Errors in Gimbal Axes 
by 
J. HOTHMER 
International Training Centre for Aerial Survey, Delft. 
When adjusting instruments it is sometimes doubtful whether the residual projection 
«en still be reduced and by what means. The residual projection errors may be due 
ii urces of errors. As in all high precision instruments one or more gimbal axes 
Jl mr the accuracy of projection, it seems useful to derive some formulas for 
EY the gimbal axis and to demonstrate their effect on the projection. 
e E ublieation has not been written with the intention to encourage the user to 
n NT axes by himself, but only to help him analyzing residual projection errors. 
di : an adjustment is unavoidable, yet if the adjustment instruction book of the 
i indicates that it can not be carried out by the user himself, then it should be left 
m a competent specialist of the factory. If the projection errors (as caused by 
i : the different gimbal axes) do not exceed 0,01 mm, we get from the following 
ms " n the requirement that the various errors e, in gimbal axes must be adjusted 
cu mean square error of 3 u. If this precision can be obtained, then the adjustment 
ih be made by a specialist of the 
qun 
eo 
fury only. Zz 
| Derivation of a formula for the 
projection errors. 
  
  
  
(is the center of the gimbal axis ^ D 
sem The secondary axis has an " p 
wentricity e,. The projection ray B,B ; o^ 
ifersects the xy-plane of the gimbal ce" es U- > 
ais system in point B, off the pri- t ‘ A. > 
nary rotation axis for the eccentricity ET IMG Y |^. ix 
«ad off the secondary rotation axis OXAS a 
fir the eccentricity e.. 
Fig. 1 
  
  
Fig. 2 represents a cross section 
parallel to the zy-plane, showing the 
situation after a rotation « around 
the primary axis. The projection ray 
occupies a position BB. Fis. 3 do- 
monstrates the si- 
S. S 7^ tuation after a 
v. rotation f around 
NE | era x 
the secondary 
axis. The projec- 
tion ray occupies 
a position B,"B^. 
We read from 
fig. 2 and 3 
Ay = GR = 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
   
  
    
   
  
  
  
  
  
  
  
  
  
   
   
   
  
  
  
  
  
  
  
   
  
AI Kae