IS'.) 5.] 1 lie Kinematics of Machines. 171 



although the relative motion of the four links will in all cases remain 

 unaltered, the absolute movement, or movement relatively to the 

 user of the machine, will in general be different for each fixing, and 

 constitute a new machine movement. Changing the fixed or frame 

 link is called the "inversion of the chain." 



The author makes use of the term " primary pieces," originally 

 suggested by Rankine for those links which are in sequence with 

 and directly connected to the frame link, and shows that if, after 

 inversion, the new primary pieces have the same kind of motions as 

 the previous primary pieces had, the consequent machine movement 

 is not a new one, but a repetition of a previous one. 



and r ~J only can four different 

 yC Sy 



machine movements be obtained by inversion. From the others 3, 2, 

 or only 1 can be derived. 



They are distinguished from one another in the formula by using 

 a thick line for the frame link. Thus 



signifies a machine movement like that employed in the 

 crank and connecting-rod engine. 



is exemplified in the oscillating engine much used in paddle- 

 wheel steamers. 



is found in Stannab's pendulum pump, and 



is the movement adopted by Rigg in the design of his high 

 speed engine. The intimacy of the relation of this engine 

 to the preceding ones is here for the first time indicated. 



In all, thirty-two and only thirty-two distinct machine movements 

 can be derived from the fourteen previously enumerated mechanisms 

 by inversion. 



It is shown that Reuleaux's principle of inversion can be applied 

 with more advantage and consistency if a machine movement is 

 analysed into its component motions than if a machine is analysed 

 into its component pairs, and the notation lends itself to a very clear 

 exhibition of the eflect of inversion. 



The author next discusses the relation of cams and spur-wheel 

 mechanisms to the foregoing kinematic chains, showing that they 

 are the result of the suppression of one of the previous four links and 

 the amalgamation of the two adjoining simple motions into one more 

 complex. A comparison is also made with belt gearing and expres- 

 sive formulas suggested. 



The author tben passes to the consideration of machines the parts 

 of which do not move parallel to one plane. 



