Question

How do the equations of motion change between the stance phase of running and the double support phase of walking if the task was to create the equations of motion between the person on the ground?

Answer 1

In a walking , one leg moves forward while the other leg stays on the ground. When walking at natural speed, the swinging leg uses muscle force to move forward and immediately relaxes, allowing the force of gravity to move it to the ground. Simultaneously, the planted leg moves forward with largely passive rotation at the hip. The plant leg only needs to stay straight and the swinging leg’s knee only slightly bends to allow it to pass underneath the body.

The swinging leg can be modelled as a physical pendulum: a thin uniform rod of mass m rotating about a point a distance r from its center of mass. Swinging freely under gravitational acceleration (g) such a physical pendulum with moment of inertia I will have equation of motion given by

For running the the legs do not move at their natural frequencies. Instead, the muscles produce forces (hence torques) to move the body forward. The maximum force a muscle can produce, F_max, is proportional to its cross sectional area A. The maximum torque that the muscle can exert about its pivot point, T_max is proportional to the product of F_max and the length of leg ie L . Here the equation of motion depends on max torque applied T_max

(where Tmax= Fmax X L )