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