Wednesday, January 16, 2013

The Biomechanical Model for Minimum Movement Time during Running Walking and Road Cycling 05: The Linear Speed - Angular Velocity Principle

The fourth fundamental Biomechanical principle included in this model is the Linear Speed - Angular Velocity Principle. This principle explains how we create joint linear speed. This principle states that an increase in joint linear speed (s) (i.e., the straight line speed) of a point on a rotating body segment is caused by an increase in the body segment’s angular velocity (ω) (i.e., the rotational speed of the body segment) and/or an increase the radius of rotation (rrot) (i.e., the linear distance from the axis of rotation to the point of interest on the rotating body segment). For most human movement, the radius of rotation is the distance from one joint to the next joint connected by a body segment (e.g., the radius of rotation for the upper leg segment would be the distance from the knee joint to the hip joint).

Click on "read more" to view my description of the application of the Linear Speed - Angular Velocity Principle to real-world running.

Let's examine what happens when the hip experiences an extension angular velocity.  When the hip extends both the torso and the upper leg can rotate.  How they rotate is determined by any constraints (restrictions) on each body segment's movements.

Let's assume your feet are on the ground and you are trying to jump straight up into the air.  The ground constrains your feet, your ankles and your knees from moving downward.  Since your desired outcome is to go straight up, your feet, ankles and knees will be constrained from moving horizontally by muscle contractions.  In this situation, when the hip extends, the upper leg will rotate around the knee joint and the torso will rotate around the hip joint.  Thus, a hip extension angular velocity will cause the hip joint and all joints above the hip to move upward.

Now, let's assume your feet are in the air.  When you perform a hip extension movement, the knee and ankle joints are free to move vertically and horizontally.  In this case, when the hip extends, the upper leg and torso body segments will both rotate around the hip joint.  The upper leg segment will rotate downward and backward and the torso segment will rotate upward and backward.  The hip will not move. This is why kicking your legs when your feet are off the ground has very little effect on high you jump.

So, when you run, your foot, ankle, and knee are constrained against moving downward and backward.  This means a hip extension angular velocity will cause the upper leg segment to rotate around the knee joint.  When this happens, the hip joint will experience an increase in upward and forward linear speed.  Any other body parts attached at the hip (e.g, the torso and the head) will experience the same increase in linear speed.

There are two factors that determine the magnitude of the increase in linear speed: the radius of rotation and the angular velocity.  The radius of rotation for the upper leg segment is the length of the femur.  The longer the femur, the greater the increase in linear speed.  Thus, a runner with longer leg bones has a Biomechanical advantage.  This does not mean a person with shorter legs cannot run just as fast.  The person with shorter legs needs to improve the second factor, the magnitude of the angular velocity.  An increase in angular velocity will cause an increase in linear speed.  How we increase the angular velocity at a joint will be discussed in an upcoming post.

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