the mast is self deployable (Zd). If this condition is not satisfied the springs will not be
able to apply sufficient force in the z direction towards the end of deployment to fully
deploy the mast. Hence the deflection (dmin) of the spring when the mast is fully
deployed (0 = 450) can be obtained from,
Kdmin cos45 > K ((Lmax Ld) +dmin) cos d
(Lmax Ld )COS 0d
dmin > max c (3.13)
cos45 -cos d
Where, Ld is the length of the strut and 0d is angle of the springs at position Zd (the
location from which the device is self-deployable).
For any level 'j', where j = 1 to N; numbered from the level farthest from the fixed link to
the level closest to the fixed link, where Wts is the weight of the top member
At any instant Zi the minimum stiffness of the spring (Kj) can be determined from,
6Kj ((Lmax- Li) +dmin) cosOd = 3Wp (j) + 6Ws (j-1) +6Wts cos (90-0d) cos0,
3W(j) +6W,(j-1) +6W, cos(90-0d)cosO,
Kj = (3.14)
6(((Lmax L) + dm) cos d
Kj is determined for every position from Zd to H1 for small position intervals, where
H1 is the height of a single level. The maximum value of Kj is taken to be the minimum
required stiffness for that particular level. Hence, the minimum required stiffness and
deflection of the springs for the level 'j' are determined. The Matlab program
"PROG1M" as shown in the appendix A, is used to perform this calculation.
3.4.2 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 (3.13) and (3.14). In any level ('j'), for any values of
stiffness and deflection of springs above the minimum required values, the instantaneous