3.4.3 Alteration of the Stiffness of the Springs

 From equation (3.20) the time taken to deploy the various levels is determined. For

reasons due to uniformity and better performance (more importantly in space

applications) the stiffness of the springs should be designed in such a way that the time

taken to fully deploy any level in the structure remains a constant. This is an

approximation method and the solution obtained is not accurate.

 Let the stiffness of the springs for any level be Kj. During the deployment of a level

the time taken (ti) over any position interval Zi to Zi+1 is known. For some position

interval Zi to Zi+l the time taken (ti) would be the least when compared to the time taken

by the level to deploy through any other position interval. Let this value of time be

assigned to the variable LT. Then, from equation (3.18)

Time taken for the mast to deploy from

 Zo to Z1 = LT lo = ti

 Z1 to Z2 = LT 112 = t2

 Z2 to Z3 = LT 123 = t3

 Zn-1 to Zn = LT l(n-1)n = tn (3.22)

From equation (3.22),

 LT (loi+ 112 + 123 + 134 + ............... .. + l(n-1)n)= TT (3.23)

 LT' (loi+ 112 + 123 + 134 +................... + l(n-)n) = GT (3.24)

Where, GT is the new 'time' within which the level should completely deploy and LT' is

the new 'least time' for some position interval Zi to Zi+1. In both equations (3.23) and

(3.24), (lo + 112 + 123 +134 +................... + l(n-1)n) remain the same since the time taken

for any two corresponding position interval in two different levels is proportional. The