THE MACHINE WITH INPUT 

 and join them into a single long chain 



4/8 



input 



etc., 



so that A affects B, B affects C, and so on, by Z: 



1 2 



Z: I 



« ^ r 



If the input to A is kept at a, what happens to the states down the chain ? 

 Ex. 8: (Continued.) What happens if the input is now changed for one step 

 to ^ and then returned to a, where it is held? 



4/8. Coupling with feedback. In the previous section, P was 

 coupled to R so that P's changes affected, or determined in some 

 way, what 7?'s changes would be, but P's changes did not depend 

 on what state R was at. Two machines can, however, be coupled 

 so that each affects the other. 



For this to be possible, each must have an input, i.e. parameters. 

 P had no parameters, so this double coupling cannot be made 

 directly on the machines of the previous section. Suppose, then, 

 that we are going to couple R (as before) to S, given below: 



S could be coupled to affect Rhy Y (if R's parameter is «) : 



f state of 5": , e f 



Y: 



\value of a: ''^ 3 1 



and R to affect S by X (if 5"s parameter is ^): 



[state of R: .a b c d 

 ■ lvalue of ^: ^ 1 1 2 



To trace the changes that this new whole machine (call it T) will 

 undergo, suppose it starts at the vector state {a,e). By Y and X, 

 the transformations to be used at the first step are iRj and 5*3. They, 

 acting on a and e respectively, will give d and/; so the new state of 

 the whole machine is {d,f). The next two transformations will be 

 Ri and 5*2, and the next state therefore {b,f); and so on. 



Ex. 1 : Construct 7"s kinematic graph. 



Ex. 2 : Couple S and R in some other way. 



Ex. 3: Couple S and R so that 5* affects R but R does not affect S. 

 Consider the effect in Xof putting all the values of ^ the same.) 



51 



(Hint: 



