorough understanding of the course content in the tests. Laudem is given to students who, having done all the tests so correctly, have demonstrated a particular brilliance in the exposition and in the preparation of the written tests.

Vladimir M. Zatsiorsky:Kinetics of human motion, Human Kinetics (2002) Aydin Tozeren,Human body dynamics : Classical mechanics and human movement Springer (2000) Arthur Chapman, Biomechanical analysis of fundamental human movements Human Kinetics (2008) Masud Chaichian, Mechanics : An intensive courseSpringer (2012)

- Biomedical Engineering (Corso di Laurea Magistrale (DM 270/04))

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