## 5 Hand-Arm System Standards  
The following research emphasizes the importance of hand-arm vibration transmissibility standards and the need to comply with them. The old standard SR EN 5349/86 through Annex A, in conformity with [1], gave us formulas regarding the connection between \(\mathrm{a_{R,MS}}\) acceleration at a \"_weighted energy_\" exposure of 4 h and the frequency in the dominant axis of vibration before the appearance of the first symptoms of finger whitening. The measurements made according to Equation (4) are illustrated in Table 5 and correspond to a period of symptom dominance for subjects exposed to vibration, between 10% and 50% of whom show symptoms. The weighted acceleration R.M.S. was calculated to be between 2 and 50 m/s\({}^{2}\) (the values in parentheses were calculated using Equations (5) and (6) in the following paragraph). The connection between exposure to vibration and weighted acceleration R.M.S is given by Equation (4). \[\frac{\mathrm{D_{y}}}{\mathrm{year}}=31.8\bigg{(}\frac{\mathrm{A(8)}}{\mathrm{ m/s^{2}}}\bigg{)}^{-1.06} \tag{4}\]  
Equation (4) is derived from [9] and presents the following:  
\(A(8)\) is the daily vibration exposure (8 h energy equivalent vibration);  
\(D_{y}\) is the group mean total (lifetime) exposure duration, in years. For example, Table 5 shows that, at daily exposures of 4 h of weighted energy, for 2 years, at a weight acceleration R.M.S. of 14 m/s\({}^{2}\), 10% of the people exposed to said vibrations developed symptoms of finger whitening. As the exposure period increased (>10 years) and the \(\mathrm{a_{R,MS}}\) decreased (up to 2 m/s\({}^{2}\)), the percentage of subjects exposed to vibration who reported the appearance of VWF symptoms increased (>30%). \[\mathrm{E}=9.5\cdot\frac{\mathrm{C}^{1/2}}{\mathrm{a_{hw}(4)}} \tag{5}\]  
\[\mathrm{E}=\frac{9.5}{\mathrm{a_{hw}(4)}}\cdot\bigg{[}\mathrm{C}\cdot\frac{ \mathrm{T(4)}}{t}\bigg{]}^{1/2} \tag{6}\]  
where \(E=\) vibration exposure (years) before VWF, and \(a_{hw}(4)\) has a formula similar to Equation (1), but \(T(4)=14,400\) s; all equations are in conformity with [1]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**Population Affected by Finger Whitening Syndrome [\%]**} \\ \hline
**Acceleration \(\mathrm{a_{R,M.S}}\) Weighted \(\mathrm{a_{hw}}\)** & **10\%** & **20\%** & **30\%** & **40\%** & **50\%** \\
**Corresponding to 4 h [m/s\({}^{2}\)]** & & & & & \\ \hline
2 & 15 (15) & 23 (21.2) & \textgreater{}25 & \textgreater{}25 & \textgreater{}25 \\
5 & 6 (6) & 9 (8.5) & 11 (10.4) & 12 (12) & 14 (13.4) \\
10 & 3 (3) & 4 (4.2) & 5 (5.2) & 6 (6) & 7 (6.7) \\
20 & 1 (1.5) & 2 (2.1) & 2 (2.6) & 3 (3) & 3 (3.4) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Exposure to vibration (in years) before the appearance of the first symptoms of whitening of the fingers, according to Annex A of SR EN ISO 5349/1989, in conformity with [1]. The _period of exposure to vibrations_ (_E_) can be calculated according to Equations (5) and (6) knowing the number of subjects exposed to vibrations (%), the number of years during which they were directly exposed to said vibrations (approximately 9.5 years), and the weighted acceleration R.M.S (\(\mathrm{a_{hw}}\)), corresponding to 4 h weighted energy. If the exposure duration and vibration amplitude are constant over time, the dominance is directly proportional to daily exposure to vibration. In conformity with [1] and SR EN ISO 5349/86, an acceleration of 0.8 m/s\({}^{2}\) was proposed for a hand's vibration exposure of 4 h \"weighted energy\" and a frequency of 16 Hz. Figure 13 shows the nomogram of the daily exposure to vibrations of people and the exposure related to a \"weighted energy\" of 4 h (the data were derived from Annex A of SR EN ISO 5349/86). Research shows that there are major differences between the transmission of vibrations from the chair on which a person sits during work to the hand and the transmission of vibrations from the tool to the hand.