15.2.1 Transition function for instantaneous discomfort
As explained in Section 11.2.3.3, the calculation of instantaneous postural discomfort starts from the relative position of each joint within its effective range of motion. For each joint j and degree of freedom d, the value rj,d is first obtained; it expresses how close the adopted angle is to the effective ROM limit. This value is then compared with two references: the threshold r0j,d, which marks the end of the central functional zone, and r100, which defines entry into the extreme zone of the effective ROM.
The purpose of the transition function is to convert this relative proximity into a percentage of instantaneous discomfort. While rj,d does not exceed r0j,d, discomfort is considered zero. When rj,d lies between r0j,d and r100, discomfort progressively increases until it reaches 100%. If rj,d exceeds r100, the indicator can continue increasing up to a bounded maximum, set at 125%, indicating that the joint is moving even closer to the effective ROM limit.
To prevent abrupt changes when the angle exceeds the threshold of the comfortable zone, Ergoniza Intelligent uses a smooth transition function. First, a normalized variable u, which can take values from 0 to 1, is calculated:
\[u_{j,d} = min\left\lbrack \max\left( \frac{r_{j,d} - {r0}_{j,d}}{1 - {r0}_{j,d}},0 \right),1 \right\rbrack\]
When
\[{r0}_{j,d} < r_{j,d} < r100\]
Equation 57
Instantaneous discomfort is then calculated using a smooth transition function:
\[\ D_{puntual,j,d} = 100 \bullet \left( 3u_{j,d}^{2} - 2u_{j,d}^{3} \right)\]
Equation 58
This function satisfies three conditions:
\[\ D_{puntual,j,d} = 0\ \mathrm{when}\ r_{j,d} \leq {r0}_{j,d\ }\]
\[\ D_{puntual,j,d} = 100\ \mathrm{when}\ r_{j,d} = r100\]
and the increase between the two values occurs gradually, without abrupt discontinuities.
When the joint exceeds r100 and continues approaching the effective ROM limit, Ergoniza Intelligent allows the indicator to exceed 100%. A second smooth transition between r100 and 1 is calculated:
\[u_{exc,j,d} = min\left\lbrack \max\left( \frac{r_{j,d} - r100}{1 - r100},0 \right),1 \right\rbrack\]
Equation 59
Instantaneous discomfort is again calculated using a smooth transition function:
\[D_{puntual,j,d} = 100 + (D_{\max} - 100)\left( 3u_{exc,j,d}^{2} - 2u_{exc,j,d}^{3} \right)\]
Equation 60
where Dmax is the maximum indicator value when the effective ROM limit is reached. In the current implementation, this value is 125.
Values above 100% should not be interpreted as an exact psychophysical measure of discomfort, but as an indication that the joint has exceeded the operational threshold for an extreme posture and is moving even closer to the effective ROM limit.