188 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



freedom system until the next front impact. The requirement for this 

 group is that 



n > 2(1 + k) 



^ k(l - k) -{- Mi2(l + ky 



and the maximum rebound is given by 



2CFi = ilfi2 -(1 - ilfi2)[(l - k') + i¥i2(l + /v)'] (35) 



It is to be noted that in the upper part of Group 1 the ampHtude in- 

 creases with successive heel impacts. This can be explored through the 

 use of Equation (22). For simplicity of mapping, however, the hmit 

 given by Equation (35) has been extended back from the lower boundary 

 of Group 2 until it intersects the line marking the first rebound ampli- 

 tude of Group 1. 



In Figs. 5 to 10 the respective regions have been identified by means 

 of the symbols indicated below: 



E. Discussion of Rebound Charts 



Aside from quantitative data contained in Figs. 5 to 10, the following 

 general trends are of interest: 



For values of ilf 12 > j, and the values of k under consideration, most 

 of the useful range of Pnf involves critical phasing and the rebound 

 maxima are relatively high. 



For values of ^ < ilfi2 < l, consistently controllable rebound ampli- 

 tude may be obtained. 



For values of Mu < i rebound increases again and the structure 

 approaches the one-degree-of -freedom case. 



VII. ANALYSIS OF REBOUND PATTERNS — THREE-DEGREES-OF-FREEDOM 

 SYSTEM 



Rebound pattern analysis as in Parts V and VI has so far not been 

 performed for the three-degree-of -freedom system, partly because of 

 complexity, and partly because for the system of Fig. 3 friction at the 

 hinging stop will greatly influence the motion. 



