11.2.4 Time-relative postural discomfort in multiple postures

11.2.4.1 Scope and quantities used to calculate discomfort in posture sequences

The calculation of discomfort in posture sequences maintains the conceptual distinction between postural discomfort and biomechanical exertion. Postural discomfort is based on the angular deviation of joints from functional or comfortable zones, whereas biomechanical exertion is calculated from moments, joint forces, and muscle capacity. This distinction is necessary because a posture can be posturally unfavorable without involving a high percentage of maximum voluntary contraction, while high muscle demand can occur in postures that are not particularly extreme from an angular perspective. This distinction is consistent with Kee and Karwowski's58F¹ studies of discomfort associated with joint deviations and with the findings of Frey Law et al.59F², which show that the relationships among perception, pain, exertion, and maximum holding time are not equivalent in static and dynamic tasks.

For each joint or degree of freedom assessed, the procedure considers three main components:

• the momentary discomfort of the current posture at each instant, corresponding to a posture adopted briefly or not sustained;

• the absolute discomfort (see Section 11.2.2), which represents the discomfort that the current postural configuration would produce if held for the baseline time used in the psychophysical comfort equations;

• the equivalent time of prior postural exposure, which summarizes cumulative exposure to angularly similar postures while accounting for distance from neutrality and partial recovery over time.

In general terms, the result can be expressed as:

\[D_{final,j}(t) = F_{j}(D_{puntual,j}(t),D_{60,j}(t),T_{eq,j}(t))\ \]

Equation 40

where:

• D_final,j​(t) is the final postural discomfort of joint or degree of freedom j at time t;

• D_puntual,j(t) is the discomfort corresponding to the current posture when it is considered momentary or unsustained;

• D_60,j(t) is the absolute discomfort of the current posture (for a 60-second exposure);

• Teq,j(t) is the equivalent time of prior exposure relevant to the current posture;

• Fj is the combination function that integrates the baseline effect of the posture and the cumulative temporal effect.

The equivalent time Teq,j(t) is not a direct sum of seconds. Only prior exposures that occurred in configurations sufficiently far from neutral, angularly similar to the current posture, and recent enough that their effects have not been fully recovered make a relevant contribution. The system therefore answers the following question: for how much prior time has the joint been in postures similar to the current one and with sufficient postural significance to influence present discomfort?

Once the equivalent time has been obtained, Ergoniza Intelligent applies a nonlinear temporal transformation to the absolute discomfort of the current posture at each instant. The use of a nonlinear relationship is supported by experimental evidence on sustained static postures. Ogutu and Park60F³ observed that the development of discomfort over time is not generally described by a linear function and that a power function with an additive term adequately represents most of the individual discomfort-time sequences analyzed.

The general procedure can be summarized as follows: at each instant, the effective posture is calculated; functional joint angles are obtained; momentary discomfort (see Section 11.2.3.3) and absolute discomfort (see 11.2.2) are determined; prior exposure equivalent to similar postural configurations is estimated; and time-relative postural discomfort is finally obtained using a combination that always preserves the baseline value of the current posture, so that the final result cannot be lower than the momentary discomfort of the current posture.

The result must be interpreted as an ergonomic indicator of equivalent postural exposure in posture sequences. It is not a clinical prediction, a direct probability of injury, an exact physiological measure of muscle fatigue, or a quantified reduction in force-generating capacity. Its main purpose is to compare design alternatives, detect moments of unfavorable postural exposure, and assess the effect of sustaining or repeating joint configurations outside the comfortable functional zone.

The following sections describe the calculations used to determine time-relative postural discomfort in multiple-posture sequences.

11.2.4.2 Measuring postural exposure time

To estimate the effect of sustaining or repeating postures in a sequence, Ergoniza Intelligent processes the posture sequence over time and calculates, for each joint and degree of freedom analyzed, how long it remains in different angular zones. The objective is not to store each posture as an independent case, but to construct a temporal representation of cumulative postural exposure.

At each instant assessed, the system reconstructs the model posture. The functional joint angles required to assess postural discomfort are calculated from that posture.

For each joint and degree of freedom j, the resulting angle is assigned to a reference angular interval. These intervals are not the same size for every movement; instead, they are adapted to the functional range and postural sensitivity of each joint. Consequently, the same angular difference in degrees does not necessarily produce the same effect in every body region.

The system accumulates exposure time in each angular interval. To prevent artificial changes when an angle fluctuates slightly around the boundary between two intervals, a stability criterion is applied to prevent spurious switching between adjacent intervals. This produces a more stable representation of calculated exposure and prevents small numerical fluctuations from repeatedly changing the assigned interval.

The recorded temporal exposure provides the basis for subsequently calculating the equivalent time T_eq,j(t). At this stage, therefore, the system is not summing past discomfort scores; it is measuring how long the joint has remained in angular configurations that may be relevant to the current posture.

This stage produces a temporal history of postural exposure for each joint and degree of freedom (Figure 54). In subsequent steps, this history makes it possible to weight prior exposure according to three criteria: similarity to the current posture, distance from neutrality, and partial recovery over time.

11.2.4.3 Equivalent postural exposure time

Using the temporal history of postural exposure described above, Ergoniza Intelligent calculates an equivalent exposure time \(T_{eq,j}(t)\) for each joint and degree of freedom j. This equivalent time represents the portion of prior exposure that remains relevant when interpreting discomfort in the current posture.

Equivalent time does not necessarily coincide with the chronological time during which the joint has been outside the neutral posture. Two exposures of equal duration may have different effects if one occurred in a configuration very similar to the current posture and the other in a different angular configuration. Similarly, a recent exposure has a greater effect than an older one because partial recovery occurs over time.

The calculation of \(T_{eq,j}(t)\) is therefore based on three criteria:

• angular similarity between the prior exposure and the current posture;

• the postural relevance of the angular interval, so that positions close to neutral contribute little or nothing;

• the remaining temporal memory, which progressively reduces the weight of older exposures.

In general terms, equivalent time can be expressed as:

\[T_{eq,j}(t) = \sum_{k < t}^{}{{\Delta t}_{k} \cdot S_{j}({\theta}_{k},\theta(t)) \cdot A_{j}(\theta_{k}) \cdot M_{j}(t - t_{k})}\]

Equation 41

where:

• T_eq,j(t) is the equivalent postural exposure time of joint or degree of freedom j at time t;

• Δt_k is the duration of prior time interval k;

• θ_k is the representative joint angle during that prior interval;

• θ(t) is the current joint angle at the time being assessed;

• S_j(θ_k,θ(t)) is the angular-similarity function between the prior exposure and the current posture;

• A_j(θ_k) is the postural activation associated with the prior angle;

• M_j(t−t_k) is the remaining temporal memory after the time elapsed since the prior exposure.

The following sections define the different components of this equation.

This approach avoids treating all prior exposures as equivalent. A prior posture very similar to the current one makes an important contribution to equivalent time if it occurred recently and was sufficiently far from neutral. In contrast, a neutral posture, an angularly different posture, or an older exposure makes a reduced or zero contribution (Figure 55).

Consequently, \(T_{eq,j}(t)\) must be interpreted as a temporal measure weighted by postural similarity, angular relevance, and partial recovery. Its function is to indicate how much prior exposure time can be considered posturally equivalent to having sustained configurations similar to the current one.

11.2.4.4 Angular similarity between prior exposure and the current posture

Not all prior exposure contributes equally to discomfort in the current posture. A prior exposure is relevant only if it occurred in an angular configuration similar to that adopted by the joint at the time being analyzed.

For each joint and degree of freedom j, Ergoniza Intelligent compares the current angle θ(t) with the representative angles of the previously occupied reference angular intervals. The contribution of each prior exposure is weighted using an angular-similarity function:

\[S_{j}(\theta_{k},\theta(t)) \in \lbrack 0,1\rbrack\]

\[ \]Equation 42

where \(S_{j} = 1\) represents maximum similarity between the prior exposure and the current posture, and \(S_{j} = 0\) indicates that the prior exposure is not considered relevant to the posture being assessed.

Conceptually, this similarity depends on angular distance:

\[\delta_{j} = \mid \theta_{k} - \theta(t) \mid \]

Equation 43

The smaller \(\delta_{j}\) is, the greater the influence of the prior exposure. For example, a prior exposure at 50° of flexion has a greater effect on a current posture at 55° than on one at 15°.

The comparison is made within the same functional direction of movement. For example, a prior exposure in flexion is not interpreted as equivalent exposure for a current posture in extension.

Angular similarity does not itself incorporate posture severity. Its function is to identify which prior exposures are posturally similar to the current one. Severity is subsequently introduced through absolute discomfort \(D_{60,j}(t)\) and through the postural relevance of the corresponding reference angular interval.

11.2.4.5 Postural relevance of the reference angular interval

In addition to similarity to the current posture, Ergoniza Intelligent considers whether the prior exposure occurred in a postural configuration sufficiently far from neutral. Time spent in positions close to the neutral posture should not contribute significantly to cumulative discomfort, even when those positions are repeated or sustained for a certain period.

Each reference angular interval therefore has an associated postural-relevance function:

\[A_{j}(\theta_{k}) \in \lbrack 0,1\rbrack\]

Equation 44

where \(A_{j}(\theta_{k})\) represents the postural significance of prior angle \(\theta_{k}\) for joint and degree of freedom \(j\).

Values close to 0 indicate that the configuration is within or close to the neutral postural zone and therefore contributes little to the equivalent time. Values close to 1 indicate that the configuration is sufficiently far from neutral to be considered relevant postural exposure.

Conceptually:

\[{A_{j}\left( \theta_{k} \right) \approx 0\ \ \ \ \ \text{if~}\theta_{k}\text{ is close to neutral} }{A_{j}\left( \theta_{k} \right) \rightarrow 1\ \ \ \ if\ \theta_{k}\text{ moves away from neutral} }\]

11.2.4.6 Temporal memory and partial recovery

Prior postural exposure does not retain the same influence on discomfort in the current posture indefinitely. After leaving an unfavorable configuration, part of its effect must be considered to recover progressively. To represent this behavior, Ergoniza Intelligent applies a temporal-memory function \(M_{j}(\tau)\), where \(\tau\) is the time elapsed between the prior exposure and the instant being analyzed:

\[\tau = t - t_{k} \]

Equation 45

The memory function is defined as a combination of two exponential components:

\[M_{j}(\tau) = w_{r} \cdot 2^{- \frac{\tau}{T_{r}}} + w_{l} \cdot 2^{- \frac{\tau}{T_{l}}} \]

Equation 46

where:

• \(M_{j}(\tau)\) is the memory factor applied to the prior exposure of degree of freedom j after time \(\tau\);

• \(w_{r}\) is the weight of the fast component;

• \(T_{r}\) is the half-life of the fast component;

• \(w_{l}\) is the weight of the slow component;

• \(T_{l}\) is the half-life of the slow component.

The half-lives are the times required for the influence of a prior exposure to be reduced by half.

The first term on the right side of Equation 46 represents relatively rapid initial recovery. The second represents slower recovery associated with the persistence of a residual fraction of the prior exposure. The weights of the two components satisfy:

\[w_{r} + w_{l} = 1 \]

Equation 47

This structure approximates multicomponent behavior without introducing a complex physiological model (Figure 56).

The selection of a memory function with more than one component is supported by the literature on recovery after fatigue. Yates et al.61F⁴ observed that recovery of dynamic muscular endurance did not follow a single phase: it progressed rapidly at first, reached approximately 50% after 2 minutes and 15 seconds, was slightly below 90% after 20 minutes, and was best fitted by a three-component exponential curve. Other studies of localized fatigue models, such as Iridiastadi and Nussbaum62F⁵, also note that recovery is one of the most difficult aspects to represent in intermittent tasks and that its behavior depends on loading conditions.

In the context of the 3CC-r model, Looft et al.63F⁶ demonstrate the importance of distinguishing recovery during rest intervals. Frey Law et al.64F⁷ show that the relationships among maximum holding time, pain, and perceived exertion are not equivalent in static and dynamic tasks. Taken together, these findings indicate that recovery should not be represented by a single universal behavior.

The biexponential function used by Ergoniza Intelligent is adopted as an operational simplification: it preserves the concept of rapid initial recovery and residual persistence, but avoids presenting the postural-discomfort calculation as an exact physiological model of muscle fatigue.

The following values are used in the initial Ergoniza Intelligent configuration:

\[{w_{r} = 0.70,T_{r} = 120\text{\:\,}s }{w_{l} = 0.30,T_{l} = 600\text{\:\,}s}\]

With these values, 70% of the prior exposure is associated with a relatively fast recovery component with a half-life of 2 minutes (after 120 seconds, it retains 50% of its initial effect; after another 120 seconds, it retains 25%; and so on). The remaining 30% is associated with a slower component with a half-life of 10 minutes. A short break therefore partially reduces cumulative exposure but does not eliminate it completely, while a longer break substantially reduces the influence of prior exposures, although residual memory may remain if the postures are repeated.

Figure 57: Temporal fatigue decay panel.

Recovery does not apply while a joint remains continuously within the same reference angular interval. In that case, exposure time continues to accumulate. Recovery acts when the joint leaves that configuration or during rest periods between activity repetitions.

The system thus distinguishes between an unfavorable posture sustained continuously and a prior exposure followed by a period of partial recovery. These default values must be interpreted as model parameters, not as universal constants. They were selected to represent appreciable recovery during the first few minutes without immediately eliminating the effect of repeated postural exposures. Users can modify them in the Activity Repetitions settings (Figure 57) by adjusting both the relative weights of the two components and their half-lives. This dialog can be opened with the Timing button on the left sidebar (in Multiple Postures mode) or with the clock icon at the bottom of the Postural Risk panel shown in Figure 59. The Temporal Fatigue Decay section is collapsed by default when the Activity Repetitions dialog opens. Click it to expand it.

11.2.4.7 Activity repetitions and rest periods between repetitions

The analyzed posture sequence does not necessarily represent the entire workday or work period; it may instead represent a characteristic cycle that repeats several times. Ergoniza Intelligent can analyze the development of postural discomfort over repeated cycles of a posture sequence (Figure 58).

In this case, the user-defined posture sequence is interpreted as a baseline activity cycle. In the Repetitions and Rest Periods section of the Activity Repetitions dialog (Figure 57), the user can specify which repetition to represent and how much rest occurs between one repetition and the next.

The system can therefore assess, for example, the postural discomfort corresponding to the first repetition of a task, an intermediate repetition, or a later repetition after prior exposure has accumulated.

If the duration of the baseline cycle is \(T_{c}\), the rest period between cycles is \(T_{d}\), and \(n\) repetitions are analyzed, the total duration represented by the activity is:

\[T_{total} = n \cdot T_{c} + (n - 1) \cdot T_{d}\]

Equation 48

The selected repetition is assessed while accounting for exposure accumulated during preceding repetitions. During activity cycles, exposure accumulates in the corresponding reference angular intervals; during rest periods, cumulative exposure is attenuated according to the temporal-memory function described above.

This procedure does not modify the visible animation or create new postures on the timeline. The displayed sequence remains the baseline cycle, but the calculation incorporates the effect of prior repetitions. The same posture within the cycle can therefore produce a different result when analyzed as part of the first repetition or as part of a later repetition.

If the first repetition is selected, there is no cumulative prior exposure from earlier cycles. If a later repetition is selected, the result depends on three factors: the postural severity of the baseline cycle, the number of prior repetitions, and the duration of the rest periods. Short rest periods retain more memory of prior exposures, while long rest periods reduce their influence to a greater extent.

The simulation of repetitions must be interpreted as an operational representation of cyclic activities. Its validity depends on the baseline cycle being sufficiently representative of the actual activity. If actual repetitions are not homogeneous, or if there are important variations in pace, pauses, loads, or postures, the result must be interpreted as an approximation of the represented pattern rather than an exact reconstruction of the entire activity.

11.2.4.8 Final calculation of time-relative discomfort

After calculating momentary discomfort \(D_{puntual,j}(t)\), absolute discomfort \(D_{60,j}(t)\), and equivalent exposure time \(T_{eq,j}(t)\), Ergoniza Intelligent obtains final time-relative discomfort for each joint and degree of freedom \(j\).

First, a temporal value associated with equivalent time is calculated:

\[D_{temporal,j}(t) = D_{60,j}(t) \cdot \left( \frac{T_{eq,j}(t)}{60} \right)^{\alpha_{j}} \]

Equation 49

where \(\alpha_{j}\) is the time exponent associated with the joint and degree of freedom being assessed. This exponent adapts the influence of time to the expected behavior of each body region.

However, the final result is not obtained by applying this expression directly in every case. Ergoniza Intelligent maintains the momentary discomfort of the current posture as the minimum reference. An extreme posture therefore retains its relevance even if it is adopted only briefly or there is no cumulative prior exposure.

The calculation applies the following criteria:

\[D_{final,j}(t) = D_{puntual,j}(t)\ \ \text{if }T_{eq,j}(t) = 0\]

Equation 50

When equivalent time is greater than zero but no more than 60 seconds—the temporal basis of absolute discomfort—the result progresses from momentary discomfort toward absolute discomfort:

\[D_{final,j}(t) = D_{puntual,j}(t) + \left\lbrack D_{60,j}(t) - D_{puntual,j}(t) \right\rbrack \cdot \left( \frac{T_{eq,j}(t)}{60} \right)^{\alpha_{j}} \]

Equation 51

This expression applies when \(D_{60,j}(t) > D_{puntual,j}(t)\). If momentary discomfort is already equal to or greater than absolute discomfort, the system does not force the result to decrease.

When equivalent time exceeds 60 seconds, the full temporal law is allowed to act, but the final value cannot be lower than momentary discomfort:

\[D_{final,j}(t) = \max\left( D_{puntual,j}(t),D_{temporal,j}(t) \right)\]

\[\text{if}{\ \ T}_{eq,j}(t) > 60 \]

Equation 52

This approach produces a coherent transition among three situations: a posture adopted instantaneously, a posture with an equivalent exposure of 60 seconds or less, and a posture with cumulative exposure greater than the baseline reference time.

The final result therefore combines two distinct effects. First, it preserves the discomfort inherent in the current postural configuration. Second, it increases the result when there is a relevant temporal history of sustaining or repeating similar postures. Time-relative discomfort does not replace momentary discomfort; it uses it as the minimum baseline and modifies it according to cumulative postural exposure.

11.2.4.9 Accounting for orientation relative to gravity

Orientation relative to gravity for the upper limb is considered in posture sequences using the same general criterion described for single-posture analysis in Section 11.2.2.1. Its purpose is to adjust upper-arm and forearm discomfort when the segment's actual spatial orientation makes the posture more favorable than the relative angle between segments alone would indicate.

In sequence analysis, this correction is calculated at each instant assessed. If Gravity Adjustment is enabled (Figure 52), Ergoniza Intelligent checks the orientation of the upper arm and forearm relative to the downward vertical and, when appropriate, partially reduces the corresponding discomfort. This reduction affects discomfort in the current posture and is therefore incorporated before the effect of equivalent exposure time is calculated.

The gravity adjustment does not directly modify equivalent time \(T_{eq,j}(t)\), because that quantity represents the temporal history of prior postural exposure. Its effect is introduced into the instantaneous discomfort values of the posture being assessed, that is, into the values that subsequently participate in the temporal combination.

11.2.4.10 Interpretation limits

Time-relative postural discomfort in posture sequences must be interpreted as an ergonomic indicator of equivalent postural exposure. Its purpose is to help identify unfavorable joint configurations that are sustained, repeated, or recur with insufficient rest within a temporally represented activity.

This result must not be interpreted as a clinical prediction of injury, a direct measure of muscle fatigue, or a normative criterion for task acceptability.

The calculation is based on a simplified representation of postural exposure. Although it considers the temporal history of the joint, angular similarity among exposures, the postural relevance of each reference angular interval, and partial recovery, it does not reproduce all the physiological mechanisms involved in fatigue, pain, or individual tolerance.

The result also depends on the quality of the sequence analyzed. If the recorded postures do not adequately represent the actual activity, if the temporal sampling frequency is insufficient, or if important variations are not included in the sequence, the result must be interpreted with caution. For repeated activities, the validity of the calculation also depends on the baseline cycle being representative of the actual repetitions.

Finally, the indicator does not replace biomechanical exertion analysis, lumbar compression analysis, stability assessment, or other postural methods such as REBA or LUBA. It must be used as a complementary measure specifically for assessing the temporal effect of sustaining or repeating unfavorable postural configurations.