(7) 
Kp of equation (12) equal to Kg.Kg.S in equation (16). The torques 
specified by equation (16) are automatically developed by the control 
system of Figure 2. 
Let us now determine the error nulling accelerations ay , 
end a as shown in Figure 3(c) that are produced by the control ien 
of Figure 2. Suppose the gear trains connecting the servomotors to the 
mass M associated with the tracking point are designed for the éondition 
of maximum available acceleration as discussed in Section 2. Then the 
relation for example, between motor torque T, and linear acceleration 
ay is given from equation (2) as, 
T. 2 
2L metres/(second)^, (17) 
ax old 
Using equations (16) and (17) we may therefore express the error nulling 
accelerations produced by the system of Figure 2 as, 
  
  
KpeKÇ.S. AD.cos6 
ay = 
2 Jd M 
5 metres/(second)^. (18) 
- KpKç.S-AD.sine — } 
> 
2 JM ) 
Since the resultant acceleration a normal to the contour in 
Figure 3(c) is, 
a = a,” + ay metres/(second)^, (19) 
equations (18) and (19) give this resultant acceleration as, 
Ko. K5.S 
z Ego s «AD--.K.AD metres/(second)^, (20) 
2 [J,M 
where K = KpeKgeS (21) 
7717 
Equation (20) is the key to understanding certain basic problems 
of system performance in automatic mapping machines. It represents a 
simplified description of the dynamic behaviour of the system shown in 
Figure 2. 
Equation (20) simply says that if, for any reason, the tracking 
point gets off the contour by a distance AD and hence off the topo- 
graphic surface by a height AZ , the feedback control system develops