RELAY AliMATURK HIOHOUND ANALYSIS 191 



5. Biasing Forces. 



Fi should be kept as high as practicable. 



For proper energy loss during impacts, the motion between impacts 

 must occur outside the region of the compression, i.e., the armature 

 and stop must separate. Therefore, because all practical stops have a 

 finite stiffness, the biasing forces (Fi , F2 , etc.) should produce a static 

 deflection less than say, arbitrarily, 5 per cent of the maximum expected 

 reboiuid amplitude. 



6. Design Parameters for Two-Degree-of -Freedom Systems. 



As clearly indicated in Figs. 5 to 10 for the practical range of coef- 

 ficients of restitution, most consistently good results are obtained with a 

 coupling factor Mio = tV to |. This factor is most easily adjusted by 

 correct placement of the front stop. 



For the above range of il/12 the force ratio F2/F1 should be such as to 

 make the product 



P12 ^ > 4 M12 = i 



> 3 ilf 12 = i 



> 3 Mn = 



1 



(Note: For a rectangular armature structure with the stops placed at 

 its edges M12 = I, Pn = h and force ratios in the neighborhood of 8 are 

 desirable.) 



X. ACKNOWLEDGMENT 



The analytical treatment presented in this paper contains contri- 

 butions by E. L. Norton, R. L. Peek, Jr., and the wTiter. 



Appendix I 



DERIVATION OF BASIC EQUATIONS OF MOTION THREE-DEGREE-OF-FREEDOM 

 SYSTEM 



(1) Free Interval 



The motion of the armature will be described by the displacement at 

 the stop points, Xi , X2 , .T3 . Let m be the mass and R the radius of gyra- 

 tion of the armature about the center of gravity. The latter is located 

 by the dimensions fiK, iiR, and ^R relative to the stop points (Fig. 3). 



