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The function of muscles around a simple joint.

One of the most obvious features of the human body is that it is equipped with a very large and at first sight an unnecessarily large number of muscles. For example, each arm contains no less than five muscles which are capable of producing a motion which decreases the interior angle of the elbow (MacConaill, 1946, 1949; Williams & Lissner, 1962; Basmajian, 1967), yet the elbow joint is a simple hinge, and one might suppose that only one muscle would be needed to carry out flexion. Why then has Nature provided a whole group of muscles; and, indeed, why has Nature provided most of the simple skeletal joints with more muscles than seem strictly necessary? Many anatomists have come to the conclusion that each muscle of the body has its own individual role some muscles being primarily force-producing elements, others acting mainly as stabilizing influences, and so on. Two articles on the subject have appeared (MacConaill, 1946, 1949) in which the elbow is taken as an example of a typical joint. MacConaill argues on theoretical grounds that those muscles which lie mainly along the upper arm (e.g. the biceps brachii) act as 'spurt' muscles, and those muscles which lie mainly along the forarm act as 'shunt' muscles. A 'spurt' muscle is defined as one which provides the acceleration along the curve of motion when a joint is flexed, and a 'shunt' muscle is defined as one which provides the centripetal force. Thus, according to MacConaill, spurt muscles are used to produce the movement itself and shunt muscles are used to provide a stable base for the movement. Basmajian (1967), in his comprehensive work on electromyography, claims to have partially verified these theories, and Gray's Anatomy (1973) refers the reader to theworks ofMacConaill and Basmajian. More recently, however, doubts have been expressed as to the validity of classifying muscles in this way, and experimental results have been produced which tend to disprove MacConaill's theory (Stern, 1971; Joseph, 1973). It is the purpose of this paper to examine mathematically the role of muscles acting around a typical simple joint such as the elbow. Suppose we assume the upper arm to be clamped rigidly in a vertical position, and the forearm to be, momentarily, in a horizontal position. (This is the sort of posture considered by MacConaill.) Consider first a muscle, exerting a force F, acting mainly along the upper arm (Fig. 1), and connected to the arm at distances a and b from the elbow as shown. Then the mechanical moment exerted by this muscle on the forearm about the elbow is a multiplied by the vertical component of the force in the muscle, i.e. the moment is (a) (FbI V(a2 + b2)). Consider now a similar muscle, also exerting