2.4.1 Minimum Stiffness and Deflection of the Spring
The springs closest to the fixed link have the highest stiffness value while the
springs farthest from the fixed link have the least stiffness value. The springs closest to
the fixed link have to move the maximum mass against friction hence they have the
highest stiffness compared to the other layers (Figure2-6 to Figure2-10). For any layer, at
any instant of position Xi
Working deflection of the strut from its maximum length dw = (Lmax-Li) (2.11)
(H
Angle of Strut i = (tan X ) (2.12)
The minimum deflection of spring dmin, is not taken into account in equation (2.11).
Hence at any instant of position Xi, the deflection of spring (di) is
di = dw + dmin (2.13)
The force applied by the springs in the x direction at the point from which the
structure is self deployable (Xd) must be sufficient in magnitude to overcome friction
between the vertical members and ground. Also, for successful deployment, the force at
the deployed state should be no less than the x direction force at position Xd. If this
condition is not satisfied the springs will not be able to apply sufficient force in the x
direction towards the end of deployment to fully deploy the structure. Hence the
deflection (dmin) of the spring when the structure is fully deployed (0 = 450) can be
obtained from
K dmin cos45 >K ((Lmax- Ld) + dmin) cos0d
(Lm x Ld()COSOd
dmin (> L d (2.14)
cos 45 cos 0d