Week 8 Energy Fluctuation In Locomotion Flashcards
Centre of mass trajectories in walking and running
Walking
For each stride the trajectory of the centre of mass is approximately an arc of constant radius. The elevation increases from initial contact to mid-stance, and decreases from mid-stance to toe-off. At mid-stance the elevation is at maximum and vertical ground reaction force at minimum.
Running
The elevation decreases from initial contact to mid-stance, and increases from mid-stance to toe-off. At mid-stance the elevation is at minimum and vertical ground reaction force at maximum. The ground reaction force is proportional to the “shortening” of the leg.
Potential energy PE=mgH. (Mass, gravity, height of com)
Height of com dictates
KE= 1/2mv2. Velocity is the only thing that is going to change
EE= 1/2KZ2. Eleastic energy = k= constant. Z= how much com dips down from standing position.
Highest velocity at initial contact
Mid stance at lowest velocity
Energy fluctuation in walking
Potential and kinetic energy are out of phase
Kinetic energy is highest at leg switch and lowest at mid-stance
Potential energy is lowest at leg switch and highest at mid-stance
The net energy (kinetic + potential) fluctuates very little during the gait cycle
Will have elastic energy but is so little and doesn’t have major effects on net energy
Energy fluctuation in running
In the aerial phase potential and kinetic energy are out of phase, and the net energy is constant
In the stance phase both potential energy and kinetic energy are minimal at mid-stance
Consequently the fluctuations of net (potential + kinetic) energy are substantial
The sum of potential and kinetic energy is minimal at mid-stance
Total energy should remain the same
Kinetic and potential energy decrease
Elastic energy increase at same rate that total energy is decrease to remain constant
Compress the most z2 is going to be the biggest
Running: an additional energy storage mechanism
Leg tendons and ligaments behave like springs
Elastic potential energy or strain energy is stored in the tendons and ligaments as they are deformed in the first half of the contact phase
Strain energy is converted back into kinetic and potential energy in the second half of the contact phase
Models for walking and running
The “stiff leg” or “inverted pendulum” model for walking
The whole body mass is concentrated in the centre of mass
Only one leg is in contact with the ground
The leg is mass-less and of constant length (L)
The motion of the centre of mass is rotation on a trajectory with radius R= L
The “spring-mass” model for running and hopping
The whole body mass is concentrated in the centre of mass
Only one leg is in contact with the ground
The leg is a spring which generates a force proportional to the change in length
The larger the angle the longer leg
Energy should be the same at point a b and c
Height difference at b compare to a and c
Spring-mass model of hopping: energy
Hopping can be defined as “running at zero horizontal speed”, and it can be analysed using the spring-mass model
It is convenient to use a coordinate system with the origin at the initial contact level and the z axis pointing downwards
The forces involved are the weight and the force in the spring (kz) which is also the ground reaction force.
According to this model the sum of kinetic, potential, and elastic energies is constant through the stance phase
The parameters of the model are the body mass (m), leg “spring stiffness”, and the speed at initial contact (V0)
Key points
Kinetic, potential, and elastic energies of the human body fluctuate during locomotion
In walking, the fluctuation of the net energy is small. Energy has to be invested mainly at leg switch
In running and hopping there is a drop in both potential and kinetic energies at mid-stance. However, elastic energy is stored in the deformed connective tissue
The principle of energy conservation can be used to estimate the minimal possible speed of walking
The principle of energy conservation can be used to estimate the maximal ground reaction force in hopping
Total energy will always remain constant
