*2.5. Estimation of Vertical Stiffness in Joints*

The vertical oscillation of both the left and right thighs and shanks, as well as the VGRF, are represented in Equations (8)–(11) by individual parameters in a universal form. Therefore, by substituting Equations (8)–(11) into Equations (3)–(5), the vertical stiffness of the hip and knee can then be theoretically derived. Here, an equation of vertical stiffness for the left knee is displayed as:

$$k\_{lk} = \frac{m\_s g - \sum\_{n=1}^{N^F} A\_n^F M g \sin(2\pi nft + \varphi\_n) + m\_s (2\pi nf)^2 \sum\_{n=1}^{N^s} A\_n^s l \sin(2\pi nft + \varphi\_n^s)}{\sum\_{n=1}^{N^s} A\_n^s l \sin(2\pi nft + \varphi\_n^s) - \sum\_{n=1}^{N^t} A\_n^t l \sin(2\pi nft + \varphi\_n^t)},\tag{12}$$

where the superscript *F* indicates VGRF, *s* refers to the shank, and *t* corresponds to the thigh. Other theoretical equations, like the vertical stiffness of the right knee and hip, are obtained with the same process as Equation (12).
