Loads from this environment were generated from a finite element random vibration model using Finite  Element Modeling And Postprocessing (FEMAP) as the pre and post processor and MSC NASA Structural  Analysis (NASTRAN) as the solver. These loads were applied to the various parts as appropriate to show  positive margins using factors of safety of 2.0 on ultimate and 1.5 on yield strength. Overall, the stresses  were low enough from the random vibration environment such that fatigue analysis was not necessary.  In both the R&R and hinge mechanisms, the thermal environment needed to be considered. Due to the  coefficient of thermal expansion mismatches between parts, the mechanism may bind at the temperature  extremes if enough dimensional tolerance is not accounted for in the design. The extreme hot and cold  environment of 61°C to -51°C was evaluated on all of the moving parts. The analysis was also done by  assuming the worst case tolerance stack that would result in the tightest fit at the installation temperature  of 22°C. The analysis results showed the critical case is the cold environment and a gap of 7.6 µm (0.0003  in) between the hinge pin and the hinge bracket.  The critical analyses for these mechanisms, kinematic and dynamic analysis, were performed to ensure  the mechanisms would have enough torque and force to release the arrays and deploy them at the  appropriate angle. NASA-STD-5017 [8] was used as a guide to perform the analysis and calculate the  margins.  The kinematics and dynamics of rotating the arrays to the deployed state via the preloaded SMAs formed  the main analysis for the hinge mechanism. This analysis considered both design criteria of (i) sufficient  torque to open the SA and (ii) minor impact force as to not damage the solar cells when the array deployed  to the open configuration and contacted the hard stops. This was done by hand sketching free-body  diagrams and developing the equations of motion. The free-body diagram listed the driving forces (the  torque supplied by the SMA) and the resistive forces and torques (friction from the bushings to the hinge  pin, friction from the latch hook, and the inertia of the SA that is needed to be deployed). The friction from  the latch hook was difficult to quantify since it is a unique design and required building and testing hardware.  Early attempts to approximate it did not align well with the test data. The bushing friction was easier to  approximate since it is a cylinder on a pin and the manufacturer’s suggested friction coefficients were used  for estimating friction. The normal force on the bushings was conservative because it used the weight of  the array from 1g of acceleration even though the deployment occurs in orbit. The inertia resistive torque  was approximated by using the equation of motion, the known final deployment angle of 135°, and  assuming a reasonable deployment time of 1.0 second (based on test observations). The equation of  motion is a 1 degree of freedom rotation and derived using Eqs. 1-3. The torque supplied from the SMA  was also difficult to approximate due to the hinge mechanism’s unique springs. This also required building  and testing the hardware. These values were then entered into the torque margin calculation from NASASTD-5017 [8] with appropriate factors for whether it was an analysis or test value.  Angular acceleration IT=α (1)  Angular velocity  tαωω+=0(2)  Angular displacement 2 2 021 21tITt t→ + =α ω θ (3)  where:  T = SA inertia resistive torque, I = SA mass moment of inertia,0ω= initial angular velocity is 0,  t= time  The R&R required analysis of the mechanisms to ensure the two-stage concept would release the SAs.  Starting with the first stage, the linear actuator, two aspects of the design were considered. These were the  pin-puller activation force and the stroke margin. For the activation force, the linear actuator needed to pull  the pin to disengage the release plate. To do this, the SMA linear actuator needed to overcome the pinching  friction force that came from the 2nd stage compression springs. An analytical estimate was originally done  based on the friction coefficient and geometry, however this proved to be inaccurate. Once the hardware  NASA/CP—2018-219887 384