68 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 



RATIO X,/Atf?o 



Fig. 27 — Relation between mechanical output and armature travel. 



tivity is attained if the lever arm is chosen to satisfy this condition, and 

 in this case Y c = Tl^max/4. 



For the case of a Hnear load, varying from F2 at .r = to zero at 

 X = X2 , the load is given by: 



F 



= 4-l)> 



where ih = X2/(A(Ro)- For the pull curve to be tangent to this load curve, 

 the values of both F and clF/dx given by this last equation and by (31) 

 must be equal at the point of tangency, Xi . These two conditions give 

 two expressions for the ratio F2/F0 . Equating these, there is obtained 

 the following equation for the point of tangency: 



Wi = 



2W2 - 1 



(36) 



The work done against the load is F2X2/2, and the ratio of this to TFmax 

 is therefore /'Vt2/(2A(RoFo). Substituting the expression for F2/F0 ob- 

 tained as described, and the expression for Ui given by (36), there is ob- 

 tained the following expression for the fraction of TTmax realized against 

 a linear load: 



Wn 



(3^1 + 1) ^ 

 4(wi + D' 



(37) 



