Gear tooth loadinq  The gear teeth were analyzed using a short cantilever beam formula from Roark. The three gear passes  were analyzed using the 5 g load case. The stress levels for the three passes are as follows:  First Pass = 17.0 MPa (2.47 ksi)  Second Pass = 17.4 MPa (2.52 ksi)  Third Pass = 11.4 MPa (1.66 ksi)  All gears are made of titanium, which has a yield strength of 869 MPa (126 ksi). The minimum margin of  safety is therefore 49.  Axial load reuuirements  Large axial loads are imparted into the actuator from two sources:  The defined acoustic load for one mirror is 6480 N  The angle of the actuator is 15 degrees  The load is shared between all 6 actuators 1. Launch Load:  6480 N /6/cos15 = 1118 N (251 Ib) x 1.4 = 1565 N (352 Ib).  2. Ground Test Load:  The maximum axial force on a single actuator during ground test is 378 N (85 Ib).  A factor of 5 is put on this value to protect against damage during ground test operations.  378 X 5 = 1890 N (425 Ib).  Since the ground test load is greater than the launch load, it was used for design calculations.  Lenath  The length of the actuator was calculated based on a nominal deployed actuator length of 138.8 mm. The  bipod assembly is required to retract 12.5 mm to the stowed position and extend 5.0 mm to the maximum  deployed position. The actuator is also required to translate the bipod at the same piston, which requires  additional length.  Launch Restraint  The original concept was to pull the mirrors down upon some mechanical hard stop until the motor stalls.  There are two reasons why this concept was discarded: 1. The large force exerted by the actuator would  require a huge increase in mass in order to withstand the stall forces. 2. When a stepper motor stalls, step  count is lost.  Another concept was to incorporate some extra feature in order to stop the motor when a certain preload  was reached. Several techniques were investigated and discarded including: load cell (adds extra wires,  mass, electronics); slip or magnetic clutch (lose step count, adds mass); visual indicator (impractical for all  but the outermost actuators). In all cases, the extra feature adds mass and complexity. Also, the hard stop  must be designed to be loaded to some factor above launch loads multiplied by some safety factor.  The current launch restraint design is such that motion is restrained in the plane of the mirror and allowed  in the direction perpendicular to the mirror. The actuators, therefore, constrain the motion of the mirror in  the perpendicular direction. The actuators must withstand axial loads in both tension and compression.  Power-train Summary  The stepper motor is integrated with a 60:l planetary gearhead to form what is called the gearmotor. The  output of the gearmotor drives a 3:l spur gear in the first gear pass. The drive torque then branches to  the fine stage and/or the coarse stage. The fine stage has a 1:l bevel gear for the second gear pass to  change the axis of rotation by 90 degrees to drive the fine stage flexure. The coarse stage has a tumbler  type coupling that has 324 degrees of backlash before driving an 8:l spur gear for the third gear pass to  the coarse drive shaft. The coarse drive shaft is an 8-mm-diameter ball screw with a 2-mm pitch.  247