Wednesday, January 15, 2014

Walking Mechanics: What is Center of Mass and How Do We Control It?

Understanding mechanics provides the foundation for strong understanding of human movements.

Why would you care about movement mechanics? Well perhaps you have some questions about joint loading, energy expenditure, technique...and grasping basic principles may lead you to better understanding to answer such questions (and also realize that usually it is not as black and white as some may say).

For instance, why do we expend energy when walking on flat ground?

Short Take Home Message:

The need to keep angular momentum low (no rotating) constrains our choices in how we move.

Longer Explanation (Just go to "summary" if it's too long-winded)

Center of Mass
Now, biomechanics can have many levels of analysis, but we must start with the most basic, which would take us back to physics and representing the entire body as one point mass, called your Center of Mass (CM). We'll stick to 2D.

The CM is a theoretical point in which allow Newton's Law's of Motion to be easily applied.

åF = ma,  remember? In any direction, the sum of the external forces acting on the human body must equal the mass of the body (m) times the acceleration of the CM. This is why the CM is special - even though a reaction force (Fy) is applied at the foot, the toe itself is actually not accelerating. What is guaranteed to accelerate at a known rate is the CM. Movement of any specific segment requires more information.

In the horizontal direction, the horizontal force at the feet define CM acceleration. In the vertical direction, its the vertical force at the feet minus bodyweight force (mg).

When walking on flat ground, horizontal acceleration should be 0 in theory. Once we have a forward velocity, the body should continue forward at the same velocity unless a backwards force is applied. Why would we do that? 

In the vertical direction, acceleration on average should also be 0, since our CM shouldn't be changing in vertical position (this is much different when ascending a mountain, of course). Since we have a bodyweight force acting downward, we need an equal force in the upward direction on our feet to maintain acceleration of the CM at 0. 

If these were easily maintained, then we wouldn't have to add force to the system ever. But clearly we do. Why is that?

Well there's one more direction - angular

Are you doing somersaults when hiking?

åM = Iα

The sum of the moments (M) about the center of mass must equal the inertia of the CM times the angular acceleration of the CM. Basically, if the force at the foot is not directed in the path of the CM, then it will create a moment about the CM. This, in turn will induce rotation, such as when attempting a somersault.

Take a look at the diagram below. If the resultant force acting of the feet pass through the center of mass (b), then no angular acceleration is generated. However if the force does not pass through the CM (a), then we begin rotating forward or backward.

Regulation of angular impulse during fall recovery

How do you walk?

So, in 2D, you have 3 constraints defined by CM control: 1) Horizontal acceleration ~ 0, 2) Vertical acceleration ~ 0, and 3) Angular acceleration ~ 0.

#3 is by far the least considered, but the most important. If you start rotating, you will soon be out of position to correct yourself, whereas with the first two your orientation relative to the ground still allows you to correct your balance easily.

How does this affect how you walk? Think about where your foot contacts the ground the ground. It's probably somewhat in front of the rest of your body. If that's the case, then the horizontal force must be in the negative direction so that the resultant force passes through the CM (blue). It has to to keep you from rotating. The negative force starts slowing you down, so then you must generate a positive horizontal force later to speed you back up (green). 

This means you must generate both positive and negative work in the horizontal direction, both of which require some energy.
So why do you think you put your foot ahead of you, if it produces a backwards force? Well I think that would be good discussion to continue in another post.

  • Your body can be represented as one point, called the Center of Mass, for some basic analyses. 
  • The CM must be tightly controlled in both linear and angular directions to maintain balance.
  • When walking, we produce both forward and backward forces in order to keep angular acceleration minimal.
  • This creates both positive and negative work which violates the generic assumption that no mechanical work is performed in the horizontal direction.

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