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Jeeves nodded grudgingly in satisfaction: behind each plate a semicircular silver skyline thrust towards the ceiling, each component utensil "at the ready", glinting softly in the chandelier's light.
At the base of the each knife, fork, spoon and grommik is a silver-plated tungsten pommel, keeping
the utensil upright when not in use.
Apart from the obvious aesthetics, the design ensures that the business end doesn't mess the tablecloth when put aside, and won't be contaminated if dropped on the floor.
________________
[addendum: Jan 19] Design:
(The cutlery sets would be designed and crafted from the ground up as weebleware of course, but for the sake of getting a rough idea of the size and shape we'll start with a standard non-weebling, 8 inch long 40 gram, utensil with a balance point 4 inches from the base, and add a pommel to it)
Weebleware pommels are fully filled spherical cones <link#5> which pack the most weebling ability into the smallest geometric shape: the greater the angle of the cone, the greater the ability imparted to the utensil.
A piece of cutlery with a fully hemispherical pommel (an extreme "cone") has full weebleability: it can't be laid flat, standing up under any condition. For the example utensil the pommel would be approximately 0.9" long and 1.8" wide, weighing 1.1 lbs.
By contrast a utensil designed for a weebling angle of 45degrees from the vertical (as suggested by [bigsleep] as being more aesthetic), is a 90 angular-degree spherical cone approximately 1" long, 1.5" wide, weighing a little over half a pound.
That sounds heavy but it really isn't: all the weight is at the diner's wrist.
[supporting math can be found in Jan.19th annotations]
nods to [po]s
tremble_20cutlery
[FlyingToaster, Jan 14 2013]
Extremely Complicated Variable Parameter Utensils
Extremely_20complic...arameter_20utensils
Candidate for this category? [csea, Jan 19 2013]
Cutlery that stands up
http://pinterest.co...241294492505315465/
Not like the idea but cool nonetheless. [Canuck, Jan 19 2013]
Spherical Cone
http://mathworld.wo.../SphericalCone.html
basically a divot taken out of a sphere. [FlyingToaster, Jan 19 2013]
Weeble wobble tongs
http://www.gizmodo....our-counters-clean/
Getting very close to baked. [AusCan531, Feb 10 2013]
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Using gravity alone, I feel, will lead to utensils that either are pleasant to use but tend to fall over, or which balance well but are horrible to use. Perhaps it would be better to embed very strong permanent magnets in the cutlery, and have the table surface generate very powerful magnetic fields at appropriate points. This would also have the benefit that when you dropped your fork, not only would it stand up weeble-like, but it would also return to its correct position. |
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Or, perhaps the butt end of each utensil could have long retractable curving blades that normally lie flush with the handle when in use. On setting the item down however, the blades spring out to form an umbrella-like shape. |
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However this solution as well as the magnetic one does not solve the dropping-on-the-floor scenario. |
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Perhaps the tungsten weight could be made to slide longitudinally inside the handle. All we would need to do is invent a mechansim so that when the utensil is being held in a human hand, the weight is slid to the centr-of-mass position. When the utensil is set down, in any orientation, the mass is slid to the butt end position. |
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The centre of mass for the proposed tableware would actually be closer to the centre of grip than the usual balance point for tableware which is at the join between handle and head, so I don't see any problems ergonomically. |
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Weight really isn't an issue: it couldn't come close to weighing too much to comfortably handle. |
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For it to stand upright when dropped onto the floor or table, the centre of mass has to be within the radius of the base from the butt end. |
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So unless these utensils look like the guard of a rapier they will be awkward to handle. |
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You could just cut some short slots in the table surface at appropriate locations ("behind each plate"), and put the ends of the tableware in the slots, one per slot. Probably not for tables covered with table-cloths, of course. |
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Tungsten weighs 19.something g/cc: twice as much as silver, and eight times as much as aluminium. |
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A standard solid silver fork weighs 20g. |
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So a small sword pommel perhaps, but not a guard. |
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[bs] so's math. Let's take an extreme case of an aluminium fork that's 7" long and weighs say 5g. The balance point is at 4" from the base of the handle |
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So all we need to do is put one cubic centimeter of tungsten 1" beyond the end of the handle and it will be balanced at the end of the handle. |
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So screw a 1.25ish" hollow sphere with a couple cc's of W inside the far end, to it. |
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[FT] we are talking at cross purposes. I am not disputing that your design will stand up weebillywobbillystylee. I am just saying that it can't do it whilst also being ergonomically balanced in the hand. |
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Thinking a weeble knife might be quite a household hazard!! |
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...and a fork only a little less so. |
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<hmmph> oh ye of little faith... |
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[bigsleep]
A hemisphere of solid tungsten 1.5" diameter contains a bit over 8cc, weighing 284g. |
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I have before me (handle towardst my hand) a stainless steel table knife, 8" length: 4" each of haft and blade. The balance point is 3.5" up the haft. I read that a silver fork weighs 20g, so I'll pretend that a stainless steel knife does also. |
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I'm going to (mentally) reshape the haft into a shortened (by 3/4") hollow open ice-cream cone shape < . The balance point is now 2.75" up the haft. To this is added the tungsten hemisphere, making it a full ice-cream cone shape <) of the original length. |
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The steel side of the weeble has a balance weight of 2.75" x 20g = 55 gram inches. |
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The tungsten side is whatever it works out for a 3/4" deep hemisphere of 284g. Even if the balance point of the tungsten is only 1/4" from the weeble point, that's still over 70 gram inches. It will weeble. |
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[pocmloc]
I don't think the weight or weight distribution would be particularly onerous except perhaps to a small child. |
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[DrCurry]
The good silverware is usually stored in a special box. But yes, space-saving caltrops - bonus. |
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It's not the onerosity I am objecting to but the ergonometry. |
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what about the ergonometry ? They aren't throwing-cutlery. |
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That's good of you to put restrictions on cutlery misuse at the table, but the ergonomics of cutlery manipulation require that the cutlery balance on the index finger, so that the item is basically held between index and thumb, and then manipulated with the rest of the fingers and the palm of the hand. Hence my rather tedious posts above. |
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20g? I'd have thought somewhere between 50g and 100g. |
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most likely 40'ish for a plain one. Although I did find an answer site that said 20, in retrospect there's the distinct possibility that they meant "how much silver is in a silver fork" rather than gross weight. |
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However I do think it would be (barely) possible to do with careful design, without having to resort to carbon-fibre or bamboo. |
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Ergonomics is a bit of a non-sequitur up to 250g or so unless you're in the habit of articulating the utensils from the fingertips rather than the wrist. |
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[bigs] ah, just saw your anno now... |
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hmm... using a weeble-angle other than horizontal makes it much more doable (it's all rather new to me). It also means that the pommel need only be a 90deg divot of a sphere instead of a full 180deg hemisphere. |
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We're possibly talking at cross-definitions. |
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If you're counting on a large weebling angle, such that the device will stand up even if layed down flat (90deg from the vertical) then you need a 180deg pommel: a full hemisphere. But if the requirement is only to remain upright from 45deg off the vertical, ie: if you wobble it too far it will fall down, then you only need a 90deg wedge for a pommel. |
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(I wanted to call the resultant pommel a quartersphere, but I'm not sure that's the correct nomenclature: it's an icecream cone with a 90deg point: think the artwork on "Topographical Oceans") |
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I rather like your proposed 45deg weeble angle though: 90 is only necessary if you want the silverware to double as caltrops under any conditions, as opposed to cutlery which will stay upright when set upright'ish, which is the spec of the idea. |
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However there's no requirement that the divot be smaller than the hemisphere. I imagine it would be carved out of a larger-sized hemisphere. |
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I would (of course) prefer to have a full weeble on general principles if nothing else. But I think a 45deg weeble would more mitigate [pocmloc]s plaint of reduced ergonomics. |
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I'm not totally positive I'm going about it in the right way though. The WP article on weebling says that the overall centre of mass must be at its lowest point when upright (which makes sense) but I'm calculating it as weight x distance-from-fulcrum for both sides (where "fulcrum" is centrepoint of the virtual sphere from which the hemisphere or icecream-cone is drawn) at the maximum required weebling angle. |
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I'm still working under the assumption that the balance-mass of the pommel must be more than the balance mass of the utensil.... ie your "b" option : it's pretty straightforward with this application since the thing's pretty much symmetrical except for one axis. |
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I found an equation for a uniform filled hemisphere: center of mass is at 3/8 times the radius (up the centerline from the base). So I've got a reasonable calculation for the case of a hemisphere (complete weeblation). |
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Given a utensil of 20cm length weighing 40g, with a centre of mass 10cm from the end, we have a balance weight of 400gcm. |
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In order to weeble, the pommel must beat that, so the equation for the pommel is: |
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((sp.gr of tungsten) times (volume of the hemisphere)) times (center of mass) must be greater than 400 gcm. |
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(All the units are grams or centimetres, so ignored for clarity) |
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(19.6) * (2/3 pi r^^3) * (3/8 r) > 400
r > (400/(19.6 * 2/3 * pi * 3/8)^^-4
r > 2.26 cm
___________________________
So the normal'ish size/weight utensil would sport a tungsten hemisphere of 4.5cm(1.78") diameter. That's quite a reasonable size. |
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Of course it would also weigh somewhat more than a pound but that's not too much of a sacrifice for art. |
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Now to go diving for an equation to solve for a 45degree weeble. |
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With a little work (such as mechanizing the variable CoM,) this idea could be a candidate for [link]. + |
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3/8 r, not 5/8 r : the cg of a hemisphere is 3/8 of the way from the baseplate to the midpoint of the curve along the axis. |
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I've been calculating using 2 balance points: the first is the utensil's, the second is the bitchy one which is the balance point of the pommel. The third balance point is the fulcrum where pommel meets utensil. The displacement measured from the fulcrum to the balance point of the pommel times the weight of the pommel needs to be more than the displacement of the utensil's balance point times its weight. |
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The flat face of the hemisphere is the |, the midpoint of which is the fulcrum of our utensil O-------|) ... (it's either a spoon or a formal table-briss) |
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I just worked it out for the icecream cone (now dubbed a "spherical cone"). It's a <), the fulcrum is the far left side of the < so our utensil is a O-------<) |
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The formulas are slightly more annoying than for the hemisphere:
Volume = 2/3 pi r^^2 h, and
Centroid = 3/8(2r - h)
where h is the height of the spherical cap, ie: the height of the ice cream on the ice-cream cone. |
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For a 45deg angle to the cone from the centerline, h works out to 0.293 * r
_____________
Based on the same cutlery as before: 40g, 20cm length with a Cg at 10cm, yielding a balance-weight of 400gcm ... |
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sp.gr times volume times Cg must be greater than 400gcm |
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(19.6)(2/3 * pi * r^^3 * .293)(3/8 * r * .707) > 400
r > (400/(19.6 * 2/3 * pi *.293 * 3/8 *.707 )^^-4
r > 2.68cm <--- the length of the pommel.
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Unlike the hemisphere, the diameter of the spherical cone pommel is *not* twice its length(r), in this case it's root2 * r = 3.796cm(1.5"). |
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Weight is 19.6 * volume = 232.74g.
_____________
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Or, to sum up the two designs:
For a 20cm long middle-balanced 40 gram utensil, using tungsten for a pommel... |
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O----------|)
A completely weebleable pommel will be a hemisphere approximately 0.9" long and 1.8" wide, weighing 1.1 lbs. |
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O----------<)
A pommel allowing the utensil a 45degree weeble in any direction from the vertical will be a spherical cone approximately 1" long and 1.5" wide, weighing half a pound. |
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k, there's most of my afternoon shot. |
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But, it means that the Idea is quite doable and the cutlery could look pretty normal. Quite comparatively heavy of course, but as long as the wielding articulation is at the wrist (the usual method) instead of the fingertips, almost unnoticeable. |
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<triumphant math results added to post text along with link to "spherical cone"> |
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//balance for eating// I half-tested the ergonomics by grabbing a one pound weight and thrashing it around a bit. |
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There's only two ways of wielding an eating utensil: a palm grip and a fingertip grip. |
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Even a full pound weight required no effort for a palm grip since the fine articulation is at the wrist which is pretty well where the weight is. The only thing I noticed was some momentum from elbow articulation. With a half pound weight I assume even that would disappear completely. The utensil, while it might earn an "oh it's heavy" comment, wouldn't be awkwardly heavy in any way. |
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The second grip, for forks and spoons, is to operate them with a fingertip/thumbtip grip (which is how I wield chopsticks, driving people who use them properly nuts). There might be a noticeable weight issue since the pommel is much further from the wrist than with the palm grip. |
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I still think the spherical cone is an optimal shape in some manner, though I'm not entirely sure what manner that is. |
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