# Biomechanical Effects on Lower Extremities in Human-Robot Collaborative Agricultural Tasks
## 2 Materials and Methods
### Data Analyses  
The hip joint center and knee joint flexion axis were determined by applying the symmetrical center of rotation estimation (SCoRE) [63] and the symmetrical axes of rotation approach (SARA) [64], respectively. This approach was combined with the Plug-in-Gait model [62] to calculate joint kinematics and kinetics according to the Vicon Nexus Advanced Gait Workflow (Nexus 2.10, Vicon Metrics Group Ltd., Oxford, UK). The kinematic and kinetic data were lowpass filtered using a 4 th order Butterworth filter with cutoff frequencies of 6 and 25 Hz, respectively [65]. Standard inverse dynamics calculations were performed combining inertial properties of the segments, GRFs, and kinematic data to extract the maximal joint moments of the dominant lower limb during the execution of the symmetric lifting task. Vertical GRFs were calculated as a percentage of body weight, whereas the hip, knee, and the ankle internal joint moments, and power were normalized to body mass. The lifting task employed in this study was separated into three phases, according to the literature [66]. More specifically:  
* The first phase was defined between the initiation of the trial and the completion of the forward bending motion to reach the agricultural crate. * The second phase lasted from the latter time point until lifting-up the crate. * The third phase was defined between the completion of the second phase and the landing of the crate on the custom-made shelf. Selected vertical GRFs along with kinematic and kinetic variables of the dominant limb (described in Table 1) were calculated for the aforementioned phases in each trial and averaged across the three trials performed at each height (Figure 3). Joint power was calculated by multiplying the net joint moment by the joint angular velocity [65]. The presented kinematic and kinetic variables are in the sagittal plane. The raw EMG data during the lifting task were filtered using a Butterworth bandpass filter (20-500 Hz), before applying an RMS algorithm (50 ms sampling window) [67]. Afterwards, the EMG data at the three selected heights were normalized to the EMG signals recorded at the lowest destination height (i.e., 70 cm). Finally, the peak and mean normalized RMS EMG were computed during the three phases of the lifting task. As far as the statistical analysis is concerned, the normal distribution was investigated using the Shapiro-Wilks test and did not differ significantly from normal. One-way ANOVA (three destination lifting heights) with repeated measures was used and existing \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Units** & **Description** \\ \hline GRF1 & \% BW & Minimum VGRF during phase 1 \\ GRF2 & \% BW & Maximum VGRF during phase 2 \\ GRF3 & \% BW & Minimum VGRF between phases 2 and 3 \\ GRF4 & \% BW & Maximum VGRF during phase 3 \\ KNEE MOMENT 1 & Nm/kg & Maximum knee extension moment during phase 1 \\ KNEE MOMENT 2 & Nm/kg & Maximum knee flexion moment during phase 2 \\ KNEE MOMENT 3 & Nm/kg & Maximum knee flexion moment during phase 3 \\ KNEE ANGLE MAX & degrees & Maximum knee flexion angle \\ HIP ANGLE MAX & degrees & Maximum hip flexion angle \\ HIP MOMENT 1 & Nm/kg & Maximum hip extension moment during phase 1 \\ HIP MOMENT 2 & Nm/kg & Maximum hip extension moment during phase 3 \\ ANKLE ANGLE MAX & degrees & Maximum dorsiflexion angle \\ ANKLE MOMENT 1 & Nm/kg & Maximum dorsiflexion moment during phase 1 \\ ANKLE MOMENT 2 & Nm/kg & Maximum dorsiflexion moment during phase 3 \\ KNEE POWER 1 & W/kg & Maximum knee absorption power \\ KNEE POWER 2 & W/kg & Maximum knee generation power \\ HIP POWER 1 & W/kg & Maximum hip absorption power \\ HIP POWER 2 & W/kg & Maximum hip generation power \\ ANKLE POWER 1 & W/kg & Maximum ankle absorption power \\ ANKLE POWER 2 & W/kg & Maximum ankle generation power during phase 2 \\ ANKLE POWER 3 & W/kg & Maximum ankle generation power during phase 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of the variables used in the present analysis.