(2) 
Suppose an automatic stereoplotting machine requires that & 
mass M kilograms be positioned on a track in a horizontal plane 
defined by co-ordinates x and y as in Figure 1. In a projection 
plotter as automated by Hobrough's method”, the mass M is that of 
a scanning head carrying en oscilloscope tube. In an analytical 
plotter of the Helava typel working in a contouring mode, the mass M 
is that of the frame that moves the pair of photographs relative to 
the scanning beams. Alternatively the scanning beams may be moved. 
The mass M is then the mass of the associated equipment. Suppose 
the propelling forces F, and F, are supplied by the torques of 
electric servomotors through suitable gear trains. To follow the 
topographical tracks characteristic of maps, the mass M must be 
driven along curved paths such as the idealized circular turn of 
radius Tr metres shown in Figure l. Consider the mass passing 
through the point p at the centre of the turn. At this point it 
will have some linear velocity v metres/second tangent to the track, 
and a linear acceleration a normal to the track that can be expressed 
as, 
2 
v 
8 = ___ metres/ (second)? , (1) 
r 
where r is the radius of the turn. For the point p in Figure 1, 
the acceleration a would be produced entirely by the x -propelling 
force F, that is determined by the associated servomotor torque T, 
In practical mapping there is some turn of minimum radius that the mass 
must execute to obtain the desired topographic resolution. In order to 
maximize the speed of plotting it is desirable that the linear velocity 
v along the track be as large as possible. 
It is of great interest to establish an upper bound for the 
velocity v that can be achieved when the resolution radius r is 
fixed and a good electric servomotor is used. 
Any servomotor can deliver some maximum torque T, newton- 
metres* on its shaft, By its nature the rotating parts of the motor 
have some rotary inertia J, kilogram -(metres)^ . If the torque 
necessary to drive the rotational friction of the motor and the sliding 
friction of the mass M is neglected, it is readily shown that the 
maximum linear acceleration a obtainable with the motor is, 
Pon “ri 
This acceleration is obtained when the ratio of translational motion 
of the mass M to the rotational motion of the motor shaft is adjusted 
a metres/ (second)? (2) 
by means of a gear train until the equivalent mass of the rotating parts 
of the motor when reflected through the gear train is equal to the mass 
M. Equation 2 assumes that the gear train has negligible inertia. 
  
* ] newton-metre = 1 x 103 ounce-inches 
7 .08