Safety Review

Since I am designing a desk that is meant to be operated by laypeople without specific training, so it is important to minimize personal injury hazards and making the device as robust to improper operation as possible. Natural selection has plenty of mechanisms through which to operate — no need for engineered products to create new ones.

Tipping

One of major risks associated with the desk is having it tip over due to a lateral load from a user leaning on the edge of the desktop (e.g., leaning in to check out a particularly interesting data point, perhaps). The strategy to address this risk is place the center of gravity and coefficient of friction between the adjustable standing desk and an existing table such that lateral loads would cause the desk to slide instead of tip. The tipping analysis can be found in the “tip vs. slide” sheet in this document. Using nominal values for these parameters, the desk will start sliding when subjected to a lateral load only 60% of that required to tip it over. This translates to a safety factor of 1.6, which doesn’t look like much for structural design, but is sufficient in this case because of the small number of input parameters (coefficient of friction, center of gravity) which are known with high certainty.

Loss-of-Power Events

Another risk is for the desktop to fall when power to the motors is unexpectedly lost. This idea was previously addressed in the concept generation phase where I did some analysis on the self-locking, leadscrew-free design (and ultimately rejected it in favor of a conventional leadscrew design). By using a relatively low-helix, single start, and sliding contact screw, I was able to make my drive system self-locking. Regardless of the loads placed on the desktop, it is impossible to back-drive the screws. The detent torque in the motors provide an additional factor of safety, but is ultimately not needed in this case.

Pinch Hazards

Having moving components in the desk means I also need to consider the presence of pinch points. The two critical pinch points are between the sides of the desktop and the exterior surface of the keeper rails, and between the bottom of the desktop and the cross ties. The clearance gap between desktop and column is approximately 2 mm. This comfortably protects against the ingress of objects above 2.5 mm in characteristic dimension. This is a IP3X rating!

The other pinch point between desktop and cross tie has a gap width that varies depending on where the desktop is within its range of motion. This does mean that bodily appendages can plausibly be trapped in this space. However, this risk is mitigated by the fact that this pinch point is obscured by the 250-mm overhang of the desktop. That is, in order to have a finger pinched within this gap, which occurs when the desktop is within 50 mm of the base, one would have to stick one’s arm below the desktop at a really awkward angle.

SNG 9: Foldable Umbrella

I own a foofoo non-circular umbrella from Senz. My defense for the foofoo-ness is that I got it as a gift through my frequent flyer program. But it does work quite well on two counts:

  1. It behaves like an airfoil whose geometry you can adjust by tilting the umbrella differently. This makes it a lot easier to hold on to in high winds
  2. The asymmetrical design is ergonomically sound. My view is that unless it is part of an umbrella hat, there aren’t many good functional reasons why umbrellas should be circular.

This week, I geek out on the folding mechanism in this umbrella. Each arm of the umbrella is made up of a series of pin-ended aluminum members (C-channel sections in pictures) joined in series. Each alternate member is then connected with a slender spring tempered wire. Basically, each section is part of a local 4-bar linkage.

Buckling

The interesting thing about this mechanism is that it exploits the buckling behavior of the spring tempered wires in its design. This marks a departure from the traditional “classroom” engineering approach where buckling is not considered until late in the design process when one verifies that the specified members are not going to buckle. This approach reminds me of a piece of MIT IP from Prof. Brian Wardle’s lab that I wrote about at work (as a technology licensing intern for the MIT TLO), where buckling is exploited to create 3D MEMS geometry using conventional 2D microfabrication workflows such as CMOS.

Bi-stable Mechanism

Back to the umbrella. In the folded configuration, the spring wires are in a relaxed state, free to rattle around in the pin-supports at their ends. In the fully open configuration, they are under tension — applying the preload to hold the mechanism in the open position and keep the fabric web taut. In between these two configurations, the wires experience compression loads large enough to cause them to buckle but not enough to cause them to yield. This allows them to act as compressive springs in this intermediate region. The result, then, is a bi-stable mechanism that stays fully open or fully closed, but is unstable in intermediate states. This is great design, and I believe not something every umbrella does! The stability of the 2 functionally relevant positions means that the latches and ball detents used to keep the umbrella open or closed actually experience very little load, allowing lighter and more easily actuated components to be used.

Variable Spring Rate

Another benefit of exploiting buckling is that you can get the spring wires to act as springs with different stiffnesses in tension vs. compression. When the umbrella is open, the wires are under axial tension with very high stiffness — great for standing up against wind loads and keeping the umbrella open. Conversely, when the mechanism is neither fully open nor fully closed, you want a spring that is strong enough to nudge it towards a stable conformation, but not one that would poke a user’s eye out. This is achieved by allowing the wires to enter the buckled state, which places them under pin-ended bending instead of axial compression — significantly reducing stiffness.  This is an excellent example of the use of self-help in mechanical design!

Buckling Direction

We have seen how buckling can be used to great effect, but it is fundamentally a phenomenon drive by instability. This makes the math a bit more complicated (i suspect this is why it isn’t classically popular in “school” engineering design) and means that it is not straightforward to predict the buckled shape of structural members. In an umbrella, this poses a number of risks, including the creation of unpredictable pinch points and inadvertent puncturing of the fabric web by a wire buckling in the wrong direction. The way the designers of this umbrella have dealt with this is by entrapping the spring wires within the adjacent channel at their midpoints using a tab. This biases the members and forces them to buckle in a predictable direction. Again, a nice touch. A minor drawback to this is that it sets up a sliding contact between the aluminum channel and the hardened steel wire in the middle of the umbrella-opening stroke, which is starting to create squeaking noises as repeated use starts to wear through the phosphate coating on the wires. On the bright side, that squeak was what prompted me to grease the contact points and, in the process, geek out about this mechanism!

Detailed Engineering and Component Sizing

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.

Slider Brackets

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.

MCM: Boxway Build 1

I had a couple of days of free time on my hands over spring break and decided to get a head start on my motion axis build. While much of the engineering design for the rest of my structure is yet to be nailed down, I have spent sufficient time tweaking my error budget and doing first-order analysis that I am confident that the preliminary component sizes I specified are at least in the ballpark — sufficiently good estimates for me to put in material orders.

I decided to build the structural members of my desk out of beech for its high stiffness-to-weight and strength-to-weight ratios. There’s also the high Janka hardness which makes it a better bearing material that resists denting under extreme load events. Finally, beech’s neutral grain appearance and favorable machining characteristics also make it a good fit for my purposes. The desktop will be made from a sheet of 18 mm Baltic birch plywood, which would give me a nice void-free edge without resorting to gluing on an edging strip. I probably could have saved  some money by using cheaper material, but I decided against doing that as the time I am spending on this desk already far outweighs material costs anyway…

To date, I have successfully glued up my boxways and waxed the internal bearing surfaces to minimize moisture absorption and provide a non-porous surface for further lubrication (I am planning to use a light PTFE-infused grease). Now that I am using solid lumber, I can build my boxways to size and plane or sand down my sliders to give the requisite clearance. This allows me to avoid shimming the glue joints with paper like I did for my linear axis demonstrator toy — I am convinced that reduces the strength of the glue joint.

Another lesson I learned from the previous build is to wax the internal surfaces before gluing in the keeper rails, which both gives me better access when buffing out the wax and acts as a glue-release agent to keep the squeeze-out from adhering to my carefully prepared bearing surfaces.

The next step for me is to build my sliders and install my leadscrews on my boxways. My original plan was to laminate three 18-mm beech boards to produce a solid 50 mm-thick slider. The primary manufacturing concern with that was my ability to drill a sufficiently straight hole for the leadscrew nut to register against. This is critical for my design as I am using flangeless leadscrew nuts that are retained with a press fit. I am considering moving to a hollow slider design that would allow me to cut a precise counterbore on the endplate to press in the leadscrew nut using a CNC router since it has a much lower profile than the full slider — which would have been easy to cut with a horizontal boring mill, but which maxes out the vertical work envelope of the small router in Makerworks.