Vector resolution

Forces produce joint movements. They simultaneously produce effects at joint surfaces like compression, distraction, and shearing or sliding. When forces are depicted as vectors, their effects at joint surfaces can be illustrated using the technique of vector resolution:

This demonstration of vector resolution illustrates the effect of teres minor at the glenohumeral joint surface.

	The muscle's force vector (TM) is illustrated, along with a reference line that represents the glenohumeral joint's surface
	The next step involves moving the muscle's vector, without tipping it or changing its orientation, so that the vector's point of application rests somewhere the reference line.
	Resolving the muscle vector involves drawing two component vectors: one that is parallel to (directly on) the reference line one that is perpendicular to the reference line. The two vectors are called components of the original vector because, when added using the technique of vector composition, their resultant or sum is the original muscle vector.

When the two component vectors are drawn to the proper lengths, they form a rectangle along with lines that attach all three vectors' tips.

Recall that the point of application of the original vector, which represents teres minor, is located on the humeral head. We interpret the component vectors' directions to mean that the teres minor causes the humeral head to compress onto the surface of the glenoid fossa, and to slide downward on the glenoid fossa.

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Vector resolution is a very useful technique. In the previous example, we determined the effect of a muscle on a joint surface. In this example, we evaluate the effect on hip joint compression and shear of the weight of the body's superincumbent mass.

	The red reference line represents the hip joint's surface. The vector W, with its point of application in the lower lumbar region, illustrates gravity's effect on the body mass that is superincumbent to the hip joints.

After resolving vector W into two components, you may compare your analysis with another.

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We can also use vector resolution to evaluate the effect of iliopsoas action on the site of an intertrochanteric fracture. The solid reference line illustrates the fracture line. The vector illustrates the effect of the iliopsoas at its point of application on the lesser trochanter.

"Sliding" the iliopsoas' force vector to the reference line and resolving it into two components reveals the muscle's effects on the proximal fracture fragment to which it attaches. The iliopsoas: distracts the proximal fracture fragment from the distal fragment shears the proximal fragment laterally with respect to the distal fragment.

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Last updated 11-16-01 Dave Thompson PT
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