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 http://geargenerator.com/ 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.

Rustic Black Walnut Wood Business Card & Brochure Display

jchismar business card brochure display

Recently my wife Amy opened InnerStasis Therapeutic Massage. Perhaps you recall the live edge sycamore desk I built for her new space.

Amy needed a way to showcase her brochures and business cards in a unique and attractive way. After considering the design for a bit she drafted up a rough design on grid paper. She wanted the displays to be constructed from black walnut. I have a lot of black walnut stored around the house and workshop but most of what I have is thick and suitable for carving.  It would be a shame to resaw the walnut I had so I decided to stop by my local lumbar yard and purchase some rustic black walnut.

With the lumber in the workshop I resawed and planed the wood square. Following the design the wood was cut to size on the table saw. The construction was simple, no joinery or hardware was used. Each part was carefully glued and clamped into place in various stages. This isn’t the most sturdy of assembly methods, but the pair of displays should last a very long time. To complete the displays I applied some water based poly and sanded the surface to a nice sheen with mineral oil and 600 grit sandpaper.

Two-Tier Unknot Corner Shelf

two-tier unknot corner shelf

A friend asked me to build this two-tier unknot corner shelf as a Valentine’s Day gift for her husband. She specifically knew the shelf she desired and clearly described its design. The project was to be built with no hardware and install easily without a hundred screws damaging the wall.
two-tier unknot corner shelfI took a day or two to think about the project and decided to build a prototype of the shelf using a two by four. I drew a schematic of the shelf on a scrap paper and transferred the measurements to the lumber. I also constructed a corner jig out of plywood. The jig keeps everything square and provides something solid to clamp to as the glue dries. With the unit complete I experimented with various ways to install it. I placed a mirror hanger on the back of each vertical support, but with no support in the corner the unit was unstable and drooped away from the wall. After much thought and experimentation I discovered the easiest and strongest support was a mortise in the shelf and a tenon attached to the wall.

two-tier unknot corner shelfThe shelf was to be a blond color with a matte finish. While visiting the wood store the decision was made to use ash wood. I purchased a beautiful piece of 5/4 ash lumber  7 1/2″ wide and 8′ long; enough lumber for two complete shelves. The lumber acclimated in my workshop a few days and it was planed to an inch thick. I proceeded to (1) crosscut the length of each section. With all six sections cut to length I (2) cut 45 degree miters for the left and right sides. (3) Each section was then ripped to 3 1/2″ width.  (4) A stacked dado blade was used to make a 1/2″ dado across the back of the top  shelf sections. Pieces of ash were glued into the ends of the dado to create a mortise.

two-tier unknot corner shelfI waited for the glue to dry and (5) cut the corner miters on the top and bottom shelf sections. I considered various ways of strengthening the joints of the assembled sections. In the end the use of biscuits was the victor. Using a power biscuit jointer I cut biscuit mortises into the surface of each joint. Working one at a time each joint was glued with a biscuit and clamped. Gluing and clamping requires patience and scrutiny to insure each connection is square in every direction.

I waited a day for the glue to set and then started the finishing process. Using a random orbital sander I sanded every surface with 80, 120, 180 grit sandpaper. The sharp ninety-degree corners and edges were slightly rounded with the gentle touch of a cabinet scraper and a sanding block. Rounding the harsh corners provides a luxurious surface to touch and allows for a durable finish.

I applied three to four coats of polyurethane finish by hand, lightly sanding between applications.  The polyurethane finish hardened over a duration of few days and then sanded with steel wool to reduce the glossy appearance.  A super silky feel and rich luster was created on the finish by buffing the surface with rottenstone. I am happy with the complete piece. At my friend’s request I delivered the shelf days before Valentine’s Day. The photos with the books are of the shelf installed in their home.

Because I made two of these shelves I have another currently stored in my shop. Maybe I’ll install it in my home or perhaps someone will be interested in purchasing it from me. Either way, it’s a win. And please be sure to have a Happy Valentine’s Day!

two-tier unknot corner shelf schematic

Bathroom Towel Caddy and Scale Garage

Now that our bathroom renovation is nearly complete we are settling in and hashing out the small details. Spare towels and washcloths were stored in a large wicker basket on the floor in the previous iteration of the bathroom. The basket has taken a beating over time and it doesn’t necessarily match the new décor therefore Amy requested a new towel caddy.

Towel Caddy Scale Garage

Several designs were drafted by Amy before she submitted the final plans for the “towel caddy / scale garage”. Amy indicated in the verbal brief included with the delivery of the design the final project will be painted white. For this reason the variety of wood is unimportant. Initially I was going to use MDF but changed my mind because I don’t believe it will tolerate the periods of high humidity in the bathroom.

In the end I used half inch thick cabinet grade plywood and capped the exposed ends with solid pine. I was going to use oak because it’s durable, but the wood grain of oak reveals through paint. Biscuit joints were utilized to reinforce areas potentially weakened by overstuffing towels into a small space. I added holes for handles to the design to make the caddy easier to move around. The build is complete and is waiting for a few coats of paint.

Wooden Holder for Bar of Shower Soap

wooden bar soap holder

The main bathroom in our home was recently remodeled. In the end the project turned out nice; not without a good deal of aggravation stemming from our contractor. A few odds and ends remain to be straightened out then we can finally, after more than four months, put the process behind us.

We’re slowly acclimating to the new decor and layout as we begin to use the space on a regular basis. The first few days I was placing my bar of soap directly on the tile ledge of the shower niche. My mind began browsing the inventory of our home for something that could be used to hold the soap. Then it dawned on me, I can make something.

As usual, the original plan was something ambitious and complicated. I took some time, gave it some thought and simmered the project down to something simple. I grabbed some poplar bits out from the scrap pile and piece of red oak dowel. After a little sawing, drilling, sanding and gluing I had myself a soap tray for the shower. It’s doing its job nicely and the more I look at it the more I like it.

Black Walnut Hardwood Amethyst Mineral Display Peg Stand / Holder

black walnut hardwood amethyst mineral display peg stand holder

My wife received an amethyst stone as a gift from friends who purchased the stone in Sedona, AZ while vacationing. She asked me to make a rectangular display stand for the cherished gift. A few specific design features were included in the initial request which included pegs for the stone to rest on and a slot in the bottom to store the information card.

My first attempt was  piece of live edge cedar that I had laying around the basement. I knew it wasn’t a rectangular base – and it was a little larger than the volume her hands originally implied. Yeah, she didn’t go for it. A day or two later I saw a schematic drawing, including measurements subtly placed on the coffee table.

I went to work on attempt number two. I grabbed a piece of black walnut, it seems each time I’m making something fancy I grab black walnut, and went to work. Once I figured out how to make the thin slot for the card the rest came together easily. After sanding I added linseed oil to make the grain pop. It’s pretty much what Amy wanted – she’s looking forward to showcasing her amethyst gift.

Acrylic / Oil Paint Artists Toolbox Carry Case

acrylic / oil paint artists toolbox carry case

Recently Amy and I joined an evening painting class at the Yard School in Montclair, NJ. Class is going well and we’re having fun and learning new skills. Purchasing the necessary materials was a job in itself; transporting the heaps of supplies to class in an organized manner proved equally overwhelming.

After the first class I returned home and constructed a handled box similar to an old fashioned toolbox. This toolbox transported the original supplies easily to our second lesson. As the second lesson concluded the teacher provided an expanded list of paints. The original list required four paints, the expanded paint list included thirteen additional colors. Our storage required expansion while maintaining a small footprint to accommodate the tight quarters of the artist’s studio.

Because Amy and I are sharing the paint I designed storage doubling as a handy paint tray. The box for the paint tubes fits inside the toolbox. The two doors on top of the paint box open two hundred and seventy degrees flush with the sides of the box. Each door includes a slot cut through the center allowing the paint tray to saddle the toolbox handle. This design seems to work well for our needs and hopefully will be used a few weeks before requiring a redesign.

How to catch a pet parakeet / budgie on the loose outside

how to catch a pet parakeet

During the last week of July a blue parakeet, or budgie, began eating at our backyard birdfeeder. It was immediately clear this bird was a pet on the run. My wife Amy scanned the local Facebook pages and learned nobody reported a missing bird. Days later she posted photos I took of the beauty on Facebook and a few parties expressed interest in the bird. A neighbor loaned us a cage to assist in the capture.

I placed the bird cage on our brick patio with the guillotine door facing the bird feeder and stacked two bricks on top of each other to make an impromptu staircase to the door. A piece of fishing line was connected to the top of the door, routed over a few impromptu pulleys and through the screen of our kitchen window. The line was pulled taunt keeping the cage door lifted up. Inside our home the terminus end of the line was tied to a rack near the window. Cut the line and the door drops.

Day after day we watched the budgie eat the seed from the ground, repeatedly circling the cage. A week passed and I watched, in shock, as our friend pecked his way onto the bricks leading to the cage door. Is this really happening? He poked his head into the cage, noticed the food tray and hopped in! From inside my home I cut the string and “Wham!” the cage door dropped trapping the feathered fugitive inside.

Hours later Amy delivered the budgie to a new home. We wish many years of enjoyment to the family.

Repair broken NRG Digital Table Warmer 231-0293

repair broken nrg digital table warmer 231-0293

A quality massage table is very important to my wife Amy, a massage therapist. Many clients find the warmth of an electronic table warmer beneficial for various reasons. Enter the NRG Digital Table Warmer 231-0293 found “on sale” for $70+ dollars. Amy purchased one of these pads; it lasted six months before the controller crapped out and died. She purchased another, stored the extra pad and plugged the new controller into the original pad. Give it about six months and that controller bit the dust as well.

Always curious with electronic stuff I took apart a controller to inspect for a blown replaceable fuse. I didn’t find any. I poked around a few of the components with my meter to test continuity, it all checked out. I sent one of the broken controllers to my electronics expert friend Charlie. He found a blown thermal fuse positioned under a resistor on the circuit board enclosed by a glob of thermal compound. When the resistor reaches a temperature above 76 degrees Celsius the fuse trips and permanently shuts down the controller. RIP.

Both Charlie and I went to work locating the manufacturer of the thermal fuse Set Fuse (www.setfuse.com), the Model Number is K0. We reached out to the very enthusiastic and helpful sales department and a week later Charlie received the fuses direct from China. He replaced the fuse and returned the controller to me. I unpacked the box, removed the controller and dashed to the massage table. With the controller attached to the pad I plugged the controller in and Voila! The controller turned on like new.

I possess the remaining replacement fuses and I’m looking forward to repairing the other blown controller. While I have the second controller disassembled I plan on measuring the temperature of the resistor while the unit is functioning to examine how close to the cutoff temperature the resistor becomes. Hopefully the new thermal cutoffs last longer than six months each. At best we extended the life of these otherwise perfectly good objects, keeping them out of the landfill for now.

Full Room Camera Obscura

full room camera obscura

A while back I purchased a lens to create a whole room camera obscura. The only room in our home with appropriate sunlight conditions is where my wife practices her trade. Lucky for me the room wasn’t in use and I was able to black out the windows (I discovered not very well) and position the lens.

My eyes adjusted to the darkened conditions of the room. I was surrounded by our backyard – albeit inverted left-right and upside-down. Amazing! A better job blacking out the windows would enhance the spectacular effect. Nonetheless I was awestruck by watching tree branches sway in the wind in real-time.

I snapped a few pictures (stitched together above) before taking the cardboard off the windows and returning the room to its original condition (debatable if you ask Amy). When the next jumbo sized cardboard box finds its way into my possession I will return to the room with loads of tape and my lens for another try.