Dividing Head Question Bonanza

[Robo_Pi]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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.