Kinematic Self-Replicating Machines
© 2004 Robert A. Freitas Jr. and Ralph C. Merkle. All Rights Reserved.
Robert A. Freitas Jr., Ralph C. Merkle, Kinematic Self-Replicating Machines, Landes Bioscience, Georgetown, TX, 2004.
B.6 Wall Stiffness During Internal Mechanical Activities
During manufacturing operations, various mechanical forces are generated inside the assembler and are ultimately transmitted to the walls, possibly producing unwanted wall deflections. Typical forces may include up to ~60 pN backpressure on the materials transport mechanisms, ~568 pN during each double-band stroke of the acoustic transducer (Section B.4.2), and up to ~17,740 pN for the most demanding possible mechanosynthetic operation which would involve the one-step mechanical decomposition of the acetylene triple carbon bond (a step not currently contemplated in any proposed mechanosynthetic sequence). Thus in the worst possible case, a mechanical point force of Fpoint ~ 17,740 pN applied to the center of the largest wall would produce the largest possible out-of-plane wall deflection. Given the high stiffness of diamond and a velocity of onset of the point force far below the speed of sound in diamond, the applied pressure may be crudely approximated as a uniform normal pressure on a clamped plate, of order ~Fpoint / Xext Yext ~ 7 atm (~2Pmax), yielding a very small out-of-plane deflection of dplate ~ 0.01 nm and a negligible in-plane wall stretch of dstretch = 0.005 nm. Applied point forces inside the molecular assembler will normally be 2 orders of magnitude smaller than this worst case condition.
Forced oscillations due to mechanical resonance with cyclically applied internal forces are highly unlikely because the assembler should have natural resonant frequencies of nresonance > 79 GHz (Section B.4.4.3) which are ~4 orders of magnitude above the driving frequency of nacoustic = 10 MHz, and also because the many mechanical structures attached to the inner surfaces of internal walls provide additional damping.
Last updated on 13 August 2005