15.2.2 Determining r0 for the upper limbs, neck, and trunk

The value of r0_j,d is not the same for every joint. Available evidence shows that postural tolerance depends on the body region and movement being analyzed. Ergoniza Intelligent therefore uses different values for each joint or functional group. For the wrist, elbow, shoulder, neck, and trunk, the LUBA method82F¹ is used as a source of relative sensitivity. LUBA assigns discomfort scores to different angular ranges of upper-limb, neck, and trunk movements. These scores are not used as the direct result for instantaneous discomfort, but as a criterion for determining when the indicator should begin to increase.

For each joint j and degree of freedom d, two values are extracted from the LUBA tables:

• S_max,j,d: maximum score assigned by LUBA to that movement;

• θ_entry,j,d: angle at which the movement enters the range with the maximum LUBA score.

The maximum score represents the relative severity of the movement. Movements with higher maximum scores are considered more sensitive and should therefore begin to be penalized earlier. A severity ratio is calculated for this purpose:

\[p_{j,d} = \frac{{Smax}_{j,d} - Smin}{{Smax}_{global} - Smin}\]

Equation 61

where Smin = 5 and Smax_global = 15 are the minimum and maximum values used to normalize LUBA scores.

An initial r0 value is obtained from this relative severity:

\[{r0}_{score\ j,d} = {r0}_{\max} - \left( {r0}_{\max} - {r0}_{\min} \right)\ \bullet \ p_{j,d}\ \]

Equation 62

where r0_min = 0.60 and r0_max = 0.85.

Thus, a movement with low relative severity begins to be penalized closer to the end of the ROM, whereas a movement with high severity begins to be penalized earlier.

However, the maximum score alone is insufficient. Two movements can have the same maximum score but reach it at very different angles. In LUBA, for example, certain shoulder-rotation movements may reach their maximum-score range at much smaller angles than other movements with the same maximum score. Ergoniza Intelligent therefore introduces a second criterion based on the angle at which the maximum-score range begins.

First, the following is calculated:

\[r_{entry\ j,d} = \frac{\theta_{entry\ j,d}}{{ROMef}_{,j,d}}\]

Equation 63

Next, the relative level that the curve should have when this entry angle is reached is defined. This level depends on the movement's relative severity:

\[u_{entry,j,d} = u_{\min} - \left( u_{\max} - u_{\min} \right)\ \bullet \ p_{j,d}\ \]

Equation 64

where u_min = 0.20 and u_max = 0.75.

This value is used to solve for the r0 that makes the transition curve reach that level at rentry:

\[{r0}_{entry\ j,d} = \frac{r_{entry\ j,d} - u_{entry\ j,d} \bullet r100}{1 - u_{entry\ j,d}}\]

Equation 65

Finally, the more preventive of the two criteria is selected as the definitive r0 value:

\[{r0}_{j,d} = min\left( {r0}_{score\ j,d} - {r0}_{entry\ j,d} \right)\]

Equation 66

LUBA is thus used to modulate the angular sensitivity of the instantaneous calculation. The result is neither the LUBA index nor a direct reproduction of its scores, but a continuous adaptation based on proximity to the effective ROM.