Before this week, I have been focusing on modelling compliances and geometric error motions to arrive at a design that could deliver the desired level of spatial precision. This past week, I focused on verifying that the component sizes dictated by stiffness requirements would provide adequate factors of safety in terms of strength and stability (i.e. not buckling).
I evaluated each structural components and joint for the various loads it experiences and considered all the failure modes I could think of. As expected, due to wood’s high stiffness-to-strength ratio (compared to, say, steel), the sizes dictated by my error budgeting resulted in large factors of safety in the 10’s for most of my wooden components. The spreadsheet I developed for these analyses can be accessed here. The most critical area I have identified as needing further attention are the steel L-brackets connecting each end of the desktop to the sliders.
One of the things I discussed with Prof. Slocum last week was the planned use of angle brackets to attach my desktop to the sliders. He pointed out that the thin (12-gauge sheet steel) leg of the angle bracket would have very low stiffness and load capacity when cantilevered like that. However, in my use case, the desktop bridges two of these brackets and behaves like a quasi-pin-ended beam. This minimizes the moment loads transmitted to the cantilevered legs of the brackets. Additionally, the attachment point to the desktop is just 25 mm away from the root of the cantilever. The conclusion of that discussion was that it will be okay in bending. This is true of both stiffness (error budget) and strength (see detailed engineering spreadsheet) requirements.
However, my detailed analysis this week revealed that the angle brackets don’t have enough load capacity against torsional loading resulting from objects or body parts placed on the desktop offset from the plane passing through the two boxways. The long, thin, rectangular cross section of the framing bracket I was planning to use is an extremely inefficient way to resist torsional loads. I was able to get away with using it from a stiffness perspective but not from a load capacity perspective. My analysis suggests that the bracket would yield at the corners — an unacceptable outcome.
I am considering a couple of new designs for the bracket, one of which could be easily fabricated by cutting and bending rectangular steel tubing. Using a hollow section would improve torsional load capacity dramatically (roughly proportional to the area enclosed by the centerline of the wall) and also bring about improvements in bending strength and stiffness. An alternative I am considering is a custom angle bracket with two parallel legs projecting out from the slider. These legs would slide into notches cut into the top and bottom of my desktop and be secured with bolts passing through the assembly. This design is attractive as it exploits sandwich theory and could give a cosmetically superior result with the use of countersunk fasteners.