302 APPLIED SCIENCE 



on the same figure show the simple dynamic frame without fric- 

 tion. The dynamic frame with friction is given in Fig. 2 1 a ; links 

 1 and 6 are determined by being made tangent to the friction 

 circles for joints ec, ea, fb, and fc. Links 2 and 5 must inter- 

 sect link 1 at the same point. If the wedge has plane joints, 

 the position of this point is indeterminate, but with fair fitting 

 it may be expected to lie at or near the centre of the joint. 

 The direction of the links 2 and 5 is fixed by the condition that 

 they shall make the stated angle with the joint, and their position 

 is without influence on the relative proportions of the links of the 

 frame. The intersection of links 6 and 5 gives the joint B; the 

 intersection of link 6 with 2 determines the joint C. Link 4 is 

 drawn making the stated angle with joint be, and by its intersec- 

 tion with 1 gives joint C r The frame is completed by drawing 

 the link 3 from C to C,. The element c has four joints, the 

 pressures on these joints are the stresses in the links 1, 4, 

 and 2, 6. The equal and opposite resultants of these two pairs 

 are met by the link 3, supplied in the original machine by the 

 rigidity of c. The machine will cease to work when the joint C, 

 falls inside the triangle CAB. The diagram suggests another 

 arrangement of the wedge machine in which the wedge might 

 be employed to open a pair of jaws corresponding to links 3 and 

 4, hinged at C r The analogy between the wedge machine and 

 the direct-acting engine is curious. The connecting rod acts 

 like a wedge, opening or closing the jaws, represented by the 

 crank and bed-plate. 



20. Spur Wheels. A simple complete machine can be made of 

 two spur-wheels b and c with bearings in the same element a, 

 and having a driving link e between a and &, and a resisting 

 link / between c and a. The simplest type of this machine is 

 shown in Fig. 22, and its dynamic frame is given in Fig. 22a; 

 the frame is drawn as follows : Links 1 and 6 are tangent to 

 the friction circles for elements e and e. Link 5 passes through 

 the pitch-point of the spur-wheels, and makes the stated angle 

 with the surface of the teeth ; in other words, it makes an angle 

 equal to <j) with the normal, which is called by RANKINE the line 

 of connection. <j> here as elsewhere signifies the angle whose 

 tangent is /A, the coefficient of friction. The intersection of 5 

 with 1 and 6 gives the joints B and C ; from B and C links 2 



