How to Analyze a Devil's Hook

[Ron247]

Just curious if anyone has ever analyzed a Devil's Hook to show mathematically how it works. I had one of these in the 60s but lost it. Never knew what it was called. Recently found out it was called a Devil's Hook and found them for sale in Magic Shops and some other novelty internet sites. Attached are some photos and a sketch of the dimensions. I know it is all or partly related to loading through the shear center. These cost about $2 and both kids and adults are amazed by them.

[URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1570801609/tips/Devils_Hook_Dimensions_lnsvc0.pdf[/url]

 

[rb1957]

it's simple, how it works. the load rotates under the balance point until the weight is aligned with the contact point.
The load piece (the wooden piece above) contacts the green plastic hinge at two points, and together with the weight, this is a three force member.
The green hinge is also a three force member (actually the same three forces, well swapping the weight for the equal ground reaction).

another day in paradise, or is paradise one day closer ?

 

[Ron247]

I was curious if someone had done the mathematics on it also. The belt almost always hangs with a slight curve to it due to how it is set in the notch. I was not sure if it was the shear center or the center of mass that has to align with the contact point on the shelf. It would be easier to review if the belt was not an old used belt but a fairly straight new one without a buckle.

The picture below is looking straight at it with a plumb bob. The string running over the top of the shelf makes it look like I am on an angle, but I am not. In looking at the specifics:
Where is the center of mass in the picture?
Where is the shear center for the combined hook and belt?
The hook touches the shelf in one place right at the edge but it is a line, not a point.

The concept of what is going on makes sense, but it looks like the math is fairly formidable.

 

[IRstuff]

Seems pretty straightforward to me; the CoM has to be to the right of your plumb line, otherwise the hook would slide off the mantel, aside from frictional restraint.

You could tape a steel ruler to the hook and see what happens.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

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[Compositepro]

I do not see any mystery. The device is merely a novelty and will only work for very specific objects. The hook will tilt either direction until the center of mass is under the edge of the shelf (the hook is designed to always bear on the shelf edge, so friction at this pint is also required). The hanging object must be shaped to hook into the slot and be long enough and stiff enough to deflect the center of mass toward balance as the hook tilts.

A similar trick is done with two cylindrical steel bars where you have to balance one over the other, oriented at 90 degrees. This can only be done when the top bar is smaller in diameter than the lower one. The diameter difference can be imperceptible. The magician will demonstrate how to do it but will switch bar positions before having someone else try. The mathematics of this trick is simple but fascinating. When the smaller bar is on top, as the bar starts to tilt, the point of contact between the bars (the pivot point) moves faster than the center of mass.

 

[Ron247]

I never said it was a mystery to me. I wondered if anyone ever did the math. There are several things that must happen for the hook to work. I do not think it works if the hanging object does not curve. It will not work if the hanging object hangs straight down and is not forced to curve. It does not work if the item inside the slot can rotate inside the slot rather than curve the object.

Of the locations you could call the CoM, none of them appear to align with the edge of shelf.
CoM of belt is center of the belt at the slot? Won't work.
CoM is halfway down the hanging ends of the belt. To me, that location does not appear to be aligned with the edge of shelf in the picture.

Just looking at the picture, it looks more like moment of mass to left of string must equal moment of mass to right of string.

But this is why I entered this post. Curious what people thought.

 

[KootK]

Fun. I think that the "trick" to it is in recognizing that there's a uni-directional moment connection between the hook and the belt that turns the the thing into a moment frame the shape of a 7. After that, it's just statics on a rigid frame as others have alluded.

 

[Ron247]

Agreed, the main trick is in the belt to hook connection. The hard part for me is what is it that has to align with the support in order for the thing to become "magic". And where would you call Center of Mass? Am I incorrect that there is some relationship to the shear center included in the puzzle or is it just that the hanging chad has to have some curvature to it.

 

[BAretired]

Just looking at the picture, it looks more like moment of mass to left of string must equal moment of mass to right of string.

That would be the same as saying the center of mass aligns with the center of string, but actually, the center of mass aligns with the edge of shelf (right edge of string).

BA

 

[rb1957]

I didn't recognise it as a belt at first (I thought it was more of a stick).

I think the CoM of the belt is to the right of the plumb line, as the plumb line is the edge of the shelf, and the hook contacts to the right of the edge.

I wonder how the fit of the belt in the notch affects things ?

another day in paradise, or is paradise one day closer ?

 

[Ron247]

Compositepro: The cylindrical steel bar trick you described. Does that have a name or is there some video of it on youtube? Sounds interesting to see.

 

[3DDave]

If the item was a folded rigid strap it would have no surprise. It needs moment continuity, as supplied by the slot.

 

[KootK]

Nothing to do with shear center and everything to do with the centroid of the combined 7-shape thing. A vertical line run through the tail of the hook "comma" should pass through the centroid of the combined shape.

 

[Ron247]

I think it is as Kootk described. There is a couple created by one face of the notch and the opposite side of the belt on the other surface. The notch is 1/8" but I think you could use a thinner material as long as it is stiff enough to allow a couple rather than to bow-up. I found an belt that has never been used but it has a heavy buckle. It works terrible as compared to one with a light buckle.

 

[Ron247]

The hook itself is very light. The one I had in the 60s was 1/2" to 3/4" thick wood. Similar size but the dimensions were probably not exactly the same.

 

[Ron247]

BA: Thanks for reminding me what Center of Mass is. I have gotten into a bad habit of confusing CoM with geometric center because I have 2 or 3 clients that do it. That explains some of my confusion in these posts. I did not realize I have picked up their bad habits. They call geometric center, Center of Mass and the other is Centroid of Mass to them.

Time for me to go back to school.

 

[PEinc]

The belt is rigid enough that it cannot rotate in the slot. Therefore, there is a rigid moment connection between the belt and the hook. The hook would not work to hang a loaded string instead of the belt.

http://www.PeirceEngineering.com

 

[BUGGAR]

Elaborating on Kootk et. al., I think the "shear center" concept is clouding the issue. I agree a C section beam spanning between two supports can support an offset load located over its shear center without rotation, but this is easier figgered as a rigid frame.

 

[Agent666]

The centre of the gravity force of the hanger thingee and the belt must align horizontally with the pin support. Equilibrium tends to do that. All of you saying the centre of mass and hence centre or line of vertical force is to the right or left of the support need to go back to statics 101.

 

[BUGGAR]

Get one of those novelty wine bottle holders and play with it. Drink the wine and see how the balance changes. drink some more wine. Does it work on an empty bottle?