OVERVIEW

The course introduces 3D biomechanical modelling and analysis of biological and bio-robotic systems. Starting from principles of physics, geometry and mechanics, students will learn to describe, compute and interpret the direct and inverse kinematics and dynamics of body segments, joints, the eye, the whole body, and interactions with robotic interfaces.

AIMS AND CONTENT

LEARNING OUTCOMES

The course aims to provide students with the theoretical, computational and methodological tools needed to formulate and solve problems in 3D biomechanics. It is designed to help students understand how concepts learned in physics, geometry, rational mechanics, dynamical systems and signal processing are applied to the quantitative analysis of biological movement and of physical interaction between the human body and robotic devices.

The main objective is for students to be able to approach a biomechanical problem as an engineering problem: defining the system, choosing the coordinates, formulating a mechanical model, computing kinematic and dynamic quantities, critically interpreting the results, and discussing the limitations and assumptions of the model.

AIMS AND LEARNING OUTCOMES

By the end of the course, students will be able to:

1. Describe a 3D biomechanical system as a set of rigid bodies, reference frames, generalized coordinates, constraints, actuators and external forces.
2. Define local and global reference frames and use rotation matrices and rigid transformations to describe the position, orientation and motion of body segments or biological systems.
3. Solve direct kinematics problems, computing the position, orientation, velocity and acceleration of points or body segments starting from joint or generalized coordinates.
4. Solve inverse kinematics problems, estimating the joint or generalized coordinates most consistent with an observed or assigned configuration.
5. Apply the equations of rigid-body dynamics to biological systems, from a single body segment to simple multi-segment chains.
6. Perform inverse dynamics analysis, estimating joint or generalized forces and moments from observed motion, inertial parameters and external forces.
7. Perform direct dynamics analysis, simulating the motion resulting from assigned forces, moments, initial conditions and constraints.
8. Analyse the physical interaction between the human body and robotic interfaces, computing the effects of external forces, wrenches, constraints and moments applied by end-effector or exoskeletal devices.
9. Critically interpret biomechanical results, distinguishing between computed quantities, measured quantities, modelling assumptions, numerical uncertainties and functional or biomedical meaning.
10. Produce a short technical report or computational notebook documenting the model, data, method, results, limitations and interpretation of a 3D biomechanical analysis.

PREREQUISITES

Basic knowledge of linear algebra, analytical geometry in space, differential calculus, general physics, mechanics of particles and rigid bodies, differential equations and scientific programming is useful.

In particular, the course will use concepts such as vectors, matrices, scalar and vector products, reference frames, rotations, time derivatives, Newton-Euler laws, dynamic equations and numerical representation of data.

TEACHING METHODS

The course includes theoretical and applied lectures, guided exercises, computational activities and the development of a final project.

Theoretical lectures will introduce the fundamental concepts and connect them to real biomechanical problems. Exercises will be based on models and data provided by the instructor and will aim to progressively build a 3D biomechanical analysis pipeline.

Attendance is strongly recommended, especially for exercises, since practical activities are an integral part of achieving the expected learning outcomes.

Students who hold valid certificates relating to Specific Learning Difficulties (SLD), disabilities or other educational needs are invited to contact the lecturer and the school’s disability liaison officer at the start of the course to agree on any teaching arrangements which, whilst respecting the course objectives, take into account individual learning styles. 

The contact details for the university’s disability liaison officer are available at the following link: https://unige.it/commissioni/comitatoperlinclusionedeglistudenticondisabilita. 

SYLLABUS/CONTENT

1. Introduction to 3D computational biomechanics

Definition of a biomechanical system. Body segments, joints, the eye, the whole body and human-robot systems as mechanical systems. Generalized coordinates, degrees of freedom, constraints, biological and robotic actuators. Difference between descriptive, kinematic and dynamic analysis.

2. Reference frames and 3D transformations

Global and local reference frames. Orthonormal bases. Rotation matrices. Rigid transformations. Homogeneous coordinates. Change of reference frame for points, vectors, forces and moments. Conventions and limitations in the description of 3D orientation.

3. Direct kinematics

Description of the pose of a rigid body. Direct kinematics of a single segment and of an articulated chain. Concatenation of transformations. Computation of the position and orientation of anatomical points, body extremities, visual axis or biological/robotic end-effector.

4. Inverse kinematics

Formulation of the inverse problem. Estimation of joint coordinates from known poses or points. Determined, overdetermined and underdetermined problems. Least squares. Kinematic constraints. Ambiguity and non-uniqueness of the solution. Applications to body segments, upper limb, lower limb and eye.

5. Velocities, accelerations and Jacobian

Linear and angular velocity. Linear and angular acceleration. Numerical differentiation. Relationship between joint velocities and Cartesian velocities. Kinematic Jacobian. Biomechanical interpretation of the Jacobian. Relationship between external forces and generalized moments through the transpose of the Jacobian.

6. Rigid-body dynamics

Mass, centre of mass, inertia tensor. Linear momentum, angular momentum, resultant forces and moments. Newton-Euler equations in 3D. Inertial parameters of body segments. Dynamics of a single biological segment.

7. Inverse dynamics

Definition of the inverse dynamics problem. Estimation of net forces and moments from motion, accelerations, inertial parameters and external forces. Inverse dynamics of an isolated segment. Inverse dynamics of simple multi-segment chains. Interpretation of net joint moments and mechanical powers.

8. Direct dynamics

Definition of the direct dynamics problem. Equations of motion in general form. Simulation of motion starting from forces, moments, constraints and initial conditions. Differences between inverse analysis and direct simulation. Numerical stability and biomechanical meaning of simulations.

9. Power, work and energy

Mechanical power of forces and moments. Joint power. Generation and absorption of energy. Functional interpretation of power in biological movements. Energy exchange between the subject and the environment or between the subject and a robotic interface.

10. Physical human-robot interaction

Contact forces, 3D wrench, mechanical constraints and exchanged power. Interaction with end-effector robots, exoskeletons and haptic interfaces. Computation of the joint effects of a robotic force applied to the hand, foot, trunk or another segment. Elements of impedance, admittance and mechanical safety in interaction.

11. Application examples on different biological systems

Analysis of an isolated body segment. Simplified analysis of eye movement. Analysis of an articulated chain of the upper or lower limb. Whole-body analysis in a functional movement. Comparison between models with different numbers of degrees of freedom.

RECOMMENDED READING/BIBLIOGRAPHY

Main recommended textbooks

• D. A. Winter, Biomechanics and Motor Control of Human Movement, Wiley.
• V. M. Zatsiorsky, Kinetics of Human Motion, Human Kinetics.
• V. M. Zatsiorsky, Kinematics of Human Motion, Human Kinetics.
• Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues, Springer.
• M. W. Spong, S. Hutchinson, M. Vidyasagar, Robot Modeling and Control, Wiley.
• R. M. Murray, Z. Li, S. S. Sastry, A Mathematical Introduction to Robotic Manipulation, CRC Press.

Teaching material

Lecture notes, slides, exercises, computational notebooks, datasets or example files will be made available through AulaWeb.

Any scientific papers, software documentation and supplementary materials will be indicated during the course.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

https://easyacademy.unige.it/portalestudenti/index.php?view=easycourse&_lang=it&include=corso

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of:

1. Individual written test on biomechanical models or data, aimed at assessing the student’s ability to set up and solve a 3D kinematics or dynamics problem.
2. Final project, individual or in small groups, concerning a 3D biomechanical analysis of a biological or bio-robotic system.
3. Oral exam on theoretical and methodological questions, aimed at assessing understanding of mechanical principles, modelling assumptions and biomechanical interpretation of the results.

The final grade will be expressed out of 30.

The instructor may include mid-term tests or intermediate assignments linked to the exercises. In that case, their contribution to the final assessment and their period of validity will be communicated at the beginning of the course and reported on AulaWeb.

ASSESSMENT METHODS

The individual written test will assess the student’s ability to apply the methods covered in the course operationally. In particular, it will assess the ability to:

• define a 3D biomechanical model;
• choose appropriate coordinates and reference frames;
• compute kinematic quantities;
• set up a direct or inverse kinematics problem;
• set up a direct or inverse dynamics problem;
• compute forces, moments or powers;
• interpret the biomechanical meaning of the results.

The final project will assess the ability to carry out a complete and documented analysis. The following aspects will be considered:

• clarity of the biomechanical question;
• correctness of the model;
• consistency between assumptions, methods and results;
• quality of graphs and numerical processing;
• ability to discuss limitations and sources of error;
• quality of the technical report or notebook;
• ability to communicate the result concisely and rigorously.

The theoretical questions will assess understanding of the physical and mechanical principles underlying 3D biomechanical analysis, with particular attention to the distinction between direct kinematics, inverse kinematics, inverse dynamics and direct dynamics.

The grade will take into account not only numerical correctness, but also reasoning ability, appropriate use of technical language and the ability to connect the mathematical result to its biomechanical meaning.

FURTHER INFORMATION

Students with valid certifications for Specific Learning Disorders (SLD) may request accommodations for exams at least 7 days prior to the exam date by filling out the “accommodation request form” (available via online services at https://modulionline.unige.it/richiesta-adattamenti# no-back), which will be automatically forwarded by the system to the instructor in charge of the course and to the faculty liaison for students with disabilities and SLDs in their School/Department. 

The student will receive a copy of their request.