depending on the displacement. The Matlab program "PROG4T" as shown in the

appendix A, is used to perform these calculations.

2.4.5 Velocity and Acceleration with Respect to Position when the Structure is
 Deployed in a Single Stage

 The instantaneous time with respect to position is the same for all the layers after

the stiffness of the spring is determined as in 2.43. The total time taken to deploy the

structure in one single stage is equal to the time taken to deploy a single layer, when the

structure undergoes stage wise deployment. The velocity and acceleration of the last

vertical member on any side is,

 N(X, )- N(X, )
 Velocity VN N= ) (2.34)
 t


 Acceleration AN VN VN (2.35)
 t

Where, Xn, Xn-1 and tn are determined from equations (2.19) and (2.20). From equations

(2.34) and (2.35) it is evident that the velocity and acceleration of the last vertical

member on any side is N times the velocity and acceleration when the structure is

deployed stage wise. The Matlab program "PROG5T" as shown in the appendix A, is

used to perform these calculations

2.4.6 Stiffness and Minimum Deflection of the Spring when an External Load is
 Applied

 Let Fapx be the external force applied in the negative x direction when the structure

is fully deployed, hence when fully deployed the springs should apply a counter active

force in the x direction equivalent to Fapx to prevent any change in the shape of the

structure.

Let, F'apx = 2Kj (dmin) cos45 (2.36)