The A/B toy

[Stewart]

The toy marked A/B on the MT toys page has always baffled me as to what it could be. It has been suggested that it depicts the Jacob's Ladder toy. There are similarities between the image and a Jacob's Ladder toy, but if that is really what Bessler was trying to show I think he would have done a better job with the diagram. I can't recall reading any other ideas as to what toy the image represents. However, we have all noticed that it resembles some sort of chain with links. There have also been suggestions that the two images (A & B) could either show two different views of the same toy, or be two different toys.

Here is my view on what the A/B images represent...

In my post "The last toy" I was struggling to accept that the last toy was a spinning top. A couple of things bothered me - the two lines splitting the top's body into three sections, and the hole in the middle section showing a rod or rods inside. I'm now convinced, thanks to John Collins, that it is a spinning top. He described a top he had as a child that had a rotating middle section with a hole in. You put the string into the hole and wind it around the spindle and winding bars inside. You hold the middle section, pull the string, put the top on the floor and watch as it flips onto the spindle point. I then thought to myself it would have been so much more obvious what the image was if Bessler had shown a piece of string coming out of the hole. When I looked at the A & B images I suddenly realised that what was missing was the string! You have to thread string through all of the holes in the hinge-pin heads and tie it off at the last pin head. You then hold the toy at the top and pull the string and the chain will bend. I remember playing with a toy snake when I was a kid that worked on this principle. Looking at image B it shows the hinge-pins alternate between the left and right sides of the chain links. Does this mean that, instead of bending, it folds up (like a paper fan) when the string is pulled? At the top of image B it shows two bars on the same hinge, but I'm not sure what these are for. One thought I had was that the string attaches to these two handles in some way and by pulling them apart or pushing them together, you cause the bending/retracting of the chain. Perhaps two pieces of string are used - one going down through the left set of pin heads and the other going down the right - tied on the bottom most pin on each side, and also to one of the handles.

If this is what the A & B images are showing, then Jeff is right when he said that all the images on the toy page show how a horizontal movement can cause a vertical movement (or visa versa).

I have attached to this post some 3D images of the how I interpreted Bessler's images of the toy. I haven't completed the 3D model yet - I'm still working out how the handles work, so I've left them off, and I've also left the string off for the moment.

I'd be greatful for your input in a couple of ways - a) what you think of the general idea and if you think it's what Bessler intended to show, b) your ideas on how it works - does it bend, fold, how the handles work etc, c) please post any pictures of toys or other devices you can find that work on this principle.

All the best
Stewart

[Jonathan]

I see what you are saying. I think that is what he was trying to show, kind of like window blinds. However, I don't think he would show the multiplicity of 'eyes' if one wasn't supposed to thread the string in some way through all of them. The 'snake' bending movement you describe can only occur if the string goes through the first eye and ties to the last. If one threads a string through all the eyes though, no amount of pulling will make it contract. However, if the links in the chain are flexible or elastic, then it would work exactly like some kinds of blinds.
Also, I don't think the two things on 'B' are handles, I think they emphasize the fact that they are jointed.

[grim]

You are correct, Stewart, it LOOKS similar to a Jacob's ladder but the hinges are different, even if it depicted the links minus the wood blocks.

A good construction display of the toy's links are at

http://www.mathematische-basteleien.de/jacob.htm

They are different.

Thoughts here were the extended multi-hinge on the left had an arrow pointing UP, rising side, and the A/B was on the down-going side, with the action depicted in the middle figures and the end result the spinning top or turning wheel.

grim

[Stewart]

Hi Jonathan

The bending movement does occur with the string through all the holes and tied at the last one - I've tested it by building a model. There are lots of applications of this bending mechanism around as well, such as for bending the fingers of a robotic hand (I've just remembered I had a toy robot hand that worked on this principle), or for guiding the end of a flexible endoscope, and I'm sure there are more, not forgetting my toy snake!
However, I'm not sure if bending is the intended purpose of the toy, or whether it is meant to fold up. I'll try building another model using two pieces of string as I mentioned in the first post and see if that makes it fold up.
You are right that one possible explanation for the two top sections on image B is that Bessler is indicating that the sections bend. I don't think that is the case however for a couple of reasons: 1) I haven't seen Bessler show two super-imposed positions of an object anywhere else, 2) it's fairly obvious that the parts must be hinged anyway, 3) why add a little touch like that when you've left off the string which is the vital part that will make people understand the image.
Thinking about it, Bessler probably left the string off of the image to make it less complicated to see the actual main structure. I expect that, if he had actually finished writing MT, Bessler would have added some text explaining that the parts hinge and that string passes through all the holes and is tied at the end etc.
I'll post some more pictures of the 3D model bending and hopefully folding soon, once I've finished testing my real model. I'll post videos of the real models working as well.

All the best
Stewart

[Stewart]

Hi Grim

I'm quite sure it isn't a Jacob's Ladder, as you say the hinges are wrong - there is no way it could work as a Jacob's Ladder as shown.
Yes I guess the way you describe the order of the toys makes sense (if there is an order at all!), they are also labelled in that order - that's something else thats a bit strange about that page as you would expect them to be label from left to right if they were unrelated images.

I've just had a thought - put a weight on the end of the chain to make it a better pendulum - then alternate the opening and closing of the handles which pulls and releases the string to make the pendulum swing. Maybe that's what Bessler is trying to show us?

All the best
Stewart

[Jonathan]

Another thing occurred to me, if one skips every other eye, it will act like a digitized version of the one I've shown. I can't wait for you to put up the new 3d image, as I have no idea what you're talking about. If the sting goes through every hole, the links must somehow be contractable for the whole thing to contract. Unless you have an unusual threading method?
I find you revelation about the movement of a weight on a pendulum very interesting...

[Stewart]

Hi Jonathan

The skipping of every other eye is what I was trying to describe as the other possible way of stringing it together in the first post. Looking at image B, thread one piece of string through the left set of holes (left of the black vertical line) and tie on the last of the left holes, then thread another piece of string down the right set of holes and tie on the last right hole. Pull both the other ends of the string together - I'm not sure what will happen, but I'm thinking it should fold up like a paper fan. I'll build a model as soon as possible to find out if it works and I'll post the results.

I've built a model of the bending method and it does work. I'll post a video when I get time, but have a go at rigging something up yourself if you're still not sure about it. In case you didn't realise, all the holes are in the head of the hinge pins and the pins aren't attached to any links so all links revolve around the pin, plus the pins are free to turn too. So while threading the string, all the holes point downwards, but as you pull the string the links bend at the hinges and the holes will turn to guide the string also. On my model I hold the top link and then alternate between pulling and releasing the string - the weight I put on the end swings backwards and forwards. I'll post more as and when I get time.

All the best
Stewart

[Jonathan]

I see, that is what I was thinking. I thought you were saying to go through all the holes with one string. Actually, now that I think about it, one can thread though all the left holes, tie to the last left one, then tie to the last right one, and thread through all the right ones, thereby using one string to do the same thing. But it doesn't matter that much.
As to the swinging pendulum, I'm reminded of something I've read somewhere, about how children swing on swings. Their laying or sitting at the right times pumps the pendulum to a higher height, so if you pull/release the strings with the right frequency you could pump the pendulum the same way. Is that what you've been doing? I'm going to go build a model, K'nex are perfect for this.

[Stewart]

Hi Jonathan

I was actually talking about both ways of stringing it together. The first way is to have one piece of string going through all the holes and tied at the bottom one. This arrangement means that when you pull the string the links bend up, like a bending finger. I know you are struggling to accept that this actually works so I have attached some videos of my models to this post. The second way of stringing it is to use two pieces of string one down the left set of holes and tied at the bottom one, and one down the right set of holes and tied at the bottom one. Pulling the string in this configuration means the chain folds up like a fan/concertina. I have also discovered that the first arrangement (single piece of string through all holes) can also work to fold the chain like a fan/concertina. I found that adding a weight to the bottom link helped it fold better this way.
For the pendulum swinging model (not shown here) I could get it to swing but I found it worked better by making the pivot points all align vertically and not offset. I think the offset nature of the pivots gives leverage and helps with the lifting/bending.
The method you mention of pumping the swing by standing and crouching has been talked about on this site and yes the toy could work in this way I guess, but that wasn't what I meant. Hopefully the attached images and videos will explain all. You're right, K'nex is good for modelling this - infact that was exactly what I used. In the videos I have recreated 3 links in the chain - the construction looks a bit overcomplicated but I was trying to get the offset pivots as close to the bars as possible as in the MT images - this isn't particularly easy with K'Nex. I also had to use sewing thread as I've run out of string. I also added another row of holes down the right side of the model (right side of image A) and a second piece of string to even the forces applied to the K'nex model to stop it from bending sideways. I hope this doesn't confuse things too much!

The attachements are as follows:

chaintoy_string.jpg - Shows the two methods of stringing the toy
chaintoy_knex1.jpg - Shows the K'nex model strung with black thread on both sides
chaintoy_knex2.jpg - Shows a close up view of the offset pivot points
chaintoy_knex1.avi - Video of chain bending by pulling the string
chaintoy_knex2.avi - Video of chain folding by pulling the string (method 1)
chaintoy_knex3.avi - Video of chain folding by pulling the string (method 2)

Click the name of the video file above to view/save.

I hope this all makes sense - it was a rushed job and the models are a bit crude, but I think it proves my point.

All the best
Stewart

[Jonathan]

That is complex! I made mine with blue sticks (1 blue~1/2 red), so it is much smaller.

[Stewart]

I have put links up for the videos - click on the file names in the last post to view/save them.

Jonathan - yes it is a bit complex, but I was trying to make it as close to the original images in MT as possible by making the pivot points of the hinges close to the main rods and also to avoid any unwanted twisting of parts as tends to happen with K'nex. Feel free to share your designs if you can simplify it - the simpler the better! I think I've proved the toy can work in three different ways (at least). I'm now just working out how the handles at the top work. I'll post my findings and update my 3D model to show the handles and string which is a much clearer way of seeing how to build it than the K'nex model! I have made other models of this with all 9 links - these were smaller of course (using blue sticks ;) ) - but I made this larger model so that it was clearer for the camera and fitted in the frame!

Does anyone have any thoughts on how this device might work in a Bessler wheel? Do all the toys somehow work together or was Bessler just trying to get us to think about other ways of translating a vertical force to a horizontal one or visa-versa?

All the best
Stewart

[Stewart]

Whoops - the links didn't work to start with. I've moved the videos to another site and have updated the links. They should work ok now.

chaintoy_knex1.avi - Video of chain bending by pulling the string
chaintoy_knex2.avi - Video of chain folding by pulling the string (method 1)
chaintoy_knex3.avi - Video of chain folding by pulling the string (method 2)

If anyone can find any photos/diagrams of this chain toy from any point in history and post them here I would be very grateful. As yet I've not managed to find any examples on the net. Many thanks.

All the best
Stewart

[grim]

Hi Stewart

If I recall correctly, and maybe John C. can say yea or nay, but I believe I read either in his book or somewhere about Bessler's other ideas/inventions like the underwater house, etc., that he had created a ladder that unfolded itself.

Your rendition you posted reminds me of those second-story emergency fire ladders.

grim

[John Collins]

Grim, I'm not aware of JB inventing an unfolding ladder. perhaps someone speculated that he had, on seeing the A/B toy?

John C.

[Jeff]

Great job, Stewart. I believe you are correct. The A/B toy is not a Jacobs Ladder. It appears that all the toys are showing a change in direction of force/movement. In his book John Collins says that Bessler suggested he (Bessler) found the secret while constructing an organ. Below is a link to a site that has to do with the mechanics of organ actions, and the "squares" seem to fit in with what the toy page is indicating. I think this ties in somehow with the "cross-bar" that was mentioned in the post between John and Patrick.

http://panther.bsc.edu/~jhcook/OrgHist/ ... orks12.htm

Jeff