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Dividing Head Question Bonanza

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Robo_Pi

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These are going to be some pretty crazy questions about uses for dividing heads. So please bear with me and don't say you weren't warned.

To begin I'm not going to be asking too many questions on how to actually operate a dividing head. I have some idea how to do that already. To make a long story short, I dug this old dividing head out of a corner where it had been sitting for years. It was all rusty. Just light surface rust, nothing serious. And so I've just finished disassembling it, cleaning it, and putting it back together. It's looks next to new now and appears to be working just fine. It's a Vertex made in Taiwan. No chuck. But it does have a blank face plate, a center, and a lathe dog holder that slides onto the center. I also have the tail-stock for it. Just for additional information I have an old cast circle cutter frame that I was able to convert into a nice bed to hold the divider and tail-stock with about 8" to 10" between centers. Not sure if that would be a useful set-up, but it looks good sitting on the bench.

In any case I would like to see if I can get this beast to start paying for itself. I bought it new several decades ago for a project, and basically only used it once. It's been serving as a door stop ever since. I think it's time it started paying for itself. So I'd like to put it to use on projects that might potentially pay for themselves. I'm open to any ideas. I currently have three ideas in the making.

First Idea - Extremely Simple Wooden Clocks:

First idea is to use it to index wooden blanks for drilling holes to make "pin gears". I actually have some ideas for replicating some antique gravity powered clocks. Specifically using flying pendulum escapements. I realize the divider head is overkill for this. A pair of simple hand-held dividers would work just fine. But I thought it might be interesting to use the divider head in the "quick-indexing" mode where just the lock pin is used instead of the holey disks. The lock pin has 24 holes. So I would need to design my gears around that.

So I guess my first question here is "How do I learn how to design pin gears around a 24-hole indexer?"

For now I'm just looking at creating two wooden pin gears that are driven at a 90 degree angle. One large diameter, and one small diameter. I'm not even worried about the actual ratio so much. The main thing in this case would be to try to design around the 24-pin indexer for now. That way I can index these really quick and easy and the results should be perfect. The idea is to make a lot of clocks in the least amount of time. Because after all, when making clocks time is important.

Like I say, this project doesn't really require a dividing head. But I thought it might be a good project just to get some initial use and practice using this tool. The first project does not need to keep any actual time. It's just going to be a mechanical contraption that is interesting to watch run with the flying pendulum escapements. I'll also be using wooden dowels as the cogs. The dowels being about 1/4" dowels. Kind of large and bulky. Later I might move on to using small metal pins, smaller gears, and maybe eventually totally metal gears, maybe even moving up to using the actual divider plates to get more complex timing.


Second Idea - Cutting a Large Number of Wooden Gears with a Router.

The idea here is to set up a router on a long track. I have a nice track to run a router on. Then use the divider in the convention gear-cutting manner to index a long stack of wooden gear blanks. Then just cutting the gear profiles with the router. The idea here is that I actually have a whole lot of projects I would like to build that use wooden gears. So the goal is to be able to cut a whole bunch of wooden gears in one quick and easy process. So this would basically be the same method as used to cut a long piece of metal on a horizontal mill, only using a router and wood instead. These wooden gears are likely to be a bit larger simply because wood demands more material. But these can also be a lot of plywood blanks pre-cut and stacked together prior to cutting the teeth.

The question here really isn't about the divider at all, but rather, "How do obtain, or cut, my own custom router bits that are shaped for the teeth profile I'll need?"

Should I just buy 1/2" diameter tool steel and grind my own router bits similar to how I might make a metal working tool? I'm thinking this is probably the best way to go since I have no clue where to buy router bits that are designed for cutting gear teeth. And even if they do making them I'm willing to bet they aren't cheap.

Anyone have any experience cutting mass quantity wooden gear blanks like this? I'm always thinking in terms of mass production. I can't afford to be spending the time cutting each gear individually. I'm, not going to make any money that way.


Third Idea - Cutting a Large Number of Plastic or Metal Gears on a Vertical Mill/Drill.

Again, I'm looking for large quantities of the finished product. I have many projects that I can use gears on. All of these projects are small lightweight projects. Like robots, Stirling engines, and other interesting projects. My main concern here is to learn how to set up for the most productive gear-cutting session. And to also keep this within the confines of the machines I already have. I don't mind having to buy gear cutters. But the key here is that I have a very cheap Mill/Lathe combo machine. It's an HQ400 Chinese machine with power feed and thread cutting gears. So if I cut gears on here in any form of "mass-production", they are going to need to be soft material. I mean, it will cut steel, but that goes a lot slower. So I'll probably be limiting myself to Plastics, Aluminum, Brass, and Bronze, etc.

I have a few questions for this, again not about the dividing head directly,. The idea is to start with a long blank of round-stock (about a foot long) and then cut the gear teeth over the whole piece of stock. Finally slicing off the individual gears for final use. So here's my questions.

Can I do this on a vertical mill?

Where should obtain the teeth cutters?

Is making my own teeth cutters a viable option? (I would prefer to make my own tooling whenever possible)

What kind of plastic is the best to start with for making plastic gears?

Any other suggestions on materials?

This pretty much ends my bonanza of questions unrelated to the Divider Head. *(kind of)

Finally I'd also be interested in any suggestions anyone might have for "Divider Head Projects" that might potentially be profitable?

I'm trying to get this thing to be useful and pay for living here. (ha ha). And since I have all these potential projects that can benefit from mass produced gears that's what I'm thinking about. Is there anything else that a dividing head is useful for?

I'm definitely going to be making the "pin-gear" clocks for sure. I was actually planning on doing that before I thought of the dividing head. But now that I got it out and it's all cleaned up and ready to go I'd like to use it. Once I get it all set up, it might save some time in drilling precise holes for pin gears. Even though that's probably overkill. But it's a nice place to start.
 

Robo_Pi

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Just for clarity on the "Pin Gears". The following video has a set up similar to what I'm hoping to build. A 90 degree angle "pin gear" drive. This is made out of wood and I'm actually working with pins close to the size used in this video. I've already built a clock using this style of gear. Only my gears were quite a bit difference in size. On my clock the vertical Gear was the drive gear. It was large at about 5" in diameter with 20 pins (or teeth).

The smaller gear on my clock only had 6 pins and was about 1-3/4" in diameter. That gear was driven by the larger gear. The larger gear was driving by gravity and a large weight. I set those gear ratios up entire off the top of my head without using much math save for some minor calculations to figure out about how far the pins had to be spaced apart.

What I'm looking for are formal equations for designing these kinds of "Pin Gears" and I'm not even sure if that's what they are officially called.

These were used in ancient times, and it's not just the pin positioning on the wheels that is important, but also the diameter of the pins themselves, as well as the height of the pins, etc. I did this all by intuition on the first clock I built. I just kind of built something that looked like it might do what I wanted it to do. And by golly it actually worked too! But it did have some slight interference here and there.

Finally, perhaps I should mention that on the clock I'm building these gears don't have anything at all to do with the timing of the clock. The timing of the clock is taken care of entirely by "flying pendulum escapements". I have equations for that part of it.

In my clock I was using a large drive wheel to amplify the force of the gravity weight. And the small driven wheel to deliver the power to the flying pendulums. Like I say it worked pretty well actually. I still have this old clock but it no longer runs as it was stored in a leaky barn and got rained on and has since warped.

I had also spaced out the pins on my old clock by hand, and they were far from perfectly spaced which contributed to intermittent binding. This is one reason why I would like to try building a new one using the precision of the dividing head.

But now I would like to find formulae for calculating the best gear ratios, pin sizes, and so forth so I can see if I can come up with some more complex designs. My original clock didn't have any hands, or keep time numerically. It just spun around at a nicely controlled rate determined by the "flying pendulum escapements". I'd just like to get back into this, only this time take it to a more serious level.

So if anyone can point me to equations for theses types of "pin gears" I'd be very grateful. I'm having difficulty finding any information on this specific design. I don't want to go back to just guessing again.


 

RJSakowski

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Lots of questions, but then you warned us.

Re: machine to use, I would use the mill/drill rather than try to build up a custom machine. On limitation will be rpm range but I think that it is workable.

Re: the dividing head, the number of teeth on your gears will depend upon the possible divisions that you can make with the dividing head. I would expect that wooden gear teeth do not have to have a precise a profile as metal gear teeth do. There are some gear design applications on line that can help you get started. One possible: http://woodgears.ca/gear_cutting/template.html

Re: the cutters for the teeth. I would try to modify an existing cutter rather than start from scratch. If you do decide to start from bar stock, I would turn the profile on a lathe and then cut the flute(s). One flute would probably work and you don't have to worry about making two the same. Machining wood usually works best at higher rpm and higher rpm tends to generate heat so HSS would be my choice, carbide if you're brave. Rake and clearance will be important. I see that HSS straight flute router bits are still available on line and that would be my starting point.

Re: type of plastic, I would suggest Delrin or Nylon. Both are used for gears and fairly strong as plastics go. They machine relatively easily.

I wouldn't think that pin diameters/spacing is all that critical as long as adequate clearance are involved. By nature, thr pin gears have a fairly large amount of backlash but as long as they are only driven in one direction, that shouldn't matter. You can reduce the backlash by reducing the clearance and the worst case clearance is at the point where the gear teeth are just engaging/disengaging.

Modern gear teeth are designed to have a fairly constant mesh. Here is a manufacture of of an end mill for cutting same. http://www.supercapitaltools.com/products1.htm
I can see some issues with using a dividing head rather than a 4th axis with this type of cutter. Basically, you would need a special cutter for each gear diameter. but I think it would work for wooden gears. with a CNC mill and 4th axis, a simple tapered cutter should be sufficient (modern gears mesh correctly with racks with triangular teeth).
 

Robo_Pi

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Re: machine to use, I would use the mill/drill rather than try to build up a custom machine. On limitation will be rpm range but I think that it is workable.
I was only thinking of building the custom machine for routing wooden gears. The reason is that I could easily make it for a 3 foot long cut length. Something that would never fit on the mill/drill. I'm thinking that I could stack a whole lot of wooden gear blanks on a piece of all-thread. Lay them in a long custom-made V-groove holder for support (also made from wood). And then place the all-thread stack between the dividing head centers. This would allow the router to make a 3-pass on each division. That would cut a lot of gears pretty darn quick. It would also be a pretty easy machine to build. In fact, since making money is a bit part of the plan here I'm starting to think that I could potentially make these mass-producing wooden gear cutting machines available for sale too.

In fact, last night while in bed I just realized that the quick-indexing feature of the dividing head could be easily replicated in wood as well. Possibly with a set of interchanging plates. No need for a worm gear dividing head. It's something I'll definitely be thinking about. It's funny how this dividing head might end up making me money just from having given me ideas.

But yeah, when I move up to metal gears in alumium, brass, or steel, I'll definitely switch over to the mill/drill machine.

I'm wondering now if the wood router could be used to cut the Delrin or Nylon gears? Or would the cutting speed be too high and melt the plastic?

Re: the dividing head, the number of teeth on your gears will depend upon the possible divisions that you can make with the dividing head. I would expect that wooden gear teeth do not have to have a precise a profile as metal gear teeth do. There are some gear design applications on line that can help you get started. One possible: http://woodgears.ca/gear_cutting/template.html
Yeah, I've been finding lots of spur gear calculators online. But the pin type gears require different spacing to be sure the pins don't bang into each other. I can probably come up with my own formulae for pin gears, but I thought it would be nice if I could find this stuff already done somewhere. No point in reinventing the pin gear if I don't need to.

Re: the cutters for the teeth. I would try to modify an existing cutter rather than start from scratch. If you do decide to start from bar stock, I would turn the profile on a lathe and then cut the flute(s). One flute would probably work and you don't have to worry about making two the same. Machining wood usually works best at higher rpm and higher rpm tends to generate heat so HSS would be my choice, carbide if you're brave. Rake and clearance will be important. I see that HSS straight flute router bits are still available on line and that would be my starting point.
Yeah I guess you're right. I could just modify HSS straight flute router bits. That will be a lot easier than starting from scratch with an HSS blank. Funny how I didn't think of that myself. This is why it's always good to bounce ideas off other people.

Re: type of plastic, I would suggest Delrin or Nylon. Both are used for gears and fairly strong as plastics go. They machine relatively easily.
I was thinking Nylon myself, but I wasn't sure if that would work or not. I'm wondering if I can cut the Nylon with a wood router? Or would the cutting speed be too high and just melt the nylon?

I wouldn't think that pin diameters/spacing is all that critical as long as adequate clearance are involved. By nature, thr pin gears have a fairly large amount of backlash but as long as they are only driven in one direction, that shouldn't matter. You can reduce the backlash by reducing the clearance and the worst case clearance is at the point where the gear teeth are just engaging/disengaging.
Yeah, I'll only be using these pin gears in uni-directional machines (like clocks mostly), so lots of backlash shouldn't be a problem. In fact, that's what made it possible for the first pin-gear clock I made to be so sloppy and still work good. The pin gears would "clunk" into their next position. But in the clock all the timing is down by the flying pendulum weights, so the movement of the gears really doesn't play a role in the timing. The gears are only being used to covert the downward force of gravity into a horizontal spin along with some mechanical ratio advantage.

Modern gear teeth are designed to have a fairly constant mesh. Here is a manufacture of of an end mill for cutting same. http://www.supercapitaltools.com/products1.htm
I can see some issues with using a dividing head rather than a 4th axis with this type of cutter. Basically, you would need a special cutter for each gear diameter. but I think it would work for wooden gears. with a CNC mill and 4th axis, a simple tapered cutter should be sufficient (modern gears mesh correctly with racks with triangular teeth).
I don't have CNC capability on the mill/drill. But I am wondering whether I should go with the vertical cutter cutting the teeth slots down the center of the stock on the top. Or whether I should use something like a horizontal cutter and cut the teeth slots down the center of the stock on the side? I was actually thinking of using the latter method. Not sure why. Intuition just draws me to the horizontal type of cutter as being better. It kind of just scoops the material out from behind. While a vertical cutter is cutting circular passes. For some reason I'm intuitively attacted to have the material scooped out like a horizontal mill does instead of being "routed" out like the vertical mill would normally do.

I should be able to use the horizontal cutter in the vertical mill. I would just be cutting the groves on the side of the stock instead of on the top.

I don't know. I'm just thinking out loud at this point. Kind of brainstorming ideas.

Thanks for the quick reply and interesting ideas RJ.
 

MarkM

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I think your over thinking this project. To be very accurate and in production. Make the disks in a bolt hole circle pattern. Pick your diameter for your disk and as for length as deep as you can accuratly drill and ream a bolt hole circle. Ream your holes for your dowel pins. Cut the disks up. Make your disks makes your pins. Assemble pins with disk with your drive etc. For bolt hole circles if you have a table with a vernier scale you can pinpoint those holes. 360 degrees in a circle. Your number of holes divided by 360 gives your angle. Six holes 60 degrees for example. X and Y cordinates for each hole is x = radius times cosine of the angle and y= radius times sine of the angle. People do things there own way. My firts hole I move over the radius then add the according degree from there. Move over radius then 60 degrees then 120 degrees and so on. Do the math on paper then go hit those numbers and don t forget about backlash in the table.
 

RJSakowski

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I modeled up a couple of pin gears in SolidWorks. It's not as easy as it first seemed. Insitnctively, one would think that if there is an interference, reducing the diameter of the pin but that doesn't appear the case. Also, it looks like the transition between pins isn't a smooth one. It probably wouldn't be noticed ot the gears were being used to drive a mill wheel to grind grain but if precision motion as in a clock is desired, it could be an issue.
A little digging turned up this
http://www.odts.de/southptr/gears/pegs1.htm
Enjoy!
 

MarkM

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I went the route of x and y cord. To be able to clamp a thicker pc. Of material to the table and make more disks vs, trying to clamp to the dividing head making one or two.
 

Robo_Pi

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I modeled up a couple of pin gears in SolidWorks. It's not as easy as it first seemed. Insitnctively, one would think that if there is an interference, reducing the diameter of the pin but that doesn't appear the case. Also, it looks like the transition between pins isn't a smooth one. It probably wouldn't be noticed ot the gears were being used to drive a mill wheel to grind grain but if precision motion as in a clock is desired, it could be an issue.
A little digging turned up this
http://www.odts.de/southptr/gears/pegs1.htm
Enjoy!

Thanks RJ, that's exactly the kind of information I was seeking on the pin or peg gears. That will help a lot. They are even addressing the gears being set at 90 degrees which is what I want.

I realize this type of gear is grossly inefficient. Efficiency isn't the goal of this particular project. This is more of an "art" project. And the idea is to create a finished "clock" that conveys a very antique appearance. Keeping perfect time is secondary. Also, the timing on this design is controlled by the escapement, not by the gearing.

I don't a have picture to post right now, but this "clock" in it's simplest form only tells the most abstract form of "time".

For example, all this original clock does is create a vertical shaft that flips 1/2 revolution every second or so. The actual "flip" is very quick.

So the idea is that on the top of the clock there are two signs, one on each side of the vertical shaft. Only one sign is visible at a time. The signs switch place about once ever second or two.

Here are some ideas of what these opposing signs might have to say,

Side One: "Time to go Fishing"
Side Two: "Time to go Hunting"

Side One: "Time to do Machining"
Side Two: "Time to buy Tools"

Side One: "Time to Dance"
Side Two: "Time to Party"

My sister is into watercolor painting and sewing, so for her,...

Side One: "Time to Watercolor"
Side Two: "Time to Sew"

An avid bookworm might enjoy a clock that says

Side One: "Time to Read a Book"
Side Two: "Time to go to the Library"

You get the idea. It's just a novelty item. The flying weight escapements and peg gearing just add interest. Could do it with regular spur gears too. But the peg gearing really gives it an antique feel.

This is just for the "clock idea" which is what I started with. I might also use these peg gears on "Marble Machines" too. I also built Stirling engines as novelties and may add peg gearing to some of those models. Steam Punk Art is also on my wish list. And after I get the wooden peg gears down pat I may move on to making metal peg gears. Again, for the purpose of animated art projects. Peg gears are less common and are therefore more interesting to watch in operation. So if I can master the "art" of peg gears I'll have something fairly unique. My novelty product line can feature peg or pin gears as a dependable constant. But only if I can produce pin gears that are indeed dependable. They're no fun if they are constantly jamming up.

So yeah, THANK YOU for the webpage info you just pointed too. That's exactly the math info I was looking for. You WIN! And now so do I.
 

Robo_Pi

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I modeled up a couple of pin gears in SolidWorks. It's not as easy as it first seemed. Insitnctively, one would think that if there is an interference, reducing the diameter of the pin but that doesn't appear the case. Also, it looks like the transition between pins isn't a smooth one. It probably wouldn't be noticed ot the gears were being used to drive a mill wheel to grind grain but if precision motion as in a clock is desired, it could be an issue.
A little digging turned up this
http://www.odts.de/southptr/gears/pegs1.htm
Enjoy!
By the way, how in the world did you ever find that page on peg gears? I would have never found that page.

Thanks again! Sure pays to have someone else find an obscure web page. It was well worth posting my question on this forum!
 

RJSakowski

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I tried pin gears first, then peg gears. The pin gear had a more modern type of gear driven with a cycloidal pinion. I figured that peg would get the old fashioned type and it worked.

My interest was piqued as I saw some of the problems in design. While your application is light duty, that type of gear had done some serious work in the past. One example was the traditional Dutch windmill for either grinding grain or pumping sea water. I didn't read the information on the website but it looked like the author had worked through some of the problems that I saw.

You have to hand it to the Medieval craftsman to design a working gear without the aid of CAD or complicated mathematics.
 

Robo_Pi

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You have to hand it to the Medieval craftsman to design a working gear without the aid of CAD or complicated mathematics.
It does appear to be an easy design on the surface. I only built this one peg gear clock, and I basically built it just off the top of my head using simple obvious math. Without even really taking pin clearance into consideration much. I basically just focused on the pin spacing intuitively to make sure the pins didn't crash into each other. No fancy math. And it did work. It was binding up a little bit in certain places, but I think that was mainly due to lack of precision when drilling the pin holes.

These formulae you've pointed to account for pin length, and pin diameter, etc. You can get pretty carried away with these equations to design the best possible geometry. And that's what I would like to do just for fun and the learning process. This might be especially useful if I eventually move over to making metal pin or peg gears where it's best to get things right the first time through. With the wooden peg gears you can always do a little shaving or sanding where needed. That's a little more trouble with metal pins.

I'm just fascinated with antique technologies.

If you find anymore detailed information on making pin or peg gears I'd really appreciate it if you could post a link to it. These pin gears kind of caught my interest as novelty art. So it's something I'm looking forward to playing with. I've also recently become interested in building Stirling engings and Steampunk art. And so I might like to incorporate pin gears in those projects as well. It's all just for novelty and art.

The page you've provided is the best page I've seen yet in terms of giving some really nice equations to work with. Especially since that page addresses the 90 degree angle gears. I imagine there is probably more detailed info out there somewhere that addresses more complex pin gear configurations. I just haven't been able to find much.

Also, is there a difference between a "Pin Gear", and a "Peg Gear"? Or is that just interchangeable nomenclature? It's definitely an area of study I would like to read up on as much as I can. I'm looking forward to some day making metal pin gears, but I want to gain experience with wooden models first.
 

RJSakowski

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The model that I worked up would work too but there was an interference when the pin on one gear first made contact with the other gear. This was due to the previously engaged pin being closer to the axis of the other gear. It was apparent that for smooth operation, the length of the pins had to be considered. This explains it better than I did.
https://science.howstuffworks.com/transport/engines-equipment/gear1.htm

As to the nomenclature, I have heard both terms used for that type of gear. It seems that the term pin gear is used currently for a gear driven by an involute pinon rather than another pin gear. See also cage gears or lantern gears.
 

Robo_Pi

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Well, I'm really excited about this first web page you linked to. This will basically allow me to design gears around the diameter of the dowel rods I have on stock. I currently have a large inventory of 3/8, 1/4, 3/16, and 1/8 dowel rods. (wooden). These are probably a softwood and would be better if they were hardwood. But this will be fine for prototypes.

So now I can design the gears starting with the pin diameters that I have. That will be my first self-imposed constraint. This will then determine the spacing required between the pins on any given gear.

In my case the height of the pegs is not critical as I can easily adjust for that by simply making the precise position of the gears adjustable. So on the pin length I'll only need to be in the ballpark.

The other self-imposed constraint that I'll be giving myself for right now, will be to use the 24-pin quick-indexing ring on the divider head. That's a restriction I don't really need to adhere to, but would like to stick with if possible.

My actual gear ratios aren't critical since they aren't involved in the timing of the clock. They are more associated with power and leverage considerations. So what I can do is choose the basic ratio diameters that I would like to have, and then go with whatever works out to be close to that ratio.

I can hardly wait to get started calculating!

I just came in from blowing snow. As soon as I take a bath and change my clothes I'll start designing gears based on the wood dowels I have.

Edited to add:

I just now figured out that with a 24 hole indexing plate I can have pin gears with 2, 3, 4, 6, 8, 12, or 24 pins. Not sure how well a 2-pin gear would work, but it's on the list. My original clock had 6 pins on the small gear and 20 pins on the large gear. I have no idea how I came up with that configuration. That was all done just intuitively.

So I might try two designs to start with. A 6-pin small gear, and try that with either a 12-pin or 24-pin gear. Apparently the same 6-pin gear would work on either of the other two sized gears. Also the 12-pin and 24-pin gears should mesh well too. The pin spacing is determined by the diameter of the pins, so the pin spacing will be the same on all the gears. That's kind of interesting to know. In other words I can just make up an assortment of gears based on these pin constraints and any two gears should then mesh together nicely. That's kind of cool. If it turns out to be that easy I'll be sure to get carried away with this. :grin:
 
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Robo_Pi

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A little digging turned up this
http://www.odts.de/southptr/gears/pegs1.htm
Enjoy!
I just have to thank you for finding this fantastic web page. It may not look like much, but it was precisely what I was looking for.

It took me a while to go through their equations to fully understand them. It was a tiny bit confusing because it wasn't crystal clear what some of their variables were representing exactly.

At the bottom of that web page they link to a "Calculation Sheet" which is actually a java program that will do the calculations for you for any size pins and gears you need. At first I was having difficulty with this because I wasn't fully understanding their "minimum dist" calculation. For some reason i was thinking this was them minimum distance between pin spacing on a gear. But clearly that couldn't be right. They I finally realized that this is the minimum distance between pins on different gears when they mesh. Then it finally all made perfect sense.

Also, their java program will only take limited parameters. So you can't really put in numbers for really "sloppy" gears. That was the other thing that threw me off. I was tossing in numbers that I knew would work, but they were simply out of range of what the programmer allowed for. Whoever wrote the program expects you to be designing some pretty close-tolerance gear evidently.

The other thing that was interesting is that they are assuming the pegs just touch or "bottom out" against the opposite gear base plate. And they take into consideration the actual height of the pins. Because of this the pins need to be really short. Less than the full diameter of the pin. Unlike their pictures where the pins are actually taller than their diameter. That still doesn't seem right. Most pin gears I've seen the pins are quite a bit longer than their diameter. The pins on my original clock were 1/4" pins but about 3/4" long. That makes for a very sloppy gear design, but it works. In fact, video I posted in post #2 of this thread uses pins that are far longer than their own diameter. But then again, it's probably not a very efficient design.

Finally, I'd just like to say that the actual pin length is basically unimportant as long as the gear position can be easily adjusted. When assembling all that would be required is to adjust how much of the pins mesh. That would take care of the pin length. The only difference is that the pins wouldn't bottom out against the base of the gear. Instead just the tips of the pins would be meshing. I'll most likely go with longer pins and just make the gear positions easily adjustable.

But this Java program needs to have short pins in order to do its calculations. It's going to assume that the pins "bottom out" when meshing. I guess to write the program the programmer had to have some means of referencing a "perfect adjustment". So just calculating for when the pins bottom out gives that rock solid reference point.

Anyway, it's 5:30 AM and now I can finally go to sleep. I got this all figured out. Tomorrow I can start designing some actual gears.

Thanks again for the quick reference to this wonderful webpage and pin gear calculator. That's exactly what I was looking for.

This saved me from having to figure this stuff all out from scratch.
 

RJSakowski

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The role of pin length in the design was the issue that I saw when I was modeling. I tried varying the spacing , pin diameter, and number of pins on the gear but couldn't make the interference go away.

There is a point in the rotation where the next or previous pins interfere.. This would be like little speed bumps in the rotation which would create a rumble to the motion. By shortening the pins, the previous/next pin would roll off the end, eliminating the interference. The result would be a smooth transition from pin to pin. what bothered me about it was that this would not be a reasonable method of transmitting any significant power due to the wear which would occur.

Modern gears engage multiple teeth at once, distributing the load and providing a smooth transition. The use of an involute pinon solves the problem with modern pin gears.

One thought that I had was to modify the pin ends to something like a bullet shape to provide a smooth transition of load between pins. This would actually be easier than making an involute pinion. It doesn't solve the high stress point issue but for a light load as in your application, could work.

If you haven't done so already, I would encourage you to look at Fusion 360 as a 3D CAD application. It is free for hobbyists and offers the ability model your gears and create assemblies and see the effect of making changes to your designs. It has a fairly steep learning curve but once you have passed that obstacle, you will find it to be a very powerful tool.
 

Robo_Pi

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One thought that I had was to modify the pin ends to something like a bullet shape to provide a smooth transition of load between pins. This would actually be easier than making an involute pinion. It doesn't solve the high stress point issue but for a light load as in your application, could work.
Yes, I agree, it's easy to get carried away and try to "perfect" the peg gear system. But that really defeats its main quality which is simplicity. If we start shaping the pins into actual "teeth" we're really getting deep into "gear making" and leaving the original peg-gear simplicity behind. So yes, I too instantly thought of modifying the tops of the pegs to improve the design, but then instantly caught myself and said STOP! That actually introduces additional machining and manufacturing processes that the original peg-gear system was chosen to avoid. One of the reasons I'm going with peg gears is for simplicty of manufacturing. Just cut off a bunch of pegs to length, stick them into the holes in the wheel and your done. That one of the original attractions (along with the fact that I'm also keen on creating antique-like artwork).

So I've decided to go with unmodified pegs. None the less, I'd still like to design them to be as close in tolerance as possible. That's why I wanted these equations. This way I can actually design without having to resort to trial and error and I can shoot for the smallest amount of play tolerance that is practical for my manufacturing processes. I can already see that these equations are going to give me something far better than the original clock I had hacked together intuitively.

Also there are design considerations that must be acceptable.

1. The gears are best suited for unidirectional motion.

They can actually perform as bidirectional drives too, but there will be quite a bit of backlash slop during reversal. As long as that amount of slop is acceptable they can be used in bidirectional situations. But if the backlash slop is unacceptable then it's time to move on to better gears for that application.

2. The gears are best suited for light power transfer and probably low speeds too.

Again, these are limitations that fit the toys I'm building. Everything is extremely lightweight with no serious power involved, and the gears on my projects will also be turning an extremely low rates. High speed operation is certainly possible, but with wooden peg gears this may result in pegs wearing out very quickly, or even potentially heating up to combustible levels, and we certainly don't want that. Metal peg gears could be used for higher speed operations I imagine.

Since the above restrictions are acceptable for my intended purposes unmodified pegs should work just fine.

Like I say, I was thinking of cutting angles on the ends of the pins to accommodate closer tolerances and less backlash. But at that point I'd actually be making gear teeth. That defeats the original purpose of simplicy of manufacturing.

If you haven't done so already, I would encourage you to look at Fusion 360 as a 3D CAD application. It is free for hobbyists and offers the ability model your gears and create assemblies and see the effect of making changes to your designs. It has a fairly steep learning curve but once you have passed that obstacle, you will find it to be a very powerful tool.
I currently use Sketchup which has been serving me well thus far. Fusion 360 would need to offer some really useful additional features to make it worth my effort to re-learn a whole new CAD program. The only thing I would like to have that Sketchup doesn't have (at least not as far as I know), is an ability to animate the finished drawing. I can actually animate to a very limited degree with Sketch-up. In fact, I have also used Sketchup to make 3-D drawings, and then by simply taking screen shots of various different positions I was able to create animaged GIFs using the static 3-D drawings.

In fact, I'll be drawing up some gears in Sketchup here pretty shortly.
 

Robo_Pi

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I designed the new gears for my clock. I drew up both the original gears that I hobbled together by intuitive feel versus the newly designed gears using the formulae provided by RJ. It's a world of difference! Now I can build clocks that are actually designed instead of just guessed at.

I went with 24 pins on the newly designed clock instead of the original 20 pins to accommodate my 24 hole dividing plate. If I would have stuck with the original 20 pins the new gear would have been even much smaller yet. But this is looking good.

I'm anxious to go out and build the new clock now. But it's like minus 2 degrees out in the shop right now. So maybe tomorrow.


Gears Compared.JPG
 

Robo_Pi

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I just finished drawing up all the gears I'll be able to make with my current constraints.

Obviously the restriction of only making gears using the 24-hole quick-indexing plate is what kept this gear set small. If I remove that constraint and use the entire worm gear of the dividing head I can make gears of any peg count. But for right now I kind of like this constraint. I can just go out in the shop and set up to make these gears and then see what I can build with them. If I run into a situation where I want something different I can always lift these self-imposed constraints. These were all drawn up with 1/4 axle shafts too, but that would be easy enough to change on the fly.

I'm not sure if I'll ever actually use the 4-Peg gear, but you never know. It might come in handy as some kind of a counter, or idler between other gears. So I thought I'd draw it up anyway. The actual drawings include the dimensions. This whole thing is just to get my feet wet using this dividing head. Before too long I'll be moving up to making metal gears, and using the entire range of the dividing head. But this will be a great place to start. Any combination of these gears should mesh well together.


untitled.PNG
 

Robo_Pi

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New Dividing Head Question?

How do I set up for 9 divisions?

I have a 40:1 worm gear dividing head with the following hole plates:

Plate A: 15, 16, 17, 18 ,19, 20
Plate B: 21, 23, 27, 29, 31, 33
Plate C: 37, 39, 41, 43, 47, 49

Can I use this to set up for 9 equally spaced divisions? And if so, which hole circle do I use?

Just to show how stupid I am I did the following calculation, but it didn't work.

40/9 = 4 & 4/9

Since 4/9 can be converted to 8/18 without flunking math, I naively thought that I could use the 18 hole circle on plate A.

I set it up and tried 4 whole turns plus 8 more holes for each division.

But it didn't work. At the end of the run it overlaps and wasn't divided evenly. So apparently I'm an idiot.

Unfortunately I'm not sure how to overcome my lack of intelligence.

I did find a YouTube video that said that to divide into 9 divisions I'll need a 36 hole plate. Is that true?

My dividing head won't do 9 equally-spaced divisions with the dividing plates I have?

That doesn't seem right. This must be far more complicated than I first thought.
 

Robo_Pi

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Huh?

I just read the manual. (I always read the manuals after I can't figure out how something works). :grin:

The problem is that the manual is telling me to do precisely what I just did!

It says for a desired division T for 9 divisions, use the 18 hole plate, and 4 - 8/18 turns of the crank.

That's exactly what I'm doing? I must be counting the 8 extra holes wrong somehow?

untitled.JPG

Just for additional information I did this for 12 divisions and it worked just fine.

I did 12 divisions using 3 turns + 5 holes on a 15 hole circle and that worked out perfect.

And then I did it again using 3 turns + 6 holes on the 18 hole circle and it worked there too!

For some reason this doesn't seem to be working out when I try this for 9 divisions on 18 holes.

I'm doing 4 turns + 8 holes. That should work. The manual even verifies this should work.

I got to be doing something wrong. Maybe I should just go to bed and look at this fresh tomorrow.
 

Robo_Pi

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Ok, never mind.

For some strange reason, after I made all these posts, and downloaded the manual it's working now!

I have no clue why it wasn't working before. I tried it about 5 or 6 times and it was over-wrapping every time. Then I made these posts, downloaded the manual, and went back and tried it again and it came out perfect.

It probably knows that I read the manual now and has decided to behave itself.

Or it could be me. Who knows?
 

Robo_Pi

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I hope it's ok to express my excitement in this "beginner's" forum.

I'm not exactly a beginner as I used to be a machinist years ago. And I have owned several lathes and milling machines over the course of decades. Unfortunately I no longer have those big machines (i.e. Bridgeport mill, South Bend lathe, etc.). Now I just have a small Chinese 3-in-2 lathe/mill/drill.
I've had this dividing head for years and never really used it much. So I'm just getting it out to see what I've been missing. This is all fascinating stuff.

I'm learning a lot about how to use this dividing head pretty quickly. By the way, I found the problem I was having earlier. There is a small sheet-metal spring clip that holds the sector arms in place, and that spring clip was catching on the crank arm and moving the sector arms and that was what was throwing me off. I'll have to fix this. Currently I've just been holding the sector arms in place when measuring the hole count.

Anyway, I just noticed that in the manual to divide something into 3 equal parts they suggest using a 33 hole circle plate and using 13 turns plus 11/33. Or 11 more holes. But I see that there are many plates that can be used for a division of 3 equal parts.

For example:

15 hole circle plate = 13 turns plus 5
18 hole circle plate = 13 turns plus 6
21 hole circle plate = 13 turns plus 7
27 hole circle plate = 13 turns plus 9

And then finally as the manual suggests:

33 hole circle plate = 13 turns plus 11.

And you can even use

39 hole plate = 13 turns plus 13

So there are many more options than the manual suggests. That's good to know if you want to divide by 3 you can do it with any of the three plates that just happens to be on the divider at the time. Lots of choices. This is apparently true for quite a lot of other divisions as well.

I'm catching on quick.

Now I just need to figure out other interesting things to do with a divider besides just making gears.
 
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