# Simulation of a Lower Extremity Assistive Device for Resistance Training in a Microgravity Environment

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Actuation Type 1

#### 3.2. Actuation Type 2

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Processes used in OpenSim and MATLAB. (

**a**) Process for obtaining tracking objective data. (

**b**) Optimization process using MATLAB and OpenSim.

**Figure 2.**Actuation system configuration. (

**a**) Type 1: two forces and one torque actuators acting on the midpoint of the sole (

**b**) Type 2: rotary actuators attached to the HKA joints.

**Figure 3.**Tracking results of the generalized coordinates and generalized speeds (Type 1). Tracking results of the generalized coordinates ((

**a**–

**c**), solid lines) and generalized speeds ((

**d**–

**f**), solid lines) are shown for the right limb compared to the objective tracking data (red dashed lines). The difference between the mesh densities is small, and the results closely match the objective data for all the mesh densities. Hip flexion, knee extension, and ankle dorsiflexion are positive. See Supplementary Materials for the results of the left limb (Figure S1).

**Figure 4.**Tracking results of the muscle activation (Type 1). Tracking results of the muscle activation ((

**a**–

**i**), solid lines) are shown for the right limb compared to the objective tracking data (red dashed lines). The difference between the mesh densities is small. The shaded areas are surface EMG patterns obtained from natural speed walking in healthy adults [39,40]. It is scaled to match the simulation data for comparison. See Supplementary Materials for results on the left limb (Figure S2).

**Figure 5.**Results of the fiber length and muscle excitation (Type 1). Results of the fiber length ((

**a**–

**i**), solid lines) and muscle excitation ((

**j**–

**r**), solid lines) are shown for the right limb compared to the results of CMC data (red dashed lines). The results of the fiber length are normalized by the optimal fiber length of each muscle. The difference between the mesh densities is small. See Supplementary Materials for results on the left limb (Figure S3).

**Figure 6.**Assistive forces and torques of the external actuators (Type 1). The actuator inputs are shown for the right limb ((

**a**–

**c**), solid lines). For comparison, the GRF data are also shown for the 1 g walking (red dashed lines). Due to the periodicity constraints assigned to the actuators, the actuator inputs showed the same values at both ends. The smoother control input curves were obtained as the mesh density increased. See Supplementary Materials for results on the left limb (Figure S4).

**Figure 7.**Tracking results of the generalized coordinates and generalized speeds (Type 2). Tracking results of the generalized coordinates ((

**a**–

**c**), solid lines) and generalized speeds ((

**d**–

**f**), solid lines) are shown for the right limb compared to the objective tracking data (red dashed lines). The difference between the node densities is small, and the results closely match the objective data for all the mesh densities. Hip flexion, knee extension, and ankle dorsiflexion are positive. See Supplementary Materials for results on the left limb (Figure S5).

**Figure 8.**Tracking results of the muscle activation (Type 2). Tracking results of the muscle activation ((

**a**–

**i**), solid lines) are shown for the right limb compared to the objective tracking data (red dashed lines). The difference between the node densities is small. The shaded areas are surface EMG patterns obtained from natural speed walking in healthy adults from the literature [39,40]. It is scaled to match the simulation data for comparison. See Supplementary Materials for results on the left limb (Figure S6).

**Figure 9.**Results of the fiber length and muscle excitation (Type 2). Results of the fiber length ((

**a**–

**i**), solid lines) and muscle excitation ((

**j**–

**r**), solid lines) are shown for the right limb compared to the results of CMC (red dashed lines). The results of the fiber length are normalized by the optimal fiber length of each muscle. The difference between the mesh densities is small. See Supplementary Materials for results on the left limb (Figure S7).

**Figure 10.**Assistive torques of the external actuators (Type 2). Actuator inputs are shown for the right limb ((

**a**–

**c**), solid lines). For comparison, the differences between the results of inverse dynamics in the two environments, i.e., in the absence of GRF data at 0 g (microgravity) and in the presence of GRF data at 1 g (earth), are also shown ((

**a**–

**c**), red dashed lines). Hip flexion, knee extension, and ankle dorsiflexion are positive. See Supplementary Materials for results on the left limb (Figure S8).

**Figure 11.**Net joint torques by the muscles (Type 1). Using the state variables obtained by the optimization for Type 1, the net joint torques caused by the muscles acting on the right lower limb joints are shown for the gait cycle ((

**a**–

**c**), solid lines). In addition, the joint torque data obtained with inverse dynamics at 1 g normal walking are also shown (red dashed lines). The results of the optimization and inverse dynamics are well matched during the gait cycle. Hip flexion, knee extension, and ankle dorsiflexion are positive. See Supplementary Materials for results on the left limb (Figure S9).

**Figure 12.**Net joint torques by the muscles (Type 2). Using the state variables obtained by optimization for Type 2, the net joint torques caused by the muscles acting on the right lower limb joints are shown for the gait cycle ((

**a**–

**c**), solid lines). In addition, the joint torque data obtained with inverse dynamics at 1 g normal walking are also shown (red dashed lines). The results of the optimization and inverse dynamics are well matched during the gait cycle. Hip flexion, knee extension, and ankle dorsiflexion are positive. See Supplementary Materials for results on the left limb (Figure S10).

**Table 1.**Total number of variables, number of iterations, CPU time, minimum objective function value for the Type 1 and Type 2 simulations.

25 Nodes | 51 Nodes | 75 Nodes | 101 Nodes | ||
---|---|---|---|---|---|

TYPE 1 | Total number of variables | 1800 | 3672 | 5400 | 7272 |

Number of iterations | 105 | 42 | 58 | 39 | |

CPU time (s) | 6659 | 6600 | 14,138 | 14,277 | |

Minimum objective function value | 0.013936 | 0.011556 | 0.0043457 | 0.002848 | |

TYPE 2 | Total number of variables | 1800 | 3672 | 5400 | 7272 |

Number of iterations | 45 | 44 | 32 | 24 | |

CPU time (s) | 3172 | 6855 | 8171 | 10,725 | |

Minimum objective function value | 0.012737 | 0.0068445 | 0.0031853 | 0.0032639 |

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**MDPI and ACS Style**

Han, J.I.; Choi, H.S.; Baek, Y.S.
Simulation of a Lower Extremity Assistive Device for Resistance Training in a Microgravity Environment. *Appl. Sci.* **2020**, *10*, 1160.
https://doi.org/10.3390/app10031160

**AMA Style**

Han JI, Choi HS, Baek YS.
Simulation of a Lower Extremity Assistive Device for Resistance Training in a Microgravity Environment. *Applied Sciences*. 2020; 10(3):1160.
https://doi.org/10.3390/app10031160

**Chicago/Turabian Style**

Han, Jong In, Ho Seon Choi, and Yoon Su Baek.
2020. "Simulation of a Lower Extremity Assistive Device for Resistance Training in a Microgravity Environment" *Applied Sciences* 10, no. 3: 1160.
https://doi.org/10.3390/app10031160