20


PART I FOUNDATION CONCEPTS


B C A C


D


B


C L


Figure 1.19 Vector composition. The force from the weight of the arm and the force from the weight of the cuff, when added together, represent the total force being applied to the forearm. L, limb weight; C, cuff weight. Resultant force = C + L.


orientation, and amount of force generated by the weight of the distal limb segment.


Composition of Vector Forces


Colinear forces are two or more forces that have the same line of force, are parallel, and are in the same plane. The forces can be acting in the same direction or the opposite direction. Using a coordinate grid, the forces in one direction are considered positive, and the forces in the opposite direction are considered negative. The result of two or more forces depends on the direction and amount of each force. Two forces in the same direction are added together, and the sum of the two is recorded as positive or negative depending on the direction of the forces. If the forces are in the opposite direction, the negative number is added to the positive number, and the resultant direction results from the larger of the two numbers. Figure 1.19 illustrates the forces exerted on the distal segment of a forearm that has a cuff weight on it. The resultant force of the combined weight of the limb segment and the weight of the cuff weight represents the total amount of force acting on the limb in a down- ward direction. Because both forces are acting in the same direction along the negative y-axis, they are added together to determine the resultant force, completing the process of composition of vector forces.


Forces may lie in the same plane but, in contrast to colinear forces, may not have the same line of action. When vector forces do not act on a shared line of force, they can be composed to determine the resultant forces using the polygon method, shown in Figure 1.20.


A


Figure 1.20 The graphic polygon method for determining resultant force.


Forces A, B, and C all occur in different directions. The tail of the fi rst vector, A, is aligned with vectors B and C. By placing the vector arrows tip to tail and then complet- ing the polygon with a resultant vector, all the forces combined are composed into the total resultant force vector D.


Figure 1.21 illustrates the parallelogram method for determining the resultant force from two forces. The illustration shows the forces generated by the patella tendon (P) and the quadriceps tendon (Q). These two forces have the same point of origin, and the resultant force, the patellofemoral joint reaction force, is the resul- tant force of these two component forces. The resultant force represents the amount of compressive force gen- erated between the patella and the femur as a result of these two component forces. The forces are drawn with the tails together at the same point of origin. Drawing a dotted line representing force Q at the head of force P and a dotted line representing P at the head of force Q forms a parallelogram. The resultant force of P and Q is force R, which is represented by the diagonal from the point of origin to the intersection of the heads of the dotted lines.


Resolution of Vector Forces


Vector forces can also be broken down or separated into component vectors, a process called vector resolution or resolution of forces. This process takes an oblique vector and separates the force into its components that are per- pendicular and parallel to its line of action. Most human movement occurs as a result of internal or external forces applied at an angle. In analyzing muscle vector forces in the body, the vector is resolved, or broken down into the


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