VERNIER RESOLVER 1499 



are readily obtained by applying existing techniques to the vernier re- 

 solver. 



ACKNOWLEDGEMENT 



The development of the vernier resolver was undertaken under the 

 sponsorship of the Wright Air Development Center. The work was en- 

 couraged and furthered by J. C. Lozier of Bell Telephone Laboratories. 

 Valuable design contributions were made by J. Glass of Clifton Precision 

 Products Co. All testing and evaluating of test results was done by T. W. 

 Wakai of Bell Telephone Laboratories. 



APPENDIX 



Sy7nbols 



E Amplitude of induced voltage 



p Number of pole-shoes 



n Number of rotor teeth 



de Electrical rotor angle, equal to its geometrical angular position mul- 

 tiplied by ri 



q p divided by largest integral factor common to n and p 



n' n divided by the same factor 



V Pole-shoe number running from to (p — 1) 



m Order of Fourier component representing the pole-shoe flux as a 

 function of the electrical rotor angle, de 



ae Electrical angle between adjoining pole-shoes, equal to the geometri- 

 cal angle multiplied by n 



k A number equal to zero or to any positive integer. 



In accordance with eciuations (7) and (8) the voltage induced in the 



sine-winding coil on the i^th pole-shoe by the mth flux harmonic is: 



Esm, = Co[Am COS m (de — Vae) t siu (uCX,)]. (13) 



After trigonometric transformation: 



Esm,> = hAmtco [sin {mde — (ni —I) vae) 



(14) 

 + sin (-171 6 e -\- (m ^ I) vae)] . 



The voltage, Esm , induced in the sine winding is obtained by summing 

 the expression of (14) over all values of v. Since (pa^) is a multiple of 27r 

 the summing of all sine terms from 1^ = to 1/= {p — 1) results in zero 

 unless the angle (m ± 1) a? is an integral multiple, k, of 2ir. This condi- 

 tion is spelled out in the following equation: 



