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)