Where, Ld is the length of the strut and Od is the angle of the strut at position Xd, (the
location from which the device is self-deployable)
For any layer 'j', where j = 1 to N, numbered from the layer farthest from the fixed
link to the layer closest to the fixed link and at any instant Xi, minimum stiffness of the
spring (Kj) can be determined from
(2Kj ((Lmax- Li) + dmin) -2Wts cos (90- 0)) cos i = (.5C+j) Ff
(.5C+ j)Ff + 2W, cos(90 )cos,
Kj = (2.15)
2((Lmax L, ) + dmn )cos 0,
Kj is determined for every position from Xd to LN1 for small position intervals,
where LN1 is the length of a single layer. The maximum value of Kj is taken to be the
minimum required stiffness for that particular layer. Hence, the minimum required
stiffness and deflection of the springs for the layer 'j' are determined. The Matlab
program "PROG1T" as shown in the appendix A, is used to perform this calculation.
2.4.2 Instantaneous Time, Velocity and Acceleration with Respect to Position
The minimum required stiffness and the minimum required deflection of the
springs are known from equations (2.14) and (2.15). In any layer ('j'), for any values of
stiffness and deflection of springs above the minimum required values, the instantaneous
time, velocity and acceleration with respect to position are calculated. The total time
taken to deploy the layer is also determined. From the stages of deployment shown in
Figure 2-6 to Figure 2-10, it can be concluded that the time taken to deploy the total
structure is twice the time taken to deploy any one side of the structure as at each stage of
deployment, a layer on one side and the corresponding layer on the opposite side are
deployed simultaneously. Let X, V, A, t and Av be the values of displacement, velocity,