## 2 Materials and Methods
### Data Processing
#### 2.4.1 Data Reduction  
Vicon Nexus 2.6.1 was used to reconstruct marker trajectories and fill gaps. Raw trajectory data were filtered using a Woltring filter (MSE 15) [27]. Ground reaction force data were smoothed with a 6 Hz zero-lag 4 th order Butterworth filter [20; 28]. The final data analysis only included trials with clean, i.e., entire foot within the confines of the plate, force plate strikes (five trials on each side). Nexus was used to trim full walking and turning trials, and three representative right and three representative left gait cycles were selected and exported to Visual3D (C-Motion, Inc., Germantown, MD, USA) for further dynamic data reduction and analysis. The biomechanical model created in Visual3D included a virtual coordinate system attached to each foot (Figure 4). It was defined by markers placed on the medial and lateral malleoli and the toe (between the heads of the first and second metatarsal heads) that were projected onto the floor of the lab. In our model, the \(y\)-axis was anteroposterior and the \(x\)-axis was mediolateral. The virtual foot coordinate system was projected onto the floor since the COP is on the surface of the floor, and it estimates the position of the COP relative to the foot. The primary variables of interest, COM-COP inclination angle (Figure 5), COP-COM A/P and M/L (Figure 5), COP-XCOM A/P and M/L (Figure 6), and U\({}_{\text{MAX}}\)-XCOM A/P and M/L (Figure 6), were calculated to determine whether a difference in the reference limb existed between participants with PD and healthy CON participants at FDS, MS, and SDS of the gait cycle. Because the COM-COP inclination angle is a spatial angle, it was not determined in the foot coordinate system but relative to the laboratory coordinate system (Figure 3). Using a 15-link biomechanical model, total body COM was defined as the center of mass in three-dimensional space and was computed as the weighted average of each body segment's COM in Visual3D. Segments were modeled as geometric shapes, e.g., cones, cylinders, spheres, and ellipsoids. Segment lengths between each joint were estimated per Dempster [29; 30], and segment masses were expressed as a percentage of the  
Figure 4: Anteroposterior view of the virtual foot coordinate system with its origin located at the ankle joint center, i.e., midway between the medial and lateral malleoli, projected to the floor. For the right foot, the right-handed coordinate system was positive-x (red), positive-y (green), and positive-z (blue). FP1 = force plate one; FP2 = force plate two; FP3 = force plate three. total body mass [31]. The velocity of the COM was estimated using a first-order central difference formula. Figure 5: Center–of–mass (COM)–center of pressure (COP) inclination angle (\(\theta\)) is the spatial angle between the vertical projection on the ground of the COM and a line connecting the COM to the most lateral position of the COP. (**A**) posterior view of the COM–COP inclination angle and the linear mediolateral (M/L) distance between the vertical projection on the ground of the COM and location of the COP, i.e., COP–COM M/L, at midstance on the right; (**B**) lateral view of the COM–COP inclination angle and the linear anteroposterior (A/P) distance between the projection on the ground of the COM and location of the COP, i.e., COP–COM A/P, at first double–support; and (**C**) lateral view of the COM–COP inclination angle and COP–COM A/P at second double-support. Figure 6: Schematic illustrating the determination of the linear distance between the extrapolated center of mass (_XCOM_) and the center of pressure (COP) or \(U_{MAX}\).