# ApOL-Application Oriented Workload Model for Digital Human Models for the Development of Human-Machine Systems

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

**Sub-model A**determines the external process three-dimensional force vector ${F}_{process}$ based on experimentally determined push forces (calculated from the GRF).

**Sub-model B**uses the battery current from the experimental studies of Sänger et al., 2022 [31] and [30] to estimate the external process torque ${T}_{process}$ acting onto the screwdriver during the screw-in process.

**Sub-model C**uses the human and screwdriver motion data provided by Sänger et al., 2022 [31] to determine the load onto the DHM based on the screwdriver motion. For this purpose, a model of the screwdriver is built in MATLAB Simulink using the Simscape multibody package.

#### 2.1. Sub-Model A: Virtual Sensor to Determine the External Process Force Based on the Experimental Users Push Force

#### 2.2. Sub-Model B: Virtual Sensor for Determining the External Process Torque Based on the Battery Current from Experimental Data

#### 2.3. Sub-Model C: Virtual Sensor to Determine Interaction Forces on the DHM from Experimental Motion Data

#### 2.4. Application-Oriented Workload Model-ApOL Model

#### 2.5. Verification of the ApOL Model

**mathematical model**. Second, a

**parameter study**was conducted which shows the influence of the location of the reference point (handle position) on the user load.

**mathematical model**, the mathematical model consists of the process forces and torques as well as the mass of the screwdriver. Since the direction of the weight force vector changes in the body fixed ${COS}_{B}$ when the screwdriver is moved around, the calculated values for ${F}_{process}$ and ${T}_{process}$ were only determined for the duration of the screw-in process as the screwdriver’s position is fixed upwards (see Section 2.3 motion phase O3). Outside of the screw-in phase, the process force and torque values were set to zero. This is also due to the fact, that the process forces and torques only occur during the screw-in process. The mathematical model calculates the maximum and minimum force (${F}_{xh},{F}_{yh},{F}_{zh}$) and torque (${T}_{xh},{T}_{yh},{T}_{zh}$) values only during the screw-in process. The formulas for the maximum and minimum force and torque values can be found in Appendix A in Table A2.

**parameter study**. The parameter study was conducted to further verify the ApOL model. In total 21 cases were analyzed. To verify the model’s behavior, the reference point was altered along the three coordinates axis and the change in the load was analyzed. The initial design of the screwdriver was used as the baseline of the model. Here, x, y, and z coordinates were equal to zero (origin of ${COS}_{B}$). According to the sub-model C, the center of gravity (COG) is located slightly in front of the baseline point along the ${z}_{h}$-axis (see Figure 3). The values of the x-, y-, and z-coordinates describe the displacement of the reference point in relation to the baseline in the body-fixed coordinate system ${COS}_{B}$.

## 3. Results

#### 3.1. Sub-Model B: Virtual Sensor Battery Current–Process Torque

^{2}of the correlation for the second section (Screw-in Process) is 98%, as it fits very well from 2.45 A up to 24 A. From here, the torque increases stronger than the linear regression model. This can also be seen in Figure 4b, as the residual between the measured torque and the linear regression model shows low values up to a maximum of 0.5 Nm for torques below 12 Nm and a maximum residual of 2.2 Nm for higher torques.

#### 3.2. ApOL Model Implemented in MATLAB-Simulink

**force**${\mathit{F}}_{\mathit{x}\mathit{h}}$ (force direction is perpendicular to handle- and drill-axis) and the

**torque**${\mathit{T}}_{\mathit{x}\mathit{h}}$ (torque leads to radial/ulnar deviation of the wrist) and for the factor levels of X1–X10, the

**torques**${\mathit{T}}_{\mathit{y}\mathit{h}}$ (torque leads to extension/flexion of the wrist, torque along the handle axis)

**and**${\mathit{T}}_{\mathit{z}\mathit{h}}$ (torque leads to pronosupination forearm, torque along the forearm axis). The figures of the other forces (${F}_{yh}$, ${F}_{zh}$) and torques (${T}_{xh}$, ${T}_{yh}$, ${T}_{zh}$) can be found in Appendix B as they might be of interest to other researchers.

#### 3.2.1. Influence of the Y- and Z-Coordinate (Y Variation) of the Reference Point on the Load Components

**force**${\mathit{F}}_{\mathit{x}\mathit{h}}$ (force direction is perpendicular to handle- and drill-axis) during the whole movement cycle of the screwdriver is shown in Figure 5. The start and the end of the screw-in process are marked as dashed lines at 4 s and as dotted lines at 7.5 s. This period in the signal is referred to as the “screw-in process”. The calculated maximum and minimum values from the mathematical model are shown in red and yellow (see Appendix A Table A2 for formulas). The orientation of the screwdriver during the whole movement cycle is marked with (O1–O4), as explained in Section 2.3.

**torque**${\mathit{T}}_{\mathit{x}\mathit{h}}$ around the ${x}_{h}$-axis during the whole motion cycle for all three participants is shown in Figure 7. The qualitative progression of the curves is partly different between the users, as P1 shows two peaks and P2 and P3 both only show one.

#### 3.2.2. Influence of the X-Coordinate (X-Variation) of the Reference Point on the Load Components

**torque**${\mathit{T}}_{\mathit{y}\mathit{h}}$ (torque along the handle axis) are shown in Figure 8. Similar to Figure 7, the absolute values outside of the screw-in process are lowest for the baseline (XB) and X1 and increase towards X10.

_{max}) fit the simulated values (X10) with a rMAE of 1.7% (SD 0.6%) (see Table 4). Moreover, similar to Figure 7, the progression of the signals varies between the participants, as P1 shows again two peaks and P2 and P3 show only one peak. The minimum calculated value is equal to zero during the whole movement cycle. Furthermore, shown in Figure 8 is the calculated maximum torque without consideration of the screwdriver’s mass (green line). This signal progression is roughly 2 Nm lower than the calculated values with mass consideration (red line). The rMAE of 15.4% (SD 2.9%) between the calculated values (math, X10

_{max}, noMass, green curve) and the simulated values (X10) occur if the mass of the screwdriver is ignored.

**torque**${\mathit{T}}_{\mathit{z}\mathit{h}}$ around the ${z}_{h}$-axis (torque leads to pronosupination forearm, torque along the forearm axis) (see Figure 9) show some partly similar results to the torque ${T}_{yh}$.

_{max}) fit the maximum simulated values of ${T}_{zh}$ with a rMAE of 4.6% (SD 2.7%). The minimum calculated values (math, XB

_{min}) fit the baseline values with sufficient accuracy. The maximum offset is 0.3 Nm.

## 4. Discussion

**correlation between the process torque and the battery current**shows an acceptable coefficient of determination (R = 98%). Only for torque values higher than 12 Nm, a relative error of 15.2% can be seen, which is still reasonable since these torques only occur for a very short amount of time during the screw-in process.

**for the Y-variation**behaves as expected and is determined by the simulation model with a rMAE of 11.4% (SD 4.6%). An increase from the baseline (YB) to Y9 fits the assumption of inverse proportionality between ${F}_{x,process}$ and the lever.

**Torque**${\mathit{T}}_{\mathit{x}\mathit{h}}$(torque leads to radial/ulnar deviation of the wrist)

**for the Y-variation**is mainly influenced by ${F}_{process}$, decreasing the lever reduces the torque. This effect overlays with a torque induced by moving the reference point away from the COG. This results in an increasingly robust design moving from the baseline (YB) to Y10. The ApOL model is able to determine the torque ${\mathit{T}}_{\mathit{x}\mathit{h}}$ with rMAE of 8.5% (SD 4.5%). However, the MAE of the torque ${T}_{xh}$ is 0.5 Nm (SD 0.1 Nm).

**torque**${\mathit{T}}_{\mathit{y}\mathit{h}}$ (torque leads to extension/flexion of the wrist, torque along the handle axis) for the

**X-variation**from the XB to X10 is caused by increasing the distance between the reference point and the drill axis. This causes the ${z}_{h}$-component of ${F}_{process}$ to induce an increasing torque. The rMAE of ${\mathit{T}}_{\mathit{y}\mathit{h}}$ is 1.7% (SD 0.6%).

**torque**${\mathit{T}}_{\mathit{z}\mathit{h}}$ (torque leads to pronosupination forearm, torque along the forearm axis) for the

**X-variation**, the increase in torque from the baseline to Y10 is caused by the same effect. Here, the ${y}_{h}$-component of ${F}_{x,process}$ induces the torque causing the resulting absolute values to be smaller. The rMAE is 4.6% (SD 2.7%).

#### 4.1. Virtual Sensor for External Load–Process Torque

#### 4.2. ApOL Model in MATLAB-Simulink

#### 4.2.1. Influence of the Y- and Z-Coordinate of the Reference Point, Factor Levels Y1–Y10

**force**${\mathit{F}}_{\mathit{x}\mathit{h}}$ (force direction is perpendicular to handle- and drill-axis) and the

**torque**${\mathit{T}}_{\mathit{x}\mathit{h}}$ (torque leads to radial/ulnar deviation of the wrist) showed a considerable change. The remaining plots are presented in Appendix B.

**force**${\mathit{F}}_{\mathit{x}\mathit{h}}$ (force direction is perpendicular to handle- and drill-axis) in Figure 6, the force behaves as expected. This component is mainly influenced by the process force ${F}_{x,process}$, which is inversely proportional to the lever, represented by the value of the y coordinate. With a decreasing lever, the force component increases. For Y10, the model assumes that the torque ${T}_{process}$ is converted to ${F}_{x,process}$ does not hold, resulting in a force that is approximately zero. Since the maximum (math, Y9

_{max}) and minimum (math, YB

_{min}) calculated values fit the simulated values pretty well, the inertia forces induced by the motion of the user do not influence the results in a considerable way for this setup.

**torque**${\mathit{T}}_{\mathit{x}\mathit{h}}$ (torque leads to radial/ulnar deviation of the wrist) is mainly influenced by the process force ${F}_{process}$. When moving the reference point out of the baseline, the corresponding lever decreases, resulting in a lower torque. The second influence on ${T}_{xh}$ is the mass of the screwdriver, which induces an increasing torque when moving the reference point away from the baseline and the COG. The two phenomena overlay and result in the torque curves shown in Figure 7. For the calculated minimum (math, Y10

_{min}), only the mass is considered while the progression of the simulated values indicates an influence of ${F}_{process}$. This is caused by the fact that the screwdriver is not held perfectly upright in Position (C) during the screw-in process by the users, thus inducing an additional load component that is not considered in the mathematical model yet. Outside of the screw-in process, the mass of the screwdriver is mainly responsible for the torque curve. For the baseline, the

**torque**${\mathit{T}}_{\mathit{x}\mathit{h}}$ is always positive since the COG is located in front of the reference point. Moving the reference point up towards the drilling axle shifts the COG behind the reference point, thus the torque ${T}_{xh}$ is negative. When the screwdriver is rotated upwards, this changes and so does the torque ${T}_{xh}$. The same effect occurs after the screw-in process when the screwdriver is lowered. Another characteristic seen in Figure 7 is the robust design of the setup Y10. For the baseline (YB), the main load appears during the screw-in process, and it also varies between the users. Even though they all performed the same task, the load is dependent on the individual handling. For Y10, not only is the load approximately the same for all participants, it also only slightly increases during the screw-in process. This effect is very important, as a robust design eliminates noise factors and helps develop systems that are invariant from the user and the handling of the task. Finding robust designs helps significantly when optimizing support systems for humans.

#### 4.2.2. Influence of the X-Coordinate of the Reference Point, Factor Levels X1–X10

**torques**${\mathit{T}}_{\mathit{y}\mathit{h}}$ (torque leads to extension/flexion of the wrist, torque along the handle axis) and ${\mathit{T}}_{\mathit{z}\mathit{h}}$ (torque leads to pronosupination forearm, torque along the forearm axis) showed a considerable change. The remaining plots are presented in Appendix B.

**The torque**${\mathit{T}}_{\mathit{y}\mathit{h}}$ (torque leads to extension/flexion of the wrist, torque along the handle axis) (see Figure 8), is only induced due to the screwdriver’s mass outside of the screw-in process. Moving the reference point out of its initial position (XB), the lever towards the COG increases and so does the torque ${T}_{yh}$. When rotating the screwdriver upwards, the orientation of the COG to the reference point in the space-fixed coordinate system changes, causing the gravity to flip the torque. The same effect in the opposite direction can be seen after the screw-in process. During the screw-in process, the main influence is the process force ${F}_{process}$ and the weight force. An increase in the x coordinate also increases the lever for these forces, resulting in higher torques ${T}_{yh}$. The maximum calculated values (math, X10

_{max}) fit the simulated values (X10) with a rMAE of 1.7% (SD 0.6%). If the mass of the screwdriver were ignored, a rMAE of 15.4% (SD 2.9%) between the calculated values (math, X10

_{max}, noMass) (green curve) and the simulated values (X10) would occur. This shows the importance of modelling the mass of the technical system. For the baseline (XB), the process force ${F}_{process}$ and the weight force induces no torque around the ${y}_{h}$-axis. The values for the baseline setup are only influenced by the motion of the user. The minimum calculated values correspond to the baseline (XB) and are equal to zero. The maximum offset between these two curves is 0.4 Nm, thus the motion of the user has very little influence in this case.

**torque**${\mathit{T}}_{\mathit{z}\mathit{h}}$ (torque leads to pronosupination forearm, torque along the forearm axis) is mainly influenced by the process force ${F}_{process}$ during the screw-in process and by the weight force outside of the screw-in process. For the latter, the weight force induces a torque around the ${z}_{h}$-axis. Since the axis are body-fixed, moving the screwdriver from its initial position (O1) to its upward position (O3) decreases this torque. After the screw-in process (O4), the screwdriver is again oriented vertically so the torque increases again. These torque values match the weight force times the corresponding lever. During the screw-in process, the torque ${T}_{zh}$ increase from Y1 to Y10, as the ${y}_{h}$-component of the process force induces a torque around the ${z}_{h}$-axis. The maximum calculated values (math, X10

_{max}) fit the maximum simulated values of ${T}_{zh}$ with a rMAE of 4.6% (SD 2.7%) showing again a successful verification. The minimum calculated values (math, XB

_{min}) fit the baseline values with sufficient accuracy. The maximum offset is 0.4 Nm.

#### 4.3. Limitations of the ApOL Model

## 5. Conclusions

**variation of the y- and z-coordinate (Y variation)**, the rMAE for all forces (${F}_{xh}$ ${F}_{yh}$, ${F}_{zh}$) is 11.4% (SD 4.6%) or smaller. For the torques (${T}_{xh}$, ${T}_{yh}$ ${T}_{zh}$) the maximum rMAE 16.1% (SD 11.4%). However, the maximum MAE of the torques is 0.5 Nm (SD 0.1 Nm).

**variation of the x-coordinate (X variation)**, the rMAE is comparable but occasionally lower. The maximum rMAE for the forces (${F}_{xh},$ ${F}_{yh}$, ${F}_{zh}$) is 9.4% (SD 4.6%) with a maximum MAE of 5.1 N (SD 3.4 N). The maximum rMAE of the toques (${T}_{xh}$, ${T}_{yh}$, ${T}_{zh}$) is 8.1% (SD 2.5%). Altering the screwdriver setup led to an expected change in the interaction torques and forces estimated at the handle of the screwdriver. For ${F}_{yh}$, ${F}_{zh}$, ${T}_{xh}$, ${T}_{yh}$, and ${T}_{zh}$, a noticeable portion of the load occurred outside of the screw-in process, showing the importance of modelling the mass of the technical system. To validate the workload model, the authors recommend a coupled DHM and ApOL model simulation to determine muscle activity and compare the calculated values to experimental surface EMG measurements.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Component | Diameter in mm | Length in mm | X in mm | Y in mm | Z in mm |
---|---|---|---|---|---|

Handle | 45 | 112 | - | - | - |

Battery (3.1 Ah) | - | - | 125 | 80 | 32 |

Battery socket | - | - | 125 | 60 | 23 |

Data Logger | - | - | 125 | 80 | 50 |

Motor | 45 | 55 | - | - | - |

Gearbox | 56 | 81 | - | - | - |

Chuck | 41 | 50 | - | - | - |

Motor and gearbox housing | 59 (outer) 48 (inner) | 115 | - | - | - |

**Table A2.**Mathematical model: formulas for calculated max. and min. values. α describes the angle between the drilling axis and the ${z}_{h}$-axis during the screw-in process.

Component | Formula | Formula | Comment |
---|---|---|---|

YB and Y1–Y10 | XB and X1–X10 | - | |

${F}_{xh,max}$ | ${T}_{process}$/Y9_{y} | ${T}_{process}$/XB_{y} | - |

${F}_{xh,min}$ | ${T}_{process}$/YB_{y} | = ${F}_{xh,max}$ | - |

${F}_{yh,max}={F}_{yh,min}$ | ${F}_{process}$∗ sin(α)– ${F}_{weight}$∗ sin(α) | ${F}_{process}$∗ sin(α)– ${F}_{weight}$∗ sin(α) | No Influence of the parameter setup onto${F}_{yh}$ |

${F}_{zh,max}={F}_{zh,min}$ | ${F}_{process}$∗ cos(α)– ${F}_{weight}$∗ cos(α) | ${F}_{process}$∗ cos(α)– ${F}_{weight}$∗ cos(α) | No Influence of the parameter setup onto ${F}_{zh}$ |

${T}_{xh,max}$ | ${F}_{process}$∗ YB_{y} | ${F}_{process}$∗ XB_{y} | - |

${T}_{xh,min}$ | ${F}_{weight}$∗ YB_{y} | = ${T}_{xh,max}$ | - |

${T}_{yh,max}$ | ${T}_{process}$∗ sin(α) | ${F}_{process}$∗cos(α) ∗ X10_{x} + ${F}_{weight}$∗ cos(α) ∗ X10 _{x} | - |

${T}_{yh,min}$ | 0 (reference point is not in line with drill axis, weight induces no torque around zh-axis) | ${F}_{process}$∗cos(α) ∗ XB_{x} | - |

${T}_{zh,max}$ | ${T}_{process}$∗ cos(α) | ${F}_{process}*\mathrm{sin}\left(\alpha \right)*$ X10_{x} + ${F}_{weight}*\mathrm{sin}\left(\alpha \right)*$ X10 _{x} | - |

${T}_{zh,min}$ | 0 (reference point is not in line with drill axis, weight induces no torque around zh-axis) | ${F}_{process}*\mathrm{sin}\left(\alpha \right)*$ XB_{x} | - |

## Appendix B

**Figure A1.**Force ${F}_{yh}$ for participant 1–3 with factor levels Y1–Y10 during movement cycle. Besides minimal differences (see plot snipped), the different setups show the same load on the user, so only the calculated maximum values are included. During the screw-in process, the calculated loads show a significant offset from the simulated ones. Outside of the screw-in process, mainly the weight force of the screwdriver acts on the user. Here, the offset is even greater, showing how important it is to model the movement of the user as well as the mass and mass distribution of the technical system.

**Figure A2.**Force ${F}_{zh}$ for participant 1–3 with factor levels Y1–Y10 during movement cycle. As described in Figure A1, the different setups show the same load on the user, so only the calculated maximum values are included. Before and after the screw-in process, the simulated loads cross the zero line. This is caused by the rotation of the screwdriver, thus rotating the zh-axis out and into the vertical, along which the weight force is acting. The offset between simulated values and calculated values is caused by the weight force, showing the importance of considering it.

**Figure A3.**Torque ${T}_{yh}$ for participant 1–3 with factor levels Y1–Y10 during movement cycle. Outside of the screw-in process, the torque increases from the baseline setup to Y10. This is caused by an increasing lever from the reference point to the COG, thus inducing an increasing torque. With a maximum torque of about 1 Nm, the mass and mass distribution can be neglected in this case. During the screw-in process, only Y10 shows significant loads onto the user. This is caused by the torque not being converted to ${F}_{x,process}$. Due to the angular offset between drilling axle and the yh-axis, a slight portion of ${T}_{process}$ acts along the yh-axis. The maximum calculated values underestimate the simulated ones for P1 and overestimate them for P2 and P3. This is caused by the orientation of the screwdriver. Differences in the angle around the zh-axis cause the weight force to induce a torque that are contrary.

**Figure A4.**Torque ${T}_{zh}$ for participant 1–3 with factor levels Y1–Y10 during movement cycle. Outside of the screw-in process, the torque increases from the baseline setup to Y10. This is caused by an increasing lever from the reference point to the COG, thus inducing an increasing torque. With a maximum torque of about 1 Nm, the mass and mass distribution can be neglected in this case. During the screw-in process, only Y10 shows significant loads onto the user. This is caused by the torque not being converted to ${F}_{x,process}$. Due to the angular offset between drilling axle and the zh-axis, the majority of ${T}_{process}$ acts along the zh-axis. The maximum calculated values underestimate the simulated ones for P1 and overestimate them for P2 and P3. This is caused by the orientation of the screwdriver. Differences in the angle around the zh-axis cause the weight force to induce a torque that are contrary.

**Figure A5.**Force ${F}_{xh}$ for participant 1–3 with factor levels X1–X10 during movement cycle. As described in Figure A1, the different setups show the same load on the user, so only the calculated maximum values are included. Even though the maximum force outside of the screw-in process is fairly low at–10 N for P1 (−20 for P2 and −7 for P3) compared to the load during the screw-in process (−190 N for P1 and −140 N for P2 and P3), it is important to consider the mass and mass distribution as relative small loads can exceed the total load capacity of humans when applied in repeating causes.

**Figure A6.**Force ${F}_{yh}$ for participant 1–3 with factor levels X1–X10 during movement cycle. The load are the same for the component ${F}_{yh}$ in the variation of Y1–Y10 (see Figure A1). A detailed explanation is given below that figure.

**Figure A7.**Force ${F}_{zh}$ for participant 1–3 with factor levels X1–X10 during movement cycle. The loads are the same for the component ${F}_{zh}$ in the variation of Y1–Y10 (see Figure A2). A detailed explanation is given below that figure.

**Figure A8.**Torque ${T}_{xh}$ for participant 1–3 with factor levels X1–X10 during movement cycle. Besides minimal differences the different setups show the same load on the user, so only the calculated maximum values are included. The progression during the screw-in process is mainly influenced by ${F}_{process}$. As the lever is not altered, no change is detected. The mass only shows a minor influence outside of the screw-in process, due to the COG being located slightly off the reference point along the zh-axis, the variation from X1–X10 does not influence a mass induced torque for X1–X10. The simulated and calculated values also show only a slight offset of 0.6 Nm. Thus, considering the mass of the screwdriver is not necessary in this case.

## References

- Kok, J.; Vroonhof, P.; Snijders, J.; Roullis, G.; Clarke, M.; Peereboom, K.; van Dorst, P.; Isusi, I. Work-Related Musculoskeletal Disorders: Prevalence, Costs and Demographics in the EU: European Risk Observatory. 2023. Available online: https://osha.europa.eu/en/publications/msds-facts-and-figures-overview-prevalence-costs-and-demographics-msds-europe (accessed on 20 March 2022).
- Brenscheidt, S.; Siefer, A.; Hinnenkamp, H.; Hünefeld, L. Arbeitswelt im Wandel, Ausgabe 2018. 2022. Available online: https://www.baua.de/DE/Angebote/Publikationen/Praxis/A99.html (accessed on 20 March 2022).
- Maurice, P.; Camernik, J.; Gorjan, D.; Schirrmeister, B.; Bornmann, J.; Tagliapietra, L.; Latella, C.; Pucci, D.; Fritzsche, L.; Ivaldi, S.; et al. Objective and Subjective Effects of a Passive Exoskeleton on Overhead Work. IEEE Trans. Neural Syst. Rehabil. Eng. Publ. IEEE Eng. Med. Biol. Soc.
**2020**, 28, 152–164. [Google Scholar] [CrossRef] [PubMed] - Alabdulkarim, S.; Kim, S.; Nussbaum, M.A. Effects of exoskeleton design and precision requirements on physical demands and quality in a simulated overhead drilling task. Appl. Ergon.
**2019**, 80, 136–145. [Google Scholar] [CrossRef] - Wang, Z.; Wu, X.; Zhang, Y.; Chen, C.; Liu, S.; Liu, Y.; Peng, A.; Ma, Y. A Semi-active Exoskeleton Based on EMGs Reduces Muscle Fatigue When Squatting. Front. Neurorobot.
**2021**, 15, 625479. [Google Scholar] [CrossRef] - De Bock, S.; Ampe, T.; Rossini, M.; Tassignon, B.; Lefeber, D.; Rodriguez-Guerrero, C.; Roelands, B.; Geeroms, J.; Meeusen, R.; De Pauw, K. Passive shoulder exoskeleton support partially mitigates fatigue-induced effects in overhead work. Appl. Ergon.
**2023**, 106, 103903. [Google Scholar] [CrossRef] [PubMed] - Gull, M.A.; Bai, S.; Bak, T. A Review on Design of Upper Limb Exoskeletons. Robotics
**2020**, 9, 16. [Google Scholar] [CrossRef] - Huysamen, K.; Bosch, T.; de Looze, M.; Stadler, K.S.; Graf, E.; O’Sullivan, L.W. Evaluation of a passive exoskeleton for static upper limb activities. Appl. Ergon.
**2018**, 70, 148–155. [Google Scholar] [CrossRef] - van der Have, A.; Rossini, M.; Rodriguez-Guerrero, C.; van Rossom, S.; Jonkers, I. The Exo4Work shoulder exoskeleton effectively reduces muscle and joint loading during simulated occupational tasks above shoulder height. Appl. Ergon.
**2022**, 103, 103800. [Google Scholar] [CrossRef] [PubMed] - Moeller, T.; Krell-Roesch, J.; Woll, A.; Stein, T. Effects of Upper-Limb Exoskeletons Designed for Use in the Working Environment-A Literature Review. Front. Robot. AI
**2022**, 9, 858893. [Google Scholar] [CrossRef] [PubMed] - Alabdulkarim, S.; Nussbaum, M.A. Influences of different exoskeleton designs and tool mass on physical demands and performance in a simulated overhead drilling task. Appl. Ergon.
**2019**, 74, 55–66. [Google Scholar] [CrossRef] - van Engelhoven, L.; Poon, N.; Kazerooni, H.; Rempel, D.; Barr, A.; Harris-Adamson, C. Experimental Evaluation of a Shoulder-Support Exoskeleton for Overhead Work: Influences of Peak Torque Amplitude, Task, and Tool Mass. IISE Trans. Occup. Ergon. Hum. Factors
**2019**, 7, 250–263. [Google Scholar] [CrossRef] - Massardi, S.; Rodriguez-Cianca, D.; Pinto-Fernandez, D.; Moreno, J.C.; Lancini, M.; Torricelli, D. Characterization and Evaluation of Human-Exoskeleton Interaction Dynamics: A Review. Sensors
**2022**, 22, 3993. [Google Scholar] [CrossRef] - Grandi, F.; Peruzzini, M.; Raffaeli, R.; Pellicciari, M. Trends in Human Factors Integration for the Design of Industry 4.0. In Design Tools and Methods in Industrial Engineering II; Rizzi, C., Campana, F., Bici, M., Gherardini, F., Ingrassia, T., Cicconi, P., Eds.; Springer International Publishing: Cham, Switzerland, 2021; pp. 785–792. ISBN 978-3-030-91233-8. [Google Scholar]
- Greig, M.A.; Village, J.; Salustri, F.A.; Zolfaghari, S.; Neumann, W.P. A tool to predict physical workload and task times from workstation layout design data. Int. J. Prod. Res.
**2018**, 56, 5306–5323. [Google Scholar] [CrossRef] - Grandi, F.; Peruzzini, M.; Khamaisi, R.K.; Lettori, J.; Pellicciari, M. Digital Technologies to Redesign Automatic Machines with a Human-Centric Approach: Application in Industry. In Transdisciplinarity and the Future of Engineering; Moser, B.R., Koomsap, P., Stjepandić, J., Eds.; IOS Press: Amsterdam, The Netherlands, 2022; ISBN 9781643683386. [Google Scholar]
- Chang, J.; Chablat, D.; Bennis, F.; Ma, L. A Full-chain OpenSim Model and Its Application on Posture Analysis of an Overhead Drilling Task. In Digital Human Modeling and Applications in Health, Safety, Ergonomics, and Risk Management: 10th International Conference, DHM 2019, Held as Part of the 21st HCI International Conference, HCII 2019, Orlando, FL, USA, 26-31 July 2019 Proceedings; Duffy, V.G., Ed.; Springer: Cham, Switzerland, 2019; ISBN 978-3-030-22215-4. [Google Scholar]
- Seth, A.; Hicks, J.L.; Uchida, T.K.; Habib, A.; Dembia, C.L.; Dunne, J.J.; Ong, C.F.; DeMers, M.S.; Rajagopal, A.; Millard, M.; et al. OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. PLoS Comput. Biol.
**2018**, 14, e1006223. [Google Scholar] [CrossRef] [PubMed] - Rasmussen, J.; Damsgaard, M.; Christensen, S.T.; Surma, E. Design optimization with respect to ergonomic properties. Struct. Multidiscip. Optim.
**2002**, 24, 89–97. [Google Scholar] [CrossRef] - Auer, S.; Tröster, M.; Schiebl, J.; Iversen, K.; Chander, D.S.; Damsgaard, M.; Dendorfer, S. Biomechanical assessment of the design and efficiency of occupational exoskeletons with the AnyBody Modeling System. Z. Arb. Wiss.
**2022**, 76, 440–449. [Google Scholar] [CrossRef] - Gneiting, E.; Schiebl, J.; Tröster, M.; Kopp, V.; Maufroy, C.; Schneider, U. Model-Based Biomechanics for Conceptual Exoskeleton Support Estimation Applied for a Lifting Task. In Wearable Robotics: Challenges and Trends; Moreno, J.C., Masood, J., Schneider, U., Maufroy, C., Pons, J.L., Eds.; Springer International Publishing: Cham, Switzerland, 2022; pp. 395–399. ISBN 978-3-030-69547-7. [Google Scholar]
- Zhou, L.; Li, Y.; Bai, S. A human-centered design optimization approach for robotic exoskeletons through biomechanical simulation. Robot. Auton. Syst.
**2017**, 91, 337–347. [Google Scholar] [CrossRef] - Jensen, E.F.; Raunsbæk, J.; Lund, J.N.; Rahman, T.; Rasmussen, J.; Castro, M.N. Development and simulation of a passive upper extremity orthosis for amyoplasia. J. Rehabil. Assist. Technol. Eng.
**2018**, 5, 2055668318761525. [Google Scholar] [CrossRef] [PubMed] - Tröster, M.; Wagner, D.; Müller-Graf, F.; Maufroy, C.; Schneider, U.; Bauernhansl, T. Biomechanical Model-Based Development of an Active Occupational Upper-Limb Exoskeleton to Support Healthcare Workers in the Surgery Waiting Room. Int. J. Environ. Res. Public Health
**2020**, 17, 5140. [Google Scholar] [CrossRef] [PubMed] - Scherb, D.; Wartzack, S.; Miehling, J. Modelling the interaction between wearable assistive devices and digital human models-A systematic review. Front. Bioeng. Biotechnol.
**2022**, 10, 1044275. [Google Scholar] [CrossRef] [PubMed] - Yang, X.; Huang, T.-H.; Hu, H.; Yu, S.; Zhang, S.; Zhou, X.; Carriero, A.; Yue, G.; Su, H. Spine-Inspired Continuum Soft Exoskeleton for Stoop Lifting Assistance. IEEE Robot. Autom. Lett.
**2019**, 4, 4547–4554. [Google Scholar] [CrossRef] - Molz, C.; Yao, Z.; Sänger, J.; Gwosch, T.; Weidner, R.; Matthiesen, S.; Wartzack, S.; Miehling, J. A Musculoskeletal Human Model-Based Approach for Evaluating Support Concepts of Exoskeletons for Selected Use Cases. Proc. Des. Soc.
**2022**, 2, 515–524. [Google Scholar] [CrossRef] - Chen, W.; Wu, S.; Zhou, T.; Xiong, C. On the biological mechanics and energetics of the hip joint muscle-tendon system assisted by passive hip exoskeleton. Bioinspir. Biomim.
**2018**, 14, 16012. [Google Scholar] [CrossRef] [PubMed] - Uchida, T.K.; Seth, A.; Pouya, S.; Dembia, C.L.; Hicks, J.L.; Delp, S.L. Simulating Ideal Assistive Devices to Reduce the Metabolic Cost of Running. PLoS ONE
**2016**, 11, e0163417. [Google Scholar] [CrossRef] [PubMed] - Sänger, J.; Wirth, L.; Matthiesen, S. Development of an Alternative Approach for Estimating User Load due to Screw-in Torque in User Studies. KIT Sci. Work. Pap.
**2023**. [Google Scholar] [CrossRef] - Sänger, J.; Yao, Z.; Schubert, T.; Wolf, A.; Molz, C.; Miehling, J.; Wartzack, S.; Gwosch, T.; Matthiesen, S.; Weidner, R. Evaluation of Active Shoulder Exoskeleton Support to Deduce Application-Oriented Optimization Potentials for Overhead Work. Appl. Sci.
**2022**, 12, 10805. [Google Scholar] [CrossRef] - Kalra, M.; Rakheja, S.; Marcotte, P.; Dewangan, K.N.; Adewusi, S. Measurement of coupling forces at the power tool handle-hand interface. Int. J. Ind. Ergon.
**2015**, 50, 105–120. [Google Scholar] [CrossRef] - Landry, C.; Loewen, D.; Rao, H.; Pinto, B.L.; Bahensky, R.; Chandrashekar, N. Isolating In-Situ Grip and Push Force Distribution from Hand-Handle Contact Pressure with an Industrial Electric Nutrunner. Sensors
**2021**, 21, 8120. [Google Scholar] [CrossRef] - Komi, E.R.; Roberts, J.R.; Rothberg, S.J. Evaluation of thin, flexible sensors for time-resolved grip force measurement. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**2007**, 221, 1687–1699. [Google Scholar] [CrossRef] - Arvidsson, M.; Gremyr, I. Principles of robust design methodology. Qual. Reliab. Engng. Int.
**2008**, 24, 23–35. [Google Scholar] [CrossRef] - Miehling, J. Musculoskeletal modeling of user groups for virtual product and process development. Comput. Methods Biomech. Biomed. Engin.
**2019**, 22, 1209–1218. [Google Scholar] [CrossRef] - ISO 10068:2012-12; Mechanical Vibration and Shock—Mechanical Impedance of the Human Hand-Arm System at the Driving Point. ISO: Geneva, Switzerland, 1998.

**Figure 1.**Application-oriented workload model (ApOL model) consists of the three sub models A, B, and C.

**Figure 2.**(

**a**) Screwdriver body-fixed coordinate system ${COS}_{B}$ and world coordinate system ${COS}_{W}$ with the relevant forces during the screw-in process for determining the external load on the screwdriver. (

**b**) DHM with a reference point, force ${F}_{zh}$ and Torque ${T}_{zh}$ are shown exemplary in body-fixed coordinate system ${COS}_{B}$. Load components (${F}_{xh},{F}_{yh}$,${T}_{xh},{T}_{yh}$) are not shown.

**Figure 3.**Screwdriver with body-fixed coordinate system ${COS}_{B}$ and world coordinate system ${COS}_{W}$, external loads ${\mathit{F}}_{\mathit{p}\mathit{r}\mathit{o}\mathit{c}\mathit{e}\mathit{s}\mathit{s}}$ and ${\mathit{T}}_{\mathit{p}\mathit{r}\mathit{o}\mathit{c}\mathit{e}\mathit{s}\mathit{s}}$ resp. ${\mathit{F}}_{\mathit{x},\mathit{p}\mathit{r}\mathit{o}\mathit{c}\mathit{e}\mathit{s}\mathit{s}}$ as well as the center of gravity (COG). The position of the reference point is altered from the origin of the body fixed ${COS}_{B}$ (baseline (XB and YB)) to the positions X1–X10 and Y1–Y10 to verify the ApOL model behavior.

**Figure 4.**(

**a**) Mean process torque ${\mathit{T}}_{\mathit{p}\mathit{r}\mathit{o}\mathit{c}\mathit{e}\mathit{s}\mathit{s}}$ of 10 screw-in repetitions over the battery current of the screwdriver (blue), linear correlation of process torque ${\mathit{T}}_{\mathit{p}\mathit{r}\mathit{o}\mathit{c}\mathit{e}\mathit{s}\mathit{s}}$ and battery current $\ge $2.45 A (yellow) with R = 98%; (

**b**) Residuals for the linear correlation in Nm. Residuals <0.5 Nm for battery current <13 A; residuals <2.2 Nm for battery current $\ge $13 A.

**Figure 5.**Force ${F}_{xh}$ (force direction is perpendicular to handle- and drill-axis) for participant 1 with factor levels Y1–Y10 (positions of the reference point) during the movement cycle for the verification of the ApOL model. Increasing force ${F}_{xh}$ from the baseline (YB, original screwdriver) to Y9 within the limits of the mathematical model. Y10 is close to zero since the torque ${T}_{process}$ is not converted to ${F}_{x,process}$ (as explained in Section 2.4) but is kept as process torque ${T}_{process}$ acting on the screwdriver.

**Figure 6.**Force ${F}_{xh}$ (force direction is perpendicular to handle- and drill-axis) for participants 1–3 with factor levels Y1–Y10 during the screw-in process Increasing force ${F}_{xh}$ from the baseline (YB) to Y9 within the calculated limits. Y10 is close to zero since the torque ${T}_{process}$ is not converted to ${F}_{x,process}$.

**Figure 7.**Torque ${T}_{xh}$ (torque leads to radial/ulnar deviation of the wrist) for participants 1–3 with factor levels Y1–Y10 during the screw-in process. Reduced torque ${T}_{xh}$ from the baseline (YB) to Y7 and increases again for the remaining factor levels with different signs. Load progression is increasingly similar for all users from the baseline to Y10.

**Figure 8.**Torque ${T}_{yh}$ (torque leads to extension/flexion of the wrist, torque along the handle axis) for participants 1–3 with variations X1–X10 during screw-in process. Increasing torque from the baseline (XB) to X10. The calculated minimum (math, XB

_{min}) and maximum (math, X10

_{max}) do fit the simulated results of the baseline (XB) and factor level X10.

**Figure 9.**Torque ${T}_{zh}$ (torque leads to pronosupination forearm, torque along the forearm axis) for participants 1–3 with factor levels X1–X10 during the screw-in process. Increasing torque from the baseline (XB) to X10. The calculated minimum and maximum do fit the simulated values.

Component | Mass in kg | Simulink Model |
---|---|---|

Handle | 0.09 | |

Battery (3.1 Ah) | 0.40 | |

Battery socket | 0.09 | |

Data Logger | 0.40 | |

Motor | 0.41 | |

Gearbox | 0.51 | |

Chuck | 0.24 | |

Motor and gearbox housing | 0.09 | |

Total | 2.22 |

**Table 2.**Y-variation: Reference point with factor levels YB and Y1–Y10. This variation represents a successive relocation of the original handle of the screwdriver to the backside of the motor assembly, putting the forearm axis in line with the drilling axis.

Factor Level | YB | Y1 | Y2 | Y3 | Y4 | Y5 | Y6 | Y7 | Y8 | Y9 | Y10 |
---|---|---|---|---|---|---|---|---|---|---|---|

y in mm | 0 | 7.4 | 14.8 | 22.2 | 29.6 | 37.1 | 44.5 | 51.9 | 59.3 | 66.7 | 74.1 |

z in mm | 0 | $-5.9$ | $-11.9$ | $-17.8$ | $-23.7$ | $-29.6$ | $-35.6$ | $-41.5$ | $-47.4$ | $-53.3$ | $-59.3$ |

**Table 3.**X-variation: Reference point with factor levels XB and X1–X10. This variation is selected to validate the model’s accuracy in accommodating modifications of the reference point in all three spatial directions.

Factor Level | XB | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 | X10 |
---|---|---|---|---|---|---|---|---|---|---|---|

x in mm | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

**Table 4.**Verification of the ApOL model. The accuracy of the prediction compared to the mathematical model is presented as mean (and standard deviation (SD)) with the mean-absolute-error (MAE) and the relative mean-absolute-error (rMAE) for the X- and Y-variation.

P1−P3 | MAE [N], [Nm] | rMAE [%] | MAE [N], [Nm] | rMAE [%] | MAE [N], [Nm] | rMAE [%] |
---|---|---|---|---|---|---|

Variations | F_{xh} | F_{yh} | F_{zh} | |||

X | 5.1 (3.4) | 9.4 (4.6) | 1.0 (0.5) | 4.7 (2.8) | 1.6 (0.2) | 1.6 (0.5) |

Y | 12.0 (4.0) | 11.4 (4.6) | 1.1 (0.4) | 5.1 (2.4) | 1.1 (0.2) | 3.7 (4.5) |

T_{xh} | T_{yh} | T_{zh} | ||||

X | 0.5 (0.1) | 8.1 (2.5) | 0.2 (0.1) | 1.7 (0.6) | 0.1 (0.0) | 4.6 (2.7) |

Y | 0.5 (0.1) | 8.5 (4.5) | 0.3 (0.1) | 16.1 (11.4) | 0.3 (0.1) | 7.0 (2.6) |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sänger, J.; Wirth, L.; Yao, Z.; Scherb, D.; Miehling, J.; Wartzack, S.; Weidner, R.; Lindenmann, A.; Matthiesen, S.
ApOL-Application Oriented Workload Model for Digital Human Models for the Development of Human-Machine Systems. *Machines* **2023**, *11*, 869.
https://doi.org/10.3390/machines11090869

**AMA Style**

Sänger J, Wirth L, Yao Z, Scherb D, Miehling J, Wartzack S, Weidner R, Lindenmann A, Matthiesen S.
ApOL-Application Oriented Workload Model for Digital Human Models for the Development of Human-Machine Systems. *Machines*. 2023; 11(9):869.
https://doi.org/10.3390/machines11090869

**Chicago/Turabian Style**

Sänger, Johannes, Lukas Wirth, Zhejun Yao, David Scherb, Jörg Miehling, Sandro Wartzack, Robert Weidner, Andreas Lindenmann, and Sven Matthiesen.
2023. "ApOL-Application Oriented Workload Model for Digital Human Models for the Development of Human-Machine Systems" *Machines* 11, no. 9: 869.
https://doi.org/10.3390/machines11090869