## 2 Materials and Methods
### Analytic Model
#### 2.1.1 Static Calibration  
In the first phase, constant ACS and LCS were defined during the static calibration. Kinematic clusters in conjunction with a digitizing probe were used to define all virtual markers on the segments' anatomical points except for the pedal, where three physical markers were used. Markers, visually shown in Figure 1, were defined on the left and right anterior superior iliac spine (p1 and p2, respectively), sacrum (p3), greater trochanter (p4), medial and lateral condple (p5 and p5, respectively), tibial tuberosity (p7), medial and lateral malleolus (p8 and p9, respectively), heel (p10), metatarsal I and V (p11 and p12, respectively), and three pedal markers (p13, p14, and p15). The hip joint center was defined using three pelvis markers based on the work from [PERSON], [PERSON], and [PERSON] [15], while the knee and ankle joint centers were defined at mid-point between the medial and lateral condple and malleolus, respectively. Body mass, segment center of mass, and segment mass were based on [PERSON] (2009), while segments' length and inertial parameters of segment were based on the work from [PERSON] and [PERSON] [16]. The pedal system was defined to express all measured loads in a local pedal system using three markers such that the \(x\)-axis was positive forward, the \(y\)-axis was positive medial, and the z-axis was positive vertical upwards. The foot anatomical \(z\)-axis was defined between the underneath metatarsal II and ankle joint (positive proximal), the \(x\)-axis was perpendicular to line between metatarsal I and V, and the \(z\)-axis (positive anterior) and \(y\)-axis were perpendicular to the \(z\)- and \(x\)-axis (positive medial). Similarly, the calf \(z\)-axis was defined between the ankle and knee joint center (positive proximal), the \(x\)-axis was perpendicular to the line between medial and lateral malleolus and \(z\)-axis (positive anterior), while the \(y\)-axis was perpendicular to the \(z\)- and x-axis (positive medial). Lastly, the thigh \(z\)-axis was the line between the knee and hip joint center (positive proximal),the \(x\)-axis was perpendicular to the line between medial and lateral condyle and \(z\)-axis (positive anterior), while the \(y\)-axis was perpendicular to the \(z\)- and \(x\)-axis (positive medial). All orientations and marker placements are illustrated in Figure 1.  
All ACS including the local pedal system were transformed to the unit length and written in a matrix notation as shown in Equation (1):  
\[GA_{a}=\left[X_{x}\ Y_{x}\ Z_{x}\ X_{y}\ Y_{y}\ Z_{y}\ X_{z}\ Y_{z}\ Z_{z}\ \right] \tag{1}\]  
Figure 1: Segments’ local coordinate systems with origin in \(CoM\) are shown on leg and pedal, while marker placements are shown on pelvis (p1–p3), leg (p4–p12), and pedal (p13–p15). where \(GA_{a}\) is the transformation matrix between the GCS and ACS, while \(X\), \(Y\), and \(Z\) are the unit length vectors of the \(x\)-, \(y\)-, and \(z\)-axes of the ACS. Next, markers coordinates were expressed in the ACS as shown in Equation (2):  
\[M_{A}=\ [GA_{a}][M-CoM]^{T} \tag{2}\]  
where \(M_{A}\) is the marker coordinate expressed in the ACS, \(GA_{a}\) is as defined in Equation (1), \(M\) is the marker coordinate in the GCS, and \(CoM\) is the coordinate of the segment \(CoM\) expressed in the GCS. The LCS was defined using markers' coordinates expressed in the ACS (Equation (2)) to find the relation between the LCS and ACS. The foot LCS was established with metatarsal I and V markers and with the origin in the heel marker. On the same assumption, the LCS was established for calf and thigh, with the origin point in the lateral malleolus and lateral condyle, respectively. The LCS was established in conjunction with the medial malleolus and tibial tuberosity for the calf, and medial condyle and greater trochanter for thigh. The pedal LCS was defined with three pedal markers.