PULLEYS 425 



obtained by dropping perpendiculars from the fulcrum to the Hnes 

 of application of power and load. The ratio of these perpen- 

 diculars oivcs the ratio of the distrihutioii of j)ower and speed by 

 the lever. 



The value of the bone-muscle mechanism depends on the mass 

 of active muscular fibres, their degree of contraction and the angle 

 which they make with the bone to be moved. The very movement 

 of the bone will alter the angle of pull of the nniscle. For each 

 of its positions, the lev^er will have a moment of rotation determined 

 by the size of the angle made by the line of traction (axis) of the 

 nuiscle and the axis of the bone. By resolving the force of the 

 nniscle into two components, one of which acts along the axis 

 of the bone and the other at right angles to it, one can readily 

 perceive that the latter, the effective component, varies in value 

 directly with the sine of the angle of pull. The ineffective or 

 })arallel component varies as the cosine of the angle of pull and 

 represents the pressure exerted by the muscle on the fulcrum. 

 As the moment of rotation is equal to the tension developed {F), 

 and the perpendicular distance {d) of the axis of the muscle from 

 the fulcrum, one may write M = Fd. Then the effective com- 

 ponent is equal to F sin a where a is the angle of pull, and the 

 parallel component to F cos a. Hence, as the bony lever gets 

 pulled up, the effective component will become greater and the 

 parallel component will become less. In other words, the more 

 parallel the axis of a nniscle is to the axis of the bone which it is 

 to move, the weaker will be its action — the maximum value is 

 obtained when the line of action is at right angles to the bone. 



Pulleys. By means of a single fixed pulley the direction of a 

 force is altered, but not its magnitude. In the body, instead of 

 reducing friction by means of a rotating pulley the tendon operates 

 in a synovial sheath {q.v.). Good examples of the pulley may be 

 found in the cartilaginous loop (trochlea) for the tendon of the 

 superior oblique muscle on its way to the eyeball : and the 

 peroneus longus looping round the lateral malleolus on its passage 

 to the medial side of the foot. 



Opponents. All the muscles attached to levers in the body 

 are set in opposing pairs or antagonistic groups. As one group 

 contracts, the opposing group will relax to exactly the same 

 degree. The ulna, for instance, is pulled up towards the humerus 

 by the action of the Brachialis, and it is pulled downwards by 

 gravity and the action of the Triceps brachii nuiscle. Both 

 sets of muscles act together and harmoniously, so that in any 

 position of the ulna relative to the humerus, the opposing (nmscular 

 and gravity) forces exactly balance one another. That is, the 



