15.2.3 Determining r0 for the lower limbs using isocomfort equations

LUBA does not provide tables for the hip, knee, and ankle. For the lower limbs, Ergoniza Intelligent therefore uses an alternative procedure based on the isocomfort equations83F¹ available for these body regions (see Section 11.2.1). These equations estimate perceived comfort y as a function of joint angle:

\[y_{j,d} = f_{j,d}(ang)\]

Equation 67

For each joint j and degree of freedom d, comfort in the neutral position is calculated first:

\[{y0}_{j,d} = f_{j,d}(0)\]

Equation 68

as is estimated comfort at the effective ROM limit:

\[{yROM}_{j,d} = f_{j,d}({ROM}_{ef\ j,d})\]

Equation 69

The total decrease in comfort between the neutral position and the effective ROM is then calculated:

\[{\mathrm{\Delta}y}_{j,d} = {y0}_{j,d} - {ROM}_{j,d}\]

Equation 70

The total decrease in comfort is used to generate a score equivalent to the maximum LUBA score. This equivalent score is normalized within the available set of degrees of freedom for the lower limbs:

\[S_{eq\ j,d} = 5 + 10\ \bullet \frac{{\mathrm{\Delta}y}_{j,d} - {\mathrm{\Delta}y}_{\min}}{{\mathrm{\Delta}y}_{\max} - {\mathrm{\Delta}y}_{\min}}\]

Equation 71

where Δy_min and Δy_max are, respectively, the smallest and largest decreases in comfort observed among the available lower-limb movements in the calculation context.

An equivalent angle for entry into the high-discomfort zone is also defined. This is done by calculating the angle at which a specified proportion of the total decrease in comfort is reached. The current implementation uses 75%:

\[f_{j,d}\left( \theta_{entry\ eq\ j,d} \right) = {y0}_{j,d} - 0.75 \bullet {\mathrm{\Delta}y}_{j,d}\]

Equation 72

The value Seq_j,d is used as the equivalent of Smax_j,d, and θentry_{eq j,d} as the equivalent of θentry_j,d. From these values, r0 is calculated using the same procedure described from Equation 61 through Equation 66.

This procedure incorporates the hip, knee, and ankle without directly extrapolating LUBA beyond its anatomical scope. The underlying logic remains consistent: the indicator continues to be based on proximity to the effective ROM, while the sensitivity of each movement is adapted according to the loss of comfort estimated by the isocomfort equations.