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Mechanical and Thermal Measurements

Relatore: Prof. Marco Tarabini

Tutor: Prof. Federico Cheli

Università di Provenienza: Politecnico di Milano - Ingegneria Meccanica

Titolo della Tesi: Development of tools and systems for the protection of workers from foot-transmitted whole-body vibration

Development of tools and systems for the protection of workers from foot-transmitted whole-body vibration


Mechanical whole-body vibration (WBV) is an occupational hazard in different work sectors. It is estimated that 7% of all workers in Europe, United States, and Canada are regularly exposed to WBV [1]. WBV has been linked with an increased risk of developing low-back pain and sciatica [2], [3]. Extreme cases have been linked to fatigue failures at the endplates of the lumbar vertebrae [4]. ISO 2631-1:1997 [5] contains the guidelines for computing the vibration exposure for WBV. The Parliament and Commission of the European Community defined the limits in 2002, The results of such agreement are shown in the document “minimum health and safety requirements” for the exposure of workers to the risks arising from vibration [6]. Mechanical vibration transmitted through the feet can cause further problems in respect to the ones that are linked to WBV. Acute exposure of the extremities of the limbs in fact, can result in a reduced blood flow to the body parts, resulting in numbness and increased sensitivity to cold [7]. Chronic exposure can even result in disability. Eger et al. [8] monitored the vibration exposure of 27 miners in Northern Ohio. None of the workers were found to be subjected to a dose of vibration exposure exceeding the Exposure Action Value. However, seven of the workers were diagnosed with vibration-induced white feet. The authors suggest that this discrepancy may be linked to the frequency components of the acceleration signal.


Need for a compact vibrating platform to be integrated into the pre- existing facilities → Design and commissioning of a triaxial vibrating platform

  • support a standing person
  • generate mechanical vibration independently along the three mutually perpendicular spatial axes
  • frequency range of 0.5 Hz to 30 Hz
  • maximum acceleration of 5 m/s2
  • maximum displacement of ±20 mm along the axis composing the horizontal plane and ±30 mm along the vertical axis.

Need for a mathematical model to understand the link between foot pathologies and vibration → Creation of a lumped-parameters model of the foot-ankle system

  • represent the vibration transmissibility functions of the foot
  • represent the apparent mass of a standing person


The triaxial vibrating platform has been produced and tested (Fig.4). Experimental modal analysis has been performed to validate the FEM model of the machine, to be used in further developments (Fig.5, Fig.6)

The tests done on the machine after its realization confirm that it can generate pseudo-random noise up to 80 Hz across the three mutually perpendicular spatial axes simultaneously. The average root-mean squared error between the modulus of the spectrum of generated signal and the signal measured directly on the platform is 6,9 mm/s2 across the three axes, and it is 5,5 mm/s2 when a person is standing on the platform, i.e. lower than 1% of the imposed acceleration (Fig.7).

The design process lead to the creation of a direct numerical link between the kinematic performances of a linear delta robot and its design parameters: L = 1,205 ⋅ D + 0,635

The proposed foot-ankle model can reconstruct the average experimental transmissibility curves with a mean quadratic error equal to 0.3 ± 0.1 for the modulus and 0.3 ± 0.3 rad for the phase. The sensitivity analysis further validates the model, as the dispersion of the curves obtained from the model is lower than the experimental variability (Fig.8).


This dissertation focused on enhancing the knowledge on foot-transmitted whole-body vibration.
The first part described the design and development of the machine able to generate the mechanical stimulus through which investigate the human response to triaxial vibration. The results prove that the machine can be used to impose a signal through which it would be possible to test the response of the human body to multiaxial mechanical vibrations.
Moreover, a new method to obtain a direct mathematical link between the inverse of the conditioning number of the linear delta robot with vertical actuators and the sizes of the variables defining its kinematics was proposed. The results obtained can be used to obtain the region of the design space that satisfy a boundary imposed on the performance index, or to directly obtain the minimum dimensions of the robot that satisfy a given boundary on the inverse of the conditioning number.
The last part of the thesis focused on the development of a 2-D lumped-parameter mechanical model of the foot-ankle system. The stiffness and damping of Kelvin Voight elements have been optimized to reproduce the vibration transmissibility measured at five different locations on the foot and the apparent mass of a standing person. The results show that the modelled transmissibility fits inside the experimental variability of the measured curves. The model, therefore, can be used to estimate the effect of different corrective measures proposed to attenuate the vibration transmissibility at the extremities of the lower limbs.


[1] M. Bovenzi, C. Hulshof, An updated review of epidemiologic studies on the relationship between exposure to whole-body vibration and low back pain (1986–1997), Int. Arch. Occup. Environ. Health, vol. 72, (6), pp. 351-365, 1999.
[2] M. Bovenzi, M. Schust, M. Mauro, An overview of low back pain and occupational exposures to whole-body vibration and mechanical shocks, Med. Lav., vol. 108, (6), pp. 419-433, 2017.
[3] L. Burström, T. Nilsson, J. Wahlström, Whole-body vibration and the risk of low back pain and sciatica: a systematic review and meta-analysis, Int. Arch. Occup. Environ. Health, vol. 88, (4), pp. 403-418, 2015.
[4] H. Seidel, R. Bluethner, B. Hinz, Effects of sinusoidal whole-body vibration on the lumbar spine: the stress-strain relationship, Int. Arch. Occup. Environ. Health, vol. 57, (3), pp. 207-223, 1986.
[5] International Standards Organisation, Evaluation of Human Exposure to Whole-body Vibration. Part 1 - General Requirements, ISO2631. 1, 1997.
[6] M.J. Griffin, Minimum health and safety requirements for workers exposed to hand-transmitted vibration and whole-body vibration in the European Union; a review, Occup. Environ. Med., vol. 61, (5), pp. 387-397, May, 2004.
[7] A.J. Brammer, W. Taylor, G. Lundborg, Sensorineural stages of the hand-arm vibration syndrome, Scand. J. Work Environ. Health, pp. 279-283, 1987.
[8] T. Eger et al, Vibration induced white-feet: overview and field study of vibration exposure and reported symptoms in workers, Work, vol. 47, (1), pp. 101-110, 2014.