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,