254 



ANIMAL MECHANICS. 



when we raise the body on the toes, the heel end of the lever becomes 

 relatively longer as compared with the toe end, so that the muscular pull 

 required becomes less and less. Fig. 141 illustrates this in the case of 

 a boy's foot. With the foot upon the ground the distance ab is to be as 

 4 to 14. On raising the heel somewhat more than 2 in. see dotted 

 line the relations are altered, ab' being to b'c' as 2*8 to 2. It is true 

 that it is very tiring to stand with the body raised high on the toes, 

 but it is probable that this is due to the fact that the calf muscles 

 are shortened, and their pull in consequence greatly diminished. 



The resolution of moments into their components. The moment 

 of a force is, as appears from the construction given, smaller than the 

 force itself. The reason is that a part of the force spends itself by 

 exerting pressure on the joint. Thus in a muscle acting obliquely on a 

 bone there are two component forces to be considered, one acting in the 

 direction of the bone and producing pressure on the joint, the other 

 acting perpendicularly to the first, and producing rotation. The lines 

 representing the component forces form one half of 

 what is termed the parallelogram of forces. 



So far we have studied the action of a muscle 

 lying in the plane of movement of the bone upon 

 which it acts. If we are dealing with a joint under 

 constraint, which can, like the elbow-joint, move in 

 one plane only, we have to consider the action of 

 muscles like the pronator radii teres, which are 

 oblique to that plane. If, as in Fig. 142, we 

 represent in force and direction the action of the 

 muscle by the straight line ab, we can resolve this 

 force by the parallelogram of forces into two, one of 

 which ac lies in the plane in which movement 

 can actually take place, and the other at right 

 angles to it. The length of ac will represent the 

 force of the muscle acting so as to produce the 

 movement. The moments of flexion .will be the 

 force in this direction, multiplied by the perpendicular distance between 

 the point of rotation and the line of action of the force. The rest of the 

 force will be spent in pressure and lateral strain on the joint. . 



When we are dealing with the action of a muscle upon an un- 

 constrained joint, like that of the shoulder, the direction of the resulting 

 movement will be determined by the direction of the muscle itself. 

 If we take that plane which passes through the centre of rotation 

 of the joint, the point of insertion, and the point of origin of the 

 muscle (or the line of action of the muscle), then its contraction 

 will cause a rotation around an axis normal to that plane, and passing 

 through the centre of rotation. We may further, by means of three 

 co-ordinate planes, determine the position of these points and the 

 position of the centre of rotation, and then calculate by trigonometrical 

 methods the position of this axis, and the new positions assumed 

 by the limb, resultant upon the muscular contraction. 



It is customary to describe the action of muscles in relationship to three 

 co-ordinate planes. Thus, a portion of the deltoid is described as abducting 

 the humerus, slightly flexing it, and rotating it inwards. In other words, 

 abduction may be taken as a plus rotation on the frontal plane, and about a 

 horizontal sagittal axis; flexion, a plus rotation along a sagittal plane about 



FIG. 142. 



