Category Archives: Ex. Fitness

The Biomechanical Model for Minimum Movement Time during Running Walking and Road Cycling 07: The Joint Torque Principle

by Dr. James Kao

 The sixth fundamental Biomechanical principle included in this model is the Joint Torque Principle.  This principle states that an increase in joint torque (TJ) is caused by an increase in a muscle force (FM) pulling on the bones that are held together at the joint and/or an increase in the moment arm (dMA) (i.e., the linear distance from the joint’s axis of rotation to the line of pull of the muscle force).  The line of pull of the muscle force is determined by connecting a line between the attachments (origin and insertion) of the muscle.The equation for the Joint Torque Principle is given here.
Joint Torque Principle Equation

A graphical representation the Joint Torque Principle is presented here.
Joint Torque Principle

 

 

 

 

 

To create a larger muscle force, three factors that influence the size of the muscle force must be considered.

  • The first factor is muscle size.  A muscle with a larger physiological cross-sectional area will create more muscle force.  The method to increase physiological cross-sectional area is resistance training.
  • The second factor is muscle length.  All muscles have a natural resting length.  This natural resting length is found when the muscle is relaxed.  Muscles that are stretched to approximately 120% of their natural resting lengths generate the most muscle force.
  • The third factor is the speed of the muscle contraction.  Muscles that are concentrically contracted at slower speeds generate greater muscle force than muscles that are concentrically contracted at faster speeds.

The moment arm is the distance from joint’s axis of rotation to the line of pull of the muscle force.  If the moment arm distance is increased, the size of the joint torque will increase.

  • To increase the moment arm distance, you would need to move the line of pull of the muscle force further away from the joint’s axis of rotation.  The line of pull of a muscle force is determined by drawing a line connecting the muscle’s origin to it’s insertion. Thus, one method for moving line of pull of the muscle force would be to change the locations of the origin and insertion points for the muscle.  This is not option because it would be unethical to perform this type of surgery.
  • The only way we can change the moment arm distance is by changing the angle of the joint.  When the long axes of the two bones connected at a joint are aligned long axis to long axis (i.e., in a straight line), the moment arm distance is the smallest.  This is because the line of pull of the muscle force passes extremely close to the joint’s axis of rotation.  The maximum moment arm distance is achieved when the long axes of the two bones connected at a joint are perpendicular to each other (i.e., there is a 90 degree angle between the two long axes).  In this joint orientation, the line of pull of the muscle force is the farthest away from the joint’s axis of rotation.

Read more on these topics at Dr. Kao’s blog: http://realworldbiomechanics.blogspot.com/