84201 - Fundamentals of Biomechanics

Academic Year 2023/2024

  • Docente: Rita Stagni
  • Credits: 6
  • SSD: ING-IND/34
  • Language: Italian
  • Moduli: Maria Cristina Bisi (Modulo 1) Rita Stagni (Modulo 2)
  • Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
  • Campus: Cesena
  • Corso: First cycle degree programme (L) in Biomedical Engineering (cod. 9082)

Learning outcomes

Aim of the course is providing the students with the basic knowledge and tools inherent with an exemplary application of biomechanics: the biomechanics of human movement. To this aim the course will mix in an integrated view mechanics and neurophysiology with an exclusive emphasis on the human motor control system. Several topics related with measurement and simulation of human movement will be largely stressed and many field applications will be discussed, including orthopedics, neurology, rehabilitation, sports medicine, virtual reality.

Course contents


Presentation of the course. Classification of the course in the field of biomedical engineering. Biomechanics: definition, historical notes and application fields. The Biomechanics of Human Movement. The key concepts: movement, balance, interaction. Kinematics, Static and Dynamics. The working hypothesis: rigid body. The Galilean Scientific Method applied to the Biomechanics of Movement. Phenomenon-Observation-Representation-Analysis. The Observation: Phenomenology of the Movement. Movement Analysis: Measurement and Modeling. The Representation of Movement: Computer Graphics. Peculiar Aspects of the Biomechanics of Movement. Role of Models. Complexity vs Validity. The Material Point. Review of kinematics, statics, dynamics. Newton's Laws. Rigid Body Model in 2-D and 3-D. Multi-link model of the human body.

Review of linear and angular kinematics. Point kinematics. Rectilinear motion uniformly accelerated (fall of a grave). Rigid body kinematics. Example of multi-articulated body kinematics: double pendulum. Definition of the orientation of a body in 2D and 3D: position vector and orientation matrix. Global and local reference systems. Rules for coordinate transformation. Movement reconstruction. Definition of the reference system. Orthogonal, oblique, polar Cartesian reference systems. Components and projections. Construction of a local triad starting from a set of points (markers). Examples of local backhoe loaders. Identification of the local triad in the global triad, over time. Translation and rotation. Cosines directors in 2-D. Properties of the orientation matrix. Global-local transformations and vice versa. Corners of Cardano. Euler's angles. Experimental problems connected with kinematic measurements. Reconstruction of the instantaneous position of a point. Joint kinematics. Main functions of a joint: mobility and stability. Joint classification. Degrees of freedom of the main joints. Superficial congruence and role of the ligaments. Analytical representation of joint kinematics. Relative motion between rigid bodies. Grood & Suntay Convention. Orientation vector. The gimbal lock. Anatomical axes. Complexity of the real joints.


Definition of Movement, Balance, Interaction. The concept of Strength. System of Forces: definition and properties. Cardinal equations of statics. Recalls: Polar Moment of a Force. Active Forces and Constrain Reactions. Essential Terminology: Anatomical Planes, Articular Angles. Static. The Statics of the Rigid Body. Systems of equivalent forces. Systems of balanced forces. Concentrated and Distributed Forces. The Center of Pressure. The center of Massa. Axioms of statics. Free Body Diagram. Constraints and constraint reactions. Types of Constraints: Absolute and Relative. Order of a Constraint. Trolley, Pendulum, Hinge, Shoe, Joint. Axiom of constraints. Degrees of freedom. Statically determined and indeterminate systems. Solving static problems. Rigid articulated bodies (multilink). Example: elbow mechanics. Exercise: Biomechanics of the elbow when supporting weights. 2-D monosegmental model. 2-D bisegmental model. 2-D models for the estimation of internal forces. Modeling limits: muscle redundancy, muscle biomechanics. Solution approaches: cross-sectional area method, linear optimization method. Whole-body models.
The analysis of the dynamic equilibrium. Axioms of the dynamic equilibrium of a rigid body. Euler-Newton formulation. Cardinal equations of mechanics for a system of interacting particles. Cardinal equations of mechanics for a continuous rigid body. Mass and mass density of a body. The density of the body segments. Center of mass of a rigid body. Center of mass of a multilink. Segmentation: anatomical and biomechanical approach. The anthropometric tables (Winter, 1990). Estimated lengths of body segments (Drillis and Contini, 1966). Exercise on anthropometric tables: calculation of the center of mass. Exercise: body center of mass calculation with multilink model. Experimental determination of the center of mass. Experimental determination of the mass of a distal segment. Moment of inertia. Moment of inertia of a system of particles. Huygens-Steiner theorem. Moment of inertia of a rigid body. Turning radius. Calculation of the moment of inertia of a body segment (exercise). The control of the moment of inertia. Experimental determination of the moment of inertia of a distal segment. Inertia matrix. Poinsot's theorem. Principal axes of inertia. Ellipsoid of inertia. Multilink models of body dynamics at various degrees of freedom. The monosegmental model. The ankle strategy. Considerations on the monosegmental model. Scope of validity of the model in posturography. Direct dynamic problem for the monosegmental model. Estimation of the center of mass with time domain and frequency domain techniques. Systems vision of the COP-COM relationship. The bisegmental model. The hip strategy. The postural stabilization process. COP-EMG link. Inertial properties of the human body. Center of Massa. Moment of inertia. Principal axes of inertia and anatomical axes.

Main components: bones and cartilage, muscle, tendons, ligaments, joints. Upper limb: bones, joints, muscles. Biomechanical models of the upper limb with different level of detail. Lower limb: bones, joints, muscles. Outline of functional anatomy of the main muscle groups.
Human movement analysis: definition and application fields. Stereophotogrammetry. Calibration of the stereophotogrammetric system. Stereophotogrammetric error and possible solutions. Experimental protocols for gait analysis. Saflo, VCM and CAST. Anatomical calibration. Reconstruction of technical triples starting from clusters of noisy markers. Reconstruction of anatomical landmarks. Soft tissue artifacts. Excellent estimate of the pose. Project of the marker cluster. Optimal placement of clusters. Strength and EMG platform. The experimental analysis of the human journey. The phases of the step: step and stride. Essential space-time variables: speed, cadence and stride length. Dynamics of the step. The components of the reaction force during stance: normal walking. The butterfly diagram. COP trend during normal walking. Estimation of muscle activity from the foot-ground reaction vector alone. Limitations of the force plate in gait analysis. Kinematics of the main segments of the lower limb during walking. Joint kinematics during normal walking. Inverse dynamic problem. Theoretical foundations. Modeling hypotheses. Iterative solution. Optimization techniques for minimizing the log residue. Experimental problems. Techniques for estimating inertial parameters. Example 2-D: climbing stairs. Solution in Matlab environment. Interpretation of results. Sensitivity of the solutions to the various sources of error. Alternative approaches based on Lagrange's equations.

The teaching is integrated with the laboratory activities of the Biomechanics Laboratory course, aimed at fostering the student's ability to independently define and solve concrete problems of analysis and synthesis of movement. In this context, with direct reference to the measurement systems present in the laboratory, the main instrumental techniques for dynamics (force platform), kinematics (stereophotogrammetry) and the measurement of muscle activity (EMG) will be presented. Specific laboratory activities will be scheduled for those who decide to be evaluated only by carrying out an experimental project, so the bi-weekly tutoring, laboratory and final presentation sessions are open to all learners.




Reference book:

"Fondamenti di Meccanica e Biomeccanica del Movimento", Giovanni Legnani e Giacomo Palmieri, Ed. Città Studi

On-line material provided by the professor for integration.

Other books:
"Bioingegneria della Postura e del Movimento", A. Cappello, A. Cappozzo, P.E. di Prampero Eds., Pàtron editore, 2003

David Winter, "Biomechanics and Motor Control of Human Movement", John Wiley & Sons, 1990

Teaching methods

Classes, assistance to problem solving, introduction to the devices and methods used in a movement analysis laboratory.

Assessment methods

Test in written form (10 multiple questions, 1 open question, 2 exercises)

Alternative testing method:

Development of a group experimental project the duration of the course, monitored during tutoring sessions every other week, to be presented in written and oral format within the first testing session at the end of the teaching period. The evaluation of each participant to each project will be based on individual tutoring and final presentation.

Teaching tools

Classes, assistance to problem solving, introduction to the devices and methods used in a movement analysis laboratory.

Office hours

See the website of Rita Stagni

See the website of Maria Cristina Bisi


Good health and well-being

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.