Henry Gray (1825–1861). Anatomy of the Human Body. 1918.  
will find that muscle pull can be resolved into two components, a turning component and a friction or pressure component as shown in Fig. 369. 
 FIG. 369– No caption. (See enlarged image)

D F = the fixed bone from which the muscle takes its origin. 
D K = the movable bone. 
O I = a line from the middle of origin to the middle of insertion. 
I M = size and direction of the muscle pull. 
If the parallelogram is constructed with I t and M b ⊥ to D K, then I t = the turning component and I b = the component which acts against the joint. 
The size of the two components depends upon the insertion angle φ. The smaller this angle the smaller the turning component, and the nearer this angle φ is to 90° the larger the turning component. 
I t = I M x sin φ 
I b = I M x cos φ 
If φ = 90° cos φ = 0, sine φ = 1 hence I b = 0 and I t = I m 
If φ = 0° cos φ = 1, sine φ = 0 hence I b = 1 and I t = 0 
With movements of the bone D K the angle of insertion is continually changing, and hence the two components are changing in value. 
 FIG. 370– No caption. (See enlarged image)

If, for example, the distance from origin 0 to the joint D is greater than from D to I, as in the Brachialis or Biceps muscles, the turning component increases until the insertion angle φ = 90°, which is the optimum angle for muscle action, while the pressure component gradually decreases. If the movement continues beyond


