Forces, vectors, and vector analysis

    We infer the existence of forces when we observe masses being accelerated (or distorted).

    Some of the forces that influence human movement:

    gravity muscle
    wind / water ligament
    reaction forces bone
    external weights friction


    We depict forces using VECTORS. Vectors have four characteristics.
    1. Point of application
    2. Line of application
    3. Direction
    4. Magnitude

    The rules by which we draw a vector DEPEND ON THE TYPE OF FORCE THE VECTOR DEPICTS.



    Point of application


    Muscle's point of attachment to moving bone

    Line of application


    follows muscle or tendon fibers local to the joint being analyzed



    toward center of muscle


    arbitrary; drawn to scale

    Other important forces we'll need to depict using vectors are reaction forces.

    Time out: a dose of common sense about forces from Fred Gram, Cuyahoga Community College.


    Given a movement of the human body,
    1. Name the joint at which the movement occurs.

      Determine what segment is moving, what segment is stable, and the joint where the movement takes place.

    2. Determine the plane of movement in which the movement occurs, and the axis around which the joint moves in this plane.

    3. Draw a simple diagram that illustrates the body in the plane you have named. Estimate the location of the relevant joint axis, and label it on your diagram with a "cross." Even if the movement takes place in more than one plane, you can analyze only one plane at a time.

    4. Focus your vector analysis on the moving segment, and begin by considering the force of gravity.

      Following the rules for gravity forces, depict the force of gravity as a vector.

      Determine the vector's moment arm and determine the moment that gravity produces around the joint's axis in the plane depicted.

    5. Consider other forces, especially muscle forces, that act on the moving segment.

      Decide which muscle forces act in a direction that produces moments that oppose gravity's moment.

      Follow the rules for muscle forces to depict these muscle forces as vectors.

      Determine each muscle vector's moment arm with respect to the joint axis.

Last updated 9-11-00 ©Dave Thompson PT
return to PHTH/OCTH 7143 lecture schedule