PAMM · Proc. Appl. Math. Mech. 11, 129 – 130 (2011) / DOI 10.1002/pamm.201110056

Development of a biomechanical model to study the horizontal vibration

transmitted from shoulder to head

Aurica Truta1,∗, Aurora-Felicia Pop1, Monica Balcau1, and Mariana Arghir1,∗∗

1 Technical University of Cluj-Napoca, B-dul Muncii 103-105, Cluj-Napoca, Romania

On daily activity a human operator is exposed to vibration in working environment. So, the human body will react in different

way. The problem is how much from the initial signal will be sent to the other parts of the body and how much that motion

will be damped along the studied parts. The vibrations in horizontal plane are some unexpected, so the human operator will

not take any position to prevent them. In this condition the horizontal vibrations will have the higher effect possible. In this

paper, the shoulder, neck and the head are modeled together like a mechanical system with four degree of freedom.

c© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

In daily work we are surrounded by vibrations: in the bus, in the buildings, at the office. In their daily activity, human operators

are exposed to vibrations in their working environment. So, the human body will react in different way. The EU has a continue

preoccupation to protect humans and environment. In this context, it raises a question: how much from the initial signal will be

sent to the other parts of the body and how much that moving will be damped along the studied parts? According to estimates

made in some European countries, 4% to 7% of workers are exposed to potentially harmful whole body vibration. A long

time exposure to whole body vibration (WBV) means disorders and implicit loss in productivity. An increase in health care

costs mean additional costs to society [3].

2 Experimental

In industrial environments, the most important sources of vibrations are the equipments during the technological process [5].

The operator is considered in a standing position on a platform, working on a machine-tool fixed on the floor [4]. It ne-

glects the excitation received from the under the legs support and taken into account only the excitation received through

the hand that is in direct contact with a working part of the machine. In this paper, the shoulder, neck and the head are

modeled together like a mechanical system with four degree of freedom [2], [3]. Along the study we do not kept account

about the building vibrations. It was written the differential equation system based on mechanical simplified model (Fig.1).

Fig. 1 Simplified model for the shoulder-neck-head

The differential equations system (1) of four nonlinear equations was solved by Simulink. For system stability it was expressed

the velocities variation depending on the displacements for the given system (Fig. 2).

m1y1 + c0(y1 − u) + k0(y1 − u)− c1(y2 − y1)− k1(y2 − y1) = 0m2y2 + c1(y2 − y1) + k1(y2 − y1)− c3(y3 − y2)− k3(y3 − y2) = 0

m3y3 + c3(y3 − y2 − lθ1 cos θ1) + k3(y3 − y2 − l sin θ1) = 0

m2l

2sin θ1y2 + c3y2l cos θ1 + k3y2l sin θ1 + ct1θ1 + kt1θ1 = Jcθ1

(1)

∗ Corresponding author: Email auricatruta@yahoo.com, phone +00 40 264 401 667∗∗ Email marianaarghir@yahoo.com, phone +00 40 264 401 657

c© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

130 Section 2: Biomechanics

The entrance signal is an harmonically wave applied at the shoulder u(t) = u0 sinωt where u0 = 3.0 × 10−3m/s. It was

computed the displacements on OY1, OY2, OY3 and rotation around OX2 axis (Fig. 3).

Fig. 2 Velocities variation depending on the displacements for system (1)

Fig. 3 Displacements variation depending on the time for considered system and a detail of the diagram.

3 Conclusion

Transmitted motion on horizontal direction (Fig. 3) has the same magnitude at the end of system as initial motion from the

beginning of the system. So the motion is not amplified and it is not damped. Means that the vibrations are transmitted through

the human body, and for long time exposure they could be dangerous. There are methods to minimize the level of vibrations

and here are some of them: selecting work equipments, selecting work procedures and selecting working methods so as to

give priority to reducing the risk at source.

Acknowledgements This paper was supported by the project “Development and support of multidisciplinary postdoctoral programmes in

major technical areas of national strategy of Research - Development - Innovation” 4D-POSTDOC, contract no. POSDRU/89/1.5/S/52603,

project co-funded by the European Social Fund through Sectorial Operational Programme Human Resources Development 2007-2013.

Acknowledgements The conference fee was supported by the project “Development of a computerized system for assessing occupational

hazards type mechanical vibrations and impact on the human operator to work place” - VIBROM - Project number 92-112/2008 funded by

Ministry Education and Research from Romania (Program 4- Partnerships in priority areas)

References

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environment), Doctoral thesis, 28.10.2009, 224 pag, UTCN, Cluj-Napoca, 2009[4] A. Truta, A.F. Pop, M. Arghir, Research about transmission of the mechanical vibration done by machine-tools on the group of bones

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c© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.gamm-proceedings.com