Help with lattice hinge calculations

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Discussion Overview

The discussion revolves around calculations related to lattice hinge mechanics, specifically focusing on the relationship between the number of links (n), the bend angle, and the parameters Theta and t. Participants are exploring the implications of these parameters on the hinge's behavior.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • Joe questions the claim that n is greater than or equal to 23 when Theta is 90 degrees and t is 3, noting discrepancies in his calculations regarding the argument of arccosine.
  • Another participant calculates that the bend angle from one link to the next is 0.2/3, leading to a total number of links of approximately 23.56.
  • Joe seeks clarification on the calculation of 0.2/3, assuming it relates to the thickness and a parameter k_laser.
  • A later reply explains that the 0.2 represents the arc through which the hinge will sweep as it transitions from a flat position to a circular one.

Areas of Agreement / Disagreement

Participants appear to have differing interpretations of the calculations and parameters involved, indicating that the discussion remains unresolved with multiple competing views on the hinge calculations.

Contextual Notes

There are assumptions regarding the definitions of parameters such as k_laser and thickness that are not fully clarified, which may affect the calculations presented.

jamesson
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Can anyone confirm the claim on this site that n is greater or equal to 23 when Theta is 90 degrees and t is 3? My calculations indicate that the argument of arccosine in the numerator has to be very close to 1, but the numerator of the argument (k_laset+t) is 3.1 whereas the denominator (2*sqrt(t^2/2)) is approximately 4.242.

Thanks

Joe
 
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These are all small angles. The bend angle (in radians) from one link to the next will be 0.2/3. This is also the angle subtended by that link on the circle. The number of links is then pi/2 divided by that angle which is 23.56 by my calculation.
 
Ok, could you please explain how you arrived at that, especially 0.2/3?

EDIT: I'm assuming 0.2=2*k_laser, and 3 is thickness?
 
That is the arc thru which the "hinge" will sweep to go from flat to circle.
 

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