How to Design and Make Automata or Whirligig Gears Using the Power of Geometry

“…Chemistry is not an exact science” ~Mario Andrada

jchismar How To Make Wood Gears

In this post I will do my very best to simplify the process of designing and making gears from wood and other materials. The process to build a simple Spur Gear and Pinwheel Gear will be explained.

Thanks to my background in 3d animation I have a rudimentary understanding of geometry and mathematics. I would love to be a math magician but like many people I get lost with anything beyond algebra. Thank goodness for the internet and calculators!

jchismar N-Gon Automata GearAs my math magician friend Charlie reminded me, “To get the teeth to mesh, the spacing BETWEEN the teeth need to be the SAME on all gears.” With this in mind, using the n-gon is ideal to design a gear, the spacing between each vertex is uniform. Simply stated, an n-gon is a polygon with “n” amount of edges. The image to the left is of an eight sided n-gon. The n-gon has two radius measurements: circumcircle (rc)and incircle (ri). If you need a refresher, the radius is the distance from the center to the outer edge of the n-gon, the diameter is the complete distance from side to side (through the center). Vertices are the angular points where each edge meets (the white “edge” arrows point to vertices).

When designing gears we will focus mostly on the circumcircle radius (rc), the vertices are positioned along this radius.  The vertices will become the teeth of our gears.  If the desire is to use a gear to turn another gear uniformly each gear will be identical resulting with a 1:1 ratio. To use a drive gear to rotate a second gear at half speed the second gear needs twice as many teeth as the drive gear, a 2:1 ratio.

Below I have included a calculator to do all the hard stuff for us.

Say you want to make a pair of gears with a 2:1 ratio, the drive gear turning twice for each turn of the second. You also want the drive gear to have a 1″ radius (2″ diameter). You also want the teeth to be separated by 0.5″. This is easily accomplished with the use of the above calculator. The calculator’s default settings are Edge Length (a): 0.5 and Number of Vertices (n): 8 resulting with radius (rc)  of 0.6535. This radius is just over half of what we desire. We can’t change the Edge Length because in this example we want the tooth spacing to be .5″. Instead, increase the Number of vertices to 12. Now radius (rc) is 0.9664 just under the 1″ radius we were looking for. Perfect!

The 2:1 ratio requires the second gear to have twice as many teeth. This doesn’t mean twice the teeth makes the gear twice as large. Let’s see. In the calculator change the Number of Vertices to 16, doubling the amount of the drive gear. Radius (rc) is 1.9162.

This is important! When I started designing gears I was under the impression that to double the ratio, the radius simply needed to be doubled. This is NOT the case (thanks Charlie)! Let’s examine our calculated radius values:

  • 12 vertices Drive Gear (rc): 0.9664
  • 24 vertices Second Gear (rc): 1.9162

That’s double, right? No. It’s not double. By doubling the drive gear radius (rc), 2 x 0.9664 the product is 1.9328, a difference of 0.0166. Doesn’t seem like a huge deal, but a .0166 error can, in fact, impede the smooth operation of the gears. To emphasize this point let’s examine a more extreme 10:1 ratio example.

  • 12 vertices Drive Gear (rc): 0.9664
  • 120 vertices Second Gear (rc): 9.5552

Multiplying the 12 vertices Drive Gear (rc): 0.9664 by 10 (0.9664 x 10) results with a product of  9.664. That’s 0.1088, or a tenth of an inch, larger than calculated (rc) value.

Making Spur Gears

Right about now you’re probably thinking, “Hey John. I thought you were going to show me how to make gears, not bore me to death with math.” Well, you’re in for a treat, let make some gears! We’ll start by making a pair of spur gears: one 1:1 and another 1:2. A spur gear is a gearwheel with teeth projecting parallel to the wheel’s axis, this is the sort of gear everyone is familiar with. For this example we’ll be making wood gears. You’ll need paper, wood, glue, drill (or drill press), saw, an accurate caliper gauge and a quality pencil compass.  If you don’t own these instruments you can find them at any hardware store – or you can be like me and score vintage beauties at flea markets and estate sales. Cheap tools may work, Harbor Freight – cough, cough, but I often find cheap tools more frustrating than productive.

jchismar How to Make Wooden Gears 01
Step 1

Step 1: Layout the Gear

Laying out the gear is the most important task of making your own gears. I own a few sets of old drafting tools I picked up estate sales for a few dollars. The compasses in these sets are fantastic quality and several of them have an adjustment lock. I use several compasses, and once their settings are perfect, I don’t change a thing until every gear is marked on on wood.

First, calibrate the compasses by drawing on paper. To layout the drive gear use a pencil to draw a small dot on paper, this is the center of the first gear. Set your caliper gauge set (rc): 0.9664 (or as close to this value as the gauge allows) match the pencil compass to this value. Place the compass needle on the pencil center mark and draw the circle. Reference your caliper gauge from the center of the circle to ensure the drawn circle is correct.

Set the caliper gauge to the Edge Length (a): 0.5 and adjust a second pencil compass (preferably locking) to match. Using the circle as reference, draw ticks across the circle (rc) at .5 intervals. When you’ve gone all the way around the circumference your last tick should match the first tick exactly. Refer to the Step 1 image to see my terrible first result (red circle). If it’s not perfect, something went amiss in your settings. You’ll need to start again. This requires patience and practice. The width of the pencil line complicates creating accurate marks. You’ll need to get a feel for the process.

Once you’re comfortable laying out the gear, layout the pattern for each gear on the wood you’re using. This also may require a few tries. Working on this example required about two hours to layout eleven gears from start to finish.

jchismar How To Make Wood Gears 02
Steps 2 & 3

Step 2: Cut Out the Gear

Now you’ll need to cut the round gear from the block of wood. Generally I use the band saw or jigsaw for the task. You can use whatever works best for you: hand jigsaw, Dremel, router, etc. Cut to the outside of the radius (rc) line you created with the compass. Try not to remove the line! Once the gear is roughed out, use a disc sander to shape the circle precisely to the line (bottom left Steps 2 &3 image).

Step 3: Drill a Hole

I generally use 1/8″ wire to mount the gear to the project. The wire serves as the shaft for the gear to rotate about. I use an 1/8″ drill bit in my drill press for the task. Drill an appropriate sized hole centered on the depression you make with an awl. This is the middle of the gear.

After the gear is complete I use a small round file to enlarge the hole to make it rotate more easily on the wire shaft. But that’s the last step!

jchismar How To Make Wooden Gears
Step 4:

Step 4: Add the Teeth

This is where personal preference, practice and experience comes into play. For this example I will be using poplar that I’ve planed to .125″ thickness. The strip of .125″ poplar is ripped on the table saw to .75″ width. Individual teeth are crosscut from the strip to a .75″ length. Each tooth is .125″ x .75″ x .75″.

I’ve constructed a miter bar jig for the table saw to hold the gear while cutting a dado for each tooth around the the gear. The dado I cut is .25″ deep and .125″ wide.  With the table saw jig I am able to center the vertex ticks drawn in Step 1 spaced at .5″ around the gear. I center the tick to the blade, cut the dado. The gear is rotated to center the next tick and the next dado is cut. This process continues until each required dado is cut.

I squirt out a puddle of wood glue on a scrap. I dip the point of a wood skewer (the grocery store kind) into the glue and spread glue into a gear dado. Then, using the skewer, add a little glue to the end of a tooth square. It is important to insert the tooth square into the dado so the wood grain is perpendicular to the dado. If the tooth is attached with the grain parallel to the dado you run the risk of the tooth breaking with the grain.

Continue this process until you’ve completed the gear.

Step 5: You’ve Made a Spur Gear!

Congratulations on making your first gear! Repeat these steps for the second gear (keeping in mind the second gear is larger: 24 vertices Second Gear (rc): 1.9162).

Making Pinwheel Gears

Let’s say your project requires the drive shaft to power another element or shaft at a ninety degree angle. Enter the Pinwheel Gear. You’ll need wood, drill (or drill press), saw, an accurate caliper gauge and a quality pencil compass.

jchismar How To Make a Wood Pinwheel Gear
Step 1: Layout the Pinwheel Gear

Step 1: Layout the Gear

The layout for differential gears is the same as spur gears above. Use an awl to mark center. Then draw the circle with radius (rc) using a compass. Use the compass again to draw evenly spaced vertex ticks around the circle. Because we’ll be using nails as the teeth on these gears we’ll need to draw another larger circle outside radius (rc). In this case radius (rc) is 0.9664, I generally add an eighth of an inch (0.125) resulting with a radius of 1.0914.

Step 2: Cut Out the Gear

Cut the gear to the outside of the largest circle. Then sand precisely to the line.

Step 3: Drill a Hole

This is exactly at Step 3 for the spur gears. I drill a 0.125″ hole centered on the awl mark.

jchismar How To Make Wood Pinwheel Gear
Step 4

Step 4: Add the Teeth

I use the drill press to create an appropriately sized pilot hole at each vertex cross tick. The pilot hole should not be completely through the gear, only as deep as the nail will be driven into the wood. Here, I’m using three penny nails. Start the nail in partway then place a scrap of wood against the nail as a depth gauge. Then hammer the nail until you’re hammering the wood scrap. Continue adding nails in this fashion until your pinwheel gear is complete.

Step 5: You’ve Made a Pinwheel Gear!

You’re an expert gear maker now. Let your imagination run wild! I’d love to see the mechanical creations you’ve built.

A Note About Gears

I started the post with a quote that originated from the 2016 Rio Summer Olympics, “…Chemistry is not an exact science…” This was an Olympics official’s response to questions pertaining to why the pool smelled rotten and the water was green. I’m here to say Chemistry is and exact science. What does this have to do with making gears? Well, making gears is an exact science also. This post, however, is the groundwork to understand how to construct gears, not exact science.

Earlier I posted about building a Pegasus whirligig kit. Assembling the kit was a fun distraction, but I honestly didn’t learn much from the task. I’m a tinkerer. I enjoy spending time considering how to make things, and how things work. I find little satisfaction in following a detailed design – robots do that. I like to build the plane while it’s in the air, as they say. It’s fun to start something, and troubleshoot and modify along the way. This is how I gain a full understanding of the project. I often build many test projects before I tackle the actual build.

Creating mechanical machines is challenging. There is a lot of trial and error involved for the novice (myself included). There is more to designing precision gears than I’ve mentioned in the post. I’ll be honest, I don’t understand most of the technical mumbo jumbo, big words like dedendum, addendum, clearance and working depth versus whole depth. If things don’t work – that’s normal. It’s an entertaining learning experience. I personally find as much enjoyment in the flops as in the successes. When the project is complete, the challenge is over – and that can be a bummer.

Making gears using this method will require trial and error. The space between the gear positions will be an issue. The heads of the nails and the lack of a taper on the ends of the spur gear will likely cause these gears to jam. Consider using a metal cutting wheel to cut the heads off the nails – and taper the metal end. Also consider sanding a taper on each tooth before assembling the spur gear.

For those makers that want a detailed, guaranteed plan you can visit to design and print precise gears. This post will get you started making functioning gears. Please take what you learned here, build on it and make it your own. There’s more than one way to make a gear.

I am planning a follow up post regarding making wooden gears. There will be more information and project ideas to be found in the follow up post. In the meantime, be creative and have fun.

Whirligig Wind Farm

After completing my Maker Faire projects I jumped immediately into creating new whirligig parts to replenish my dangerously low inventory. I hustled a few days resawing and planing cypress lumber for propellers and processing poplar lumber into the various whirligig hubs. It’s amazing what a mess I can make of the workshop doing all that work. I’m also amazed at the amount of unusable lumber bits and imperfect parts that result from the task.

Call me frugal, but I save all the imperfect lumber and parts to use on many personal projects. One of these projects is the Whirligig Wind Farm. Each windmill is constructed from scraps and seconds. I prepared all the parts simultaneously but was unable to assemble the projects because I needed to help Amy tidy the yard and such for a party we were having at our home. While scrambling to organize the workshop I tossed all the completed parts into the kindling bucket.

An hour or so later I realized my mistake, dug everything out of the bin and assembled the windmills. The windmills were installed in the yard and party visitors to were invited to take one home. They were all quickly claimed and are now at their new homes. It feels good to take trash and turn it into something fun.

Buzz-saw Whirligig / Saw-Mill Buzzer

jchismar buzz saw whirligig

Also known as a button-on-a-string, the buzz-saw whirligig is a noise-making device which utilizes an object centered on a loop of cord. The buzzer described in Home-made Toys for Girls and Boys spins a cardboard saw blade to generate its hypnotizing whirring sound. Using both hands the enjoyer must hold each end of the loop and rotate the saw blade to wind the loop. The blade is whirred by adding and releasing tension on the loop which unwinds and, because of the angular momentum of the blade, winds the loop again in the opposite direction.

Making a buzzer is a fun, fast and instantly rewarding project. Cut cardboard, glue a “spool-end” on the center of each side, drill two holes for the cord in the spool-ends, thread the cord through the holes and tie the ends together to create a loop. To my amazement my first buzzer worked splendidly; however Fleur our poodle isn’t as amused by the osculating pitch emanating from the new mysterious gizmo.

I decided build a bunch of buzzers as swag for the Newark Maker Faire. Friends saved cardboard from recycling and donated it to the cause. The cord for the buzzers was retrieved from a pile of bakery string saved from years of bakery boxes. Small bits of recycled broom handle are substituted for spool-ends because I don’t have many spools in inventory.  The title artwork of my exhibit  was printed on the cardboard using a carved linoleum block. To print each buzzer ink was applied to the carved linoleum block using a brayer, the buzzer cardboard was placed over the inked block and pressure was applied to transfer the ink from the block to the cardboard. When the ink dried I cut each buzzer out with a pair of scissors.

Please stop by my exhibit at the Newark Maker Faire, Saturday April 30 to pick up your free buzzer while supplies last!

A Toy Jumping Jack and Eight-blade Windmill

“If at first you don’t succeed, that’s normal” Colbert – Live Free Or Die

jchismar jumping jack whirligig

The Toy Jumping Jack is yet another project I’m building for my Home-Made Toys exhibit for the 2016 Newark Maker Faire. The arms and legs of this toy are pivoted on brads placed through the front and back of the torso. According to the instructions a heavy linen thread is tied at the pivot of each extremity, the opposite ends of the thread are tied to a ring below the torso. Pull the ring downward and “Jack jumps comically” says Mr. Hall, author of the instructions. Why isn’t life that simple?

jchismar wooden jumping jack toyFor me, this project started right as rain. I collected a handful of thin pieces of poplar I saved from various projects and transferred the pattern for the torso, arms and legs. The pivot holes were drilled and the bandsaw was used to cut each part out. The tops of the arms and legs were painted and a strand of thick string was tied to each extremity. Four brads hold the front and back of the torso together and act as pivots for the extremities.

Drum roll please? I pulled the strings down and the arms and legs rotated skyward. Upon slackening the tension, only the legs returned down. The thick string jammed in the narrow shoulder clearance inside the torso. The thin wooden arms didn’t have weight necessary to enable gravity to do its job.

jchismar a toy jumping jack
The tangle of the dangle

The first attempt to resolve the problem was to replace the thick thread with nylon coated stainless steel thread. The new thread was better but the arms were remained too light to function properly. All the original parts were discarded and I found thicker wood to cut new heavier parts. Initially these parts worked well with the steel thread but an unsightly tangle was created when I tried to neatly tie the four lines together.

More attempts to maximize the predictable animation of the jumping jack followed .  The original thread performed best after fiddling around with how it attached to the limb and the location of the knot. Sometimes the task requires a touch more patience and attention than the originally put forth.

Jack’s head was carved from a scrap of basswood; the instructions suggest a wooden spool. This is mostly due to my abundant inventory of basswood scraps and the limited quantity of spools. The completed Jack was installed on the eight-blade windmill I constructed in an earlier post. Jack is so happy to be alive his limbs flail in the blowing wind like the excited customers in 1980’s Toyota commercials.

The Spool Hub Eight-blade Windmill eight blade windmill

Windmills and whirligigs are fascinating and inspiring. I enjoy researching and tinkering with whirligig designs and materials.  My researching efforts led me to discover A. Neely Hall, the craftsman who authored the projects which my 2016 Newark Maker Faire exhibit is based  on. His Eight-blade Windmill, utilizing a thread spool as a hub, is one of the projects I’ve been excited to try.

The illustration above, drafted excellently by Tom P. Hall, clearly describes the construction of the windmill. This windmill  design is perfect for a beginner with limited tools because it eliminates sawing a precisely angled slot to hold the propeller in the hub. Here the hub is a wooden spool with holes drilled in even intervals around the circumference. Each propeller is attached to a spoke via clinched nails. A wood carving knife is used to whittle a point at one end of the spoke to fit into the hub.


Because I am building this project as part of my Maker Faire exhibit I am observing the original instructions as literally as possible. I whittled twenty four spokes to be used on the three windmills I am constructing. Poplar wood was used for the spokes. Most of the spokes had intentionally straight wood grain which aids in easy whittling. The propellers are 3/16″ plywood I had stored in the workshop. Generally I avoid using plywood because I find it doesn’t hold up to the elements, but it was on hand. Each propeller is clinched to the spokes by first driving the nail straight through the work, bending the shank with needle-nose pliers then flattening with a hammer. eight blade windmillUnfortunately a few spokes with less than ideal grain made their way into the project. I should have discarded the poorly grained spokes immediately, but I proceeded. While tapping the imperfect spokes into the hub a telltale cracking sound verified the mistake. The pointed ends snapped off before the spoke was completely seated. To repair the broken spoke I drilled the broken spoke wood from the spool, starting with a narrow drill bit and increasing width until the desired size hole returned.  Then I drilled a one inch deep hole in the spoke where the whittled points broke off. I glued a hardwood dowel into the spoke to serve as a prosthesis which worked nicely. eight blade windmillI re-purposed the Unknot Shelf prototype (from a few weeks ago) into a stand to hold the assembled windmill propellers for brushing on paint. Each propeller will receive two coats of white paint followed by a coat or two of colorful details.  These propellers will be used in a larger project in my Maker Faire exhibit, so you’ll be seeing more on these soon.

Constructing a Vintage Cricket-Rattle : 2016 Greater Newark Maker Faire

A Neely Hall Cricket Rattle

I submitted my application to the 2016 Greater Newark, NJ Maker Faire a few days go for my exhibit titled Home-Made Toys for Girls and Boys. This year I am constructing many of the projects described in A. Neely Hall’s 1915 book Home-Made Toys for Girls and Boys. Anticipating the acceptance of my application I began building several of the toys. In the book Mr. Hall explains, “A Cricket-rattle is about the liveliest form of rattle ever devised. After constructing one for your sister or brother, you probably will decide to make one for yourself.”

john p chismar cricket rattleBecause of his bold statement I decided to make three cricket-rattles to sell or share. The first time I tried the rattle I expected a chirping sound, instead loud cracks shot straight into my ears leaving them ringing. More awesome than I anticipated! Before painting the rattles red or blue, as the instructions asserted, I decided to add tramp art carved embellishment around the fringe which I painted yellow.

I have a few other projects already completed for the faire and many more on the drawing board. With any luck my application will be accepted permitting me to proceed full speed into the past opening doorways to forgotten pastimes. I hope to see you there.

Family Christmas Craft 2015 – Giving My Father’s Puffin Whirligigs Wings

wooden alaska puffin bird wind instructions

A few years ago the Chismar family decided to stop purchasing Christmas gifts for one another. Instead, our family began to create unique crafts to exchange as gifts. The crafts include baked treats, wall clocks, rosaries, placemats and many other imaginative items. The craft exchange is always a hit with much excitement surrounding the reveal of each invention.

A few years ago my father decided to make everyone a puffin bird whirligig, replicating a whirligig he purchased on vacation in Alaska several years prior. The bodies of the puffins were carefully cut out and painted by my father’s hand. The wooden dowel used as the axle for the propeller wings were also cut, painted and inserted into the body. Unfortunately the propeller wings could not be completed in time for the holiday, so the project was packed up and stored in the garage.

About a year ago the box of puffin bodies was passed on to me, where it was stored in my workshop. This year I decided to add wings to my father’s puffin whirligigs. The original wings were plastic and attached to a dowel hub. Preferring wooden parts over plastic parts I created mini hubs and propellers from poplar scraps around the workshop. I spray painted the propeller assembly black and attached each to the axle dowel with a brass screw. It is my hope that we will enjoy our puffins for years to come.

ElectroCallioBreeze – For Greater Newark Maker Faire April 11 2015

The ElectroCallioBreeze is the product of several years of occasional experimentation. This contraption has been on my mind for some time. Preparing an exhibit for the Greater Newark Maker Faire was enough reason to invest resources to the project. My sister Suzanne acquired the xylophone at an estate sale a while ago and it sat on a shelf in my workshop reminding, er inspiring, me until now.

If the cogs were directly attached to the propeller shaft the melody would play too fast, sounding like a Wayne’s World dissolve. To slow the rotation of the cogs I created a second shaft with a belt across two different sized wooden gears. With that mechanism complete I experimented with various cogs to trigger the hammers.

Happy with the belt, gears, cogs and hammers I tested and experimented with the electrical continuity across the cogs and hammers. I consulted with electronics genius friend Charlie to insure I wasn’t going to ruin any of my electronic gizmos by attaching them to the mechanism. With a thumbs-up from Charlie I attached various gizmos to hear what would happen.

This video is of my first full-scale test of the project. Following recording the video I made several adjustments and additions for more reliable functionality. One of the additions is bushings between the hammers to prevent them from walking sideways and missing their target. After disconnecting everything I realized I had a few more noisy gizmos I wanted to attach as well. Perhaps I’ll bring the new sounds with me to the Maker Faire Saturday April 11.

Wood Wind and Wires @ the Greater Newark Mini Maker Faire in Newark, NJ – Saturday, April 11, 2015

wood wind and wires @ the greater newark mini maker faire in newark, nj

Saturday, April 11, 2015 is the Greater Newark Mini Maker Faire in Newark, NJ. For the second year in a row I will be exhibiting some of my wares. Last year my exhibit, titled Urban Lumberjack, was a collection of woodworking projects I created using found wood.

Wood, Wind & Wires is the title of my exhibit this year. I am planning a collection of small projects incorporating three of my interests: woodworking, whirligigs and hobby electronics. Charlie England, a friend and electrical / mechanical engineer, is collaborating on the project to bring everything to life.  Thank goodness because I only know enough about electronics to be dangerous.

Together we’ve been busy designing fun projects for the exhibit. Along the way there have been various levels of success. What’s the point of the exhibit? To challenge, to have fun and to explore imagination. Too many things require a reason; it is important to remember to play and sometimes discover something new in nonsense.

Wind-Driven Mechanical Whirligig Starter Kit

On a whim during early 2013 I placed a few wooden whirligig parts on eBay to see if they’d sell. To my amazement they sold out in days! I made more; those sold as well. Thanks to customer requests my production expanded to include various whirligig parts and hard to find brass hardware. Now, a year later and with thanks to my friend Judy in TN, I am proud to introduce my Wind-Driven Mechanical Whiligig Starter Kit. This kit required a good deal of thought and trial an error; I am very happy with the final product.

This kit is everything necessary to build a base and wind powered motor for your own creation. The builder is free to decide the configuration and theme on their own. I get a thrill contributing my skills to the unique creations of other whirligig enthusiasts. This kit is for sale on eBay for $25 plus s/h. Please email me, if you have any suggestions to improve the kit, or if you need a completely different setup.