N = N i + {F * tan( /g52)}     (2)  The next logical question is, under what conditions will the bar seize and not be able to be pulled out of  the device as in Figure 6?  By substituting Equation (2) into Equation (1) and rearranging terms, an  expression for f, the required force to overcome fric tion in this system, can be determined.  f = /g80 Ni / {1 - /g80*tan(/g52)}     (3)  One can see that for the classical example, or when /g52=0o, the denominator goes to 1 and the familiar  equation, f = /g80 N, exists. This is because there is no component to cause compression in the MAC  member.  Also interestingly, when /g52=90 o, the denominator goes to - /g146, and thus f goes to zero. This is  because the MAC members are at their bottom-dead-center position, and any movement of the bar will  tend to bend, or raise, the MAC member up off of the bar with decreasing normal force. But for the seizing  condition, the additional factor – compared to the classical equation – in Equation (3) plays a part. If this “Slide Factor,” S, is defined as  S = 1 / {1 - /g80*tan(/g52)},     (4)  then S can be plotted for various values of /g80 and /g52, as shown in Figure 8.   0 10 20 30 40 50 60 70 80 890.10.40.71-6.00-4.00-2.000.002.004.006.008.0010.00Slide Factor, S MAC Angle (deg)Fric  CoeffSlide Factor  for Moving Bar in "Hard" Direction

0 10 20 30 40 50 60 70 80 890.10.40.710.000.200.400.600.801.00Slide Factor, S MAC Angle (deg)Fric  CoeffSlide Factor  for Moving Bar in "Easy" Direction

Figure 8.  Threshold Values for Seizing for Various Friction and MAC Angle Values  This is a useful format to determine when the bar will be seized and when it will be free to slide. As long  as S is positive, it means that a realistic value of f (f orce required to break free ) DOES exist to give the  bar the capability of breaking free from static friction; it does become more difficult as S approaches /g146. This describes the green region in Figure 5b. After the discontinuity, for higher values of /g80 and /g52, S  values flip their sign and become negative. What this means is that the only way to break free is to apply  a negative f, which means pushing it in the opposite direction.    For the opposite case of pushing the bar in the reverse, or “easy” direction, the same essential theory  holds true, except Equation (2) contains a negative sign since the friction resulting from the applied force  F tends to reduce  the normal, or compressive, force between the MAC and the bar. That also flips the  sign in Equation (3), and results in the S-values plotted on the right in Figure 8. By the same discussion  above, since ALL of the S-values for reasonable MAC angles and friction coefficient are positive (and < 1), it is proven that it is always easy (f is always < /g80*N) to push the bar into the device as in Figure 6.  Some Results – or, DOES it Work?  Several prototypes in various stages of this application were constructed in The Aerospace Corporation’s  Space Materials Laboratory (SML), an d experiments were compared to th eoretical analyses. The first  study used laboratory instrumentation to compare the axial and transverse deflections of the small nylon  machines with and without a matrix material surroundi ng them. Figure 9 illustrates that, much like  traditional composites, the matrix material has very little effect on the behavior of the bulk material.  202