How to analyze the forces involved in a push-up and its variations?

I am working on a method to determine the forces involved in a push-up and its variations, particularly how the percentage of body weight supported by each arm changes across these variations. It would also be interesting to determine how the forces vary at different stages of a push-up (for example, when the arms are more extended versus when they are more flexed), both in a standard push-up and in an incline push-up.

I would really appreciate any help with this study. If necessary, I can try to create diagrams to better illustrate the situation described. Please do not hesitate to contact me if anything is unclear or if you need further clarification. English is not my native language, so I kindly ask you to excuse any grammatical errors.

I will present below what I have developed so far:

The human body is modeled as a rigid rod pivoting about a fixed axis located at the foot supports. The mass distribution is concentrated at a single point, the Center of Mass ($C$), while the reaction force exerted by the hands is applied along the vertical line passing through the Shoulder ($S$).

Description of the variables

Static Equilibrium

For the body to remain in static equilibrium, the sum of all forces and the sum of all moments about any point in the system must be zero:

$\sum F = 0$

$\sum \tau = 0$

The total gravitational force acting on the Center of Mass is calculated as follows:

$P = W \cdot g$

Percentage of Body Weight

The geometric relationship between the position of the Center of Mass (C) and the point where the force is applied at the shoulders (S) determines the exact percentage of body weight transferred to the arms:

$K_{arms} = \left(\frac{C}{S}\right) \cdot 100$

Upper Position (Arms Extended)

In the inclined plane configuration at the starting point, the condition for rotational equilibrium about the foot support point yields the following equation:

$F_{hands} \cdot S - P \cdot C = 0 \implies F_{hands} = P \cdot \left(\frac{C}{S} \right)$

From this point onward, I have not developed anything further yet.

How does one calculate the fraction of body weight supported by the arms in the lower position, with the elbows bent?