2.4.2 Instantaneous Time, Velocity and Acceleration with Respect to
 P o sitio n .............................................................................. 2 0
 2.4.3 Alteration of the Stiffness of the Springs ....................................... 22
 2.4.4 Forces A cting on the H inge................................................... ................ ..25
 2.4.5 Velocity and Acceleration with Respect to Position when the
 Structure is Deployed in a Single Stage ............ .. ........................26
 2.4.6 Stiffness and Minimum Deflection of the Spring when an External
 L oad is A applied .............................................................................. ..... 2 6
 2.5 N um erical E xam ple ........................................... .................. ............... 27

3 DESIGN OF A DEPLOYABLE CLOSED LOOP MAST ......................................35

 3 .1 D description of the M ast ......... ................. ........................................................35
 3.2 Stages of D eploym ent................................................. .............................. 36
 3 .2 .1 S ta g e 0 ......................................................................................3 6
 3 .2 .2 S tag e 1 ................................................................3 6
 3 .2 .3 S tag e 2 ................................................................3 7
 3.3 Principle of the Mechanism .............................. ... ........37
 3.4 D esign Problem Statem ent ....................................................................40
 3.4.1 Minimum Stiffness and Deflection of the Spring.................................... 41
 3.4.2 Instantaneous Time, Velocity and Acceleration with Respect to
 P o sition ................................................ ............... ............. ........... 42
 3.4.3 Alteration of the Stiffness of the Springs ....................................... ...... 45
 3.4.4 Forces Acting on the Hinge ............... ............ ..... ....................47
 3.4.5 Velocity and Acceleration with Respect to Position when the Mast
 is D employed in a Single Stage ............................................. ............... .... 48
 3.4.6 Stiffness and Minimum Deflection of the Spring when an External
 L oad is A applied .............................................................................. ..... 4 8
 3.5 N um erical E xam ple ........................................... .................. ............... 49

4 STIFFNESS COMPARISON OF MASTS ..................................... .................57

 4.1 Design Description of the M asts. ... ................................ ......... .. ............... 57
 4 .1 .1 M a st I ...............................................................5 7
 4 .1 .2 M a st II ...............................................................5 8
 4.1.3 Deployable Mast.................... .. ............................. 59
 4.2 Determination of Stiffness ............... ............... ................... 60
 4.3 AN SYS M odeling of the M asts................................ ......................... ........ 60
 4 .4 R e su lts...................................................................... 6 1

5 SUMMARY AND CONCLUSIONS......................................................................62

APPENDIX

A M A TLAB PRO GRAM S ................................................. ............................... 64

B FIGURES FROM ANSYS ANALYSIS ....................................... ............... 83