76 



THE HUMAN MOTOR 



B 



55. (5) The Wedge. Ajwedge is a triangular prism which is 

 used to separate two parts of a body 

 A a a from each other ; for example, to 



split logs of wood. The power P is 

 applied to the head AB, whilst the 

 point of the wedge C is driven into the 

 cleft that it is desired to enlarge. 



Let it be supposed that it is desired 

 to move a part M from a fixed body, F, 

 by driving in the wedge. When the 

 latter advances from A to A', the resist- 

 ing surface of the part M has moved 

 through IB'. The power is exerted 

 perpendicularly to AB and the resist- 

 "Fio W- ance to BC ; therefore the former has 



advanced the distance CC' = aa', and 



the^latter the distance II' = CC'. The principle of virtual work 

 gives 



P X CC' - Q X CC' or ? = (fig. 93). 



\J V~/V-/ 



In drawingTthe^parallel CD', it is easy to see that the right 

 angled triangles, CC"D' and CC'D are similar ; whence 



CC" _ CD' 

 CC' CD ' 



And in the similar triangles CDD' and A'DB', 

 CD' _ A'B' _ AB. 

 CD : ~A'D = ~AC* 



consequently : P __ AB 



~~ AC' 



The power is to the resistance as the head of the wedge is to its 

 side. Also 



AB 

 AC 



AB 2Aa .,.,..... ^ 



r~ =- -r- ' it the triangle or the prism is isosceles ; 



but 



therefore 



Aa 



AB n P 



^P = 2 tang a and ^ = 2 tang a. 



The smaller the angle a the more efficacious the wedge. 



In most of the instruments, based on the wedge, this angle is 

 made smaller the sharper the cutting edge wanted (such as the 

 knife, the razor, the axe, etc.), and the prism is isosceles. 



