296 APPLIED SCIENCE 



friction is shown in Fig. 13a. Links 1 and 4 are drawn tangent to 

 the friction circles, and link 3 is drawn from their intersection 

 A, making the stated angle with the plane joint ab. The bar 2 

 may be drawn anywhere, but is conveniently shown parallel 

 to the joint ab. When link 1 coincides with link 3 or makes a 

 greater angle with the joint ab than link 3 does, the mechanism 

 will not work. 



16. IJie Hanging Pulley. The hanging pulley becomes a 

 complete simple machine, when the driving element and resist- 

 ing element are attached to a common element, as shown in 

 Fig. 14 ; b is the fixed element, e the rope by which the effort is 

 exerted, a the pulley, / the element on which useful work is 

 done. Links 1 and 4 are drawn for the dynamic frame in two 

 parts as shown ; the moment of the couple dividing the parts 

 being that required to bend and unbend the rope, and its force 

 the force exerted on the rope. The pulley will take up a posi- 

 tion in which the link 3 drawn tangent to its two friction circles 

 cuts the intersection of 1 and 4 at A. 



It is curious to observe that while Professor REULEAUX has 

 very properly rejected the lever, inclined plane, hanging pulley, 

 and wheel and axle, as elements of kinematic analysis, neverthe- 

 less these so-called mechanical powers do furnish the character- 

 istic features of four simple machines of class 2 in which the 

 number of elements is restricted to four. We shall find that 

 the wedge is a characteristic feature in a simple machine with 

 six dynamic links of class 1. These considerations show that 

 dynamical and not kinematical reasoning guided the mecha- 

 nicians who selected the so-called ' powers.' 



17. Example of a complete Machine having a Dynamic Frame 

 of Six Links. A steam-engine with an oscillating cylinder, 

 steam piston and piston rod to represent element e, and a pump 

 to represent element /, as sketched in Fig. 15, affords an 

 example closely approximating to a simple machine of class 1 ; 

 the typical dynamic frame of this engine has already been shown 

 in Fig. 6, and is here repeated with the slight variation that the 

 pins are supposed to be fastened to 6 and d instead of e and /. 

 It must be observed that the stress cannot be axial either in the 

 driving or resisting elements ; indeed, these parts are not true 

 elements, for there is a joint between two elements in each of 



