Introduction: 3d Printed Gears: Strandbeest Turbine

(UPDATE: thanks to comments from petercd and Kiteman - I have improved the turbine design. See Step8 : Wind Catcher)

---

I've seen a lot of amazing 3d printed things, and have often found myself trying to figure out how they were designed and modelled, how they went from being an awesome idea to becoming an actual physical 3d printed object. I believe gaining such an understanding leads to a deeper appreciation of the object, as well as the ability to make or repair that object myself.

Using my Strandbeest turbine kit as an example, I'll illustrate the general process I went through to design it, as well as some of the specifics of modelling the 3d printed gears that made this design work.

Following the steps in this Instructable, you will be able to make your own Strandbeest turbine kit, and more importantly, get a general idea of the design process which you can adopt for your own 3d printed projects.

Step 1: An Idea

Everything begins with an idea.
(In this case, the initial idea wasn't even entirely original!)

Like many, I was really fascinated by the way the live-sized Strandbeests (by Theo Jansen) walk and interact with the wind. I got myself one of the 3d printed miniature strandbeests when I found out they were available at Shapeways. And when the original propeller kit came out to give the Strandbeest wind propulsion, I thought to myself 'hey, I can probably make something like that!'

I began by looking at the propeller kit to try and understand how it worked: how the kit attached to the Strandbeest, how the gear ratios converted the propeller movement to the legs. I didn't want to replicate the propeller kit, so I started looking into the difference between horizontal axis propeller-like systems vs vertical axis helicopter-like systems. (At one point, I thought maybe I could give my Strandbeest flight capabilities too!)

Without an engineering background, a lot of the maths and physics was beyond me, but I discovered 2 main characteristics of a vertical axis system that I wanted to explore: that it could be driven by wind from any direction, and be more stable spinning around its centre of mass.

Step 2: What You Will Need

Hardware:

It helps to have the Strandbeest physically in front of you, to understand how it works and to visualise how your design will interact with it. A caliper will allow you to build an accurate reference 3d model to base the design on.

Software:

It might be easier to model some of the gear parts with programs like Solidworks, but I want to show how this can be done with freely available software.

For this instructable, I will assume you already know how to build simple 3d models, and have an understanding of the nuances of modelling for 3d printing.

If you are just starting out, Sketchup is a great first program to learn to build 3d models with. If you are familiar with 3d modelling, but haven't designed specifically for 3d printing before, this article by Shapeways designer Laurie Berenhaus gives a detailed overview of the 3d-printing-specific issues that need to be considered.

Lastly, this design is made to be printed with the nylon polyamide12 material on a Selective Laser Sintering (SLS) printer. The SLS printing process offers a higher level of detail over desktop FDM printers, and the nylon material is very sturdy with a bit of flex to it, making it perfect for tiny mechanical parts.

Step 3: Measuring and Creating the Reference Model

Before we start the actual design, we need an accurate reference 3d model.

When I first started this design, I felt that it would be quite neat to fit all the new add-on parts to the center frame of the Strandbeest. So this central section is all we need for our reference model.

It is very important to work off an accurate reference model, otherwise you might find the new parts not fitting properly after they are printed. With the caliper, you can obtain fairly accurate measurements of the overall dimensions and member thicknesses. Depending on the scale of the design, it is usually ok to round measurements off to the nearest 0.5 ~ 1.0mm (even though SLS prints can produce details down to 0.2mm, the flex of the material allows a bit of tolerance)

If you don't have a caliper (or the Strandbeest), I've included my sketchup reference model that you can download and use.

Attachments

The next step is to split the design up into separate components that work together to drive the legs of the Strandbeest. Each component can then be tackled individually as a smaller, more manageable design problem.

This sort of approach work quite well for mechanical designs, especially ones that seems a little too complex at first glance.

This step is really about defining the design objectives for each of the components:

1. turbine (blue) - to catch the wind, spinning on a vertical axis

2. bevel gears (red) - to change the plane of rotation from horizontal to the vertical

3. step down gears (red & green) - using pairs of different sized gears to slow down the 'output' rotation and smooth out the Strandbeest's leg movements

4. a clip-on frame to attach to the Strandbeest and hold these add on components in place. This can be done last as its shape and size depends very much on the first 3 components.

At this stage, we also have a general idea of using the top part of the Strandbeest frame as an axle for some of the gears, and of the need to attach the last gear to the drive shaft. How to actually achieve this on a closed frame would be another design problem we'll need to tackle down the track.

Step 5: Gears 101

When I first designed this, I had no prior experience modelling gears. Luckily there are a lot of guides and tutorials on the Internet, and I found this one by Richard|Capolight particularly helpful.

With the Involute Gear plugin for Sketchup, it is quite straight forward to generate a gear profile based on a few input parameters and then push/pull the profile up to create a simple spur gear.

In more complex machines, the pressure angle of a gear will affect the efficiency and the backlash (gap movement between gears) of the system. These won't be an issue here because our gear won't be spinning at that high a speed and the tolerance of our overall system can be fairly loose.

The consideration for 3d printing is more critical: that each gear tooth needs to be thick enough (>0.7~0.8mm) to not break under load, and that there is enough clearance between the gear teeth (>0.6mm) to prevent them from fusing together during printing. For these reasons, we will use a pressure angle of 25deg, to get a wider base to the gear teeth.

For this pair of gears, we will use a step down ratio of 1:4, so that 4 revolutions of the small gear = 1 revolution of the drive shaft gear. This ratio applies to the number of teeth on each gear (8 : 32) as well as the pitch radius of the gears (3.3mm : 13.2mm). The pitch radius for each gear is calculated from the distance between the centre of the two gears, ie the distance between the drive shaft and the axle.

drive shaft~axle distance = 16.5mm = x + 4x, so x = 3.3mm and 4x = 13.2mm.

No content with a simple spur gear and wanting to make use of 3d printing's ability to construct complex geometries, we will turn this pair of gears into herringbone gears. This can be done by rotating the top face of each gear by the same amount, relative to the gear teeth (eg rotate by half a tooth), and then mirroring that section to form the other half of the gear. With herringbone gears, the pair of gears will be self centering and won't slide out along the axle.

Step 6: More Gears

We have one more set of gears to create, and this one is a bit more challenging. This is the pair of bevel gears at the top that transfer rotation from the vertical axis of the turbine to the horizontal axis of the gears. In addition, we also want this gear pair to step down.

To model this we need to consider the bezel gears as 2 pairs of gear profiles, one pair on the outside (red), one pair on the inside (blue). Start by modelling a pair of truncated cones that, when put together, form a right angle. The radiuses of the circles at the top and bottom of the cones will be the pitch radiuses of our gears (inside 3mm:9mm, outside 4mm:12mm), and the shared inclined plane will be where the 2 gears mesh.

We will use a step down ratio of 1:3 this time, due to the size restriction on the larger gear from where it sits on the axle. Along with the gears from the previous step, we will have an overall 1:12 step down, giving 12 revolutions of the turbine to 1 revolution of the Strandbeest drive shaft. The number of teeth and pitch radiuses will follow the 1:3 ratio - (8:24 teeth, inside 3mm:9mm, outside 4mm:12mm), and we will again use 25deg for the pressure angle.

Take the gear profiles and lay them onto our 2 truncated cones. Then, for our larger gear, separate out 1 gear tooth each from the inner and outer profiles.

Both tooth profiles then need to be rotated to become perpendicular to the meshing plane, using the pitch circle as the rotation axis.

Using the curviloft plugin, we can then join the 2 rotated tooth profiles to form 1 tooth of our bevel gear. Copy rotate this along 15° (360° / 24 teeth) to set the position of the next tooth, so we can add in a face to the trough between the 2 gear teeth.

Group this tooth & trough module together, copy rotate it in 15° multiples to complete the circle, close the hole in the middle and we have our first bevel gear.

Repeat the above process for the smaller gear (rotate in 45° multiples, 360° / 8 teeth) and we will have finished modelling all gears for this design.

Step 7: Attaching the Gears to the Strandbeest

The gears need to be inserted into a close loop/frame, and since we do not want to break the Strandbeest frame or the drive shaft, we will need to create openings in the gears.

The large herringbone gear need to be attached firmly onto the cruciform drive shaft. To do this, we'll modify the gear so it is made in two parts, allowing the gear to open, fit onto the shaft, and then close around it. And the two parts of the gear will need to stay firmly together when the gear is spinning.

Through trail and error, I found that leaving no gap (0mm) between the separate parts actually gave a very snug fit. With the flex and surface roughness of the SLS nylon material, the gears parts are able to hold together and onto the drive shaft fairly well. The two gear parts will need to be separated for printing though, to prevent them from fusing together during printing, due to the clearance between parts being less than 0.6mm.

The small herringbone gear and large bevel gear need to be connected to act as one component in this gear system, and be fitted onto the axle at the top of the Strandbeest frame. To achieve this, we'll make an opening from the side of the gear to the gear's centre, while keeping the gear teeth intact. With the flexibility of the material, we can make this opening (0.8mm) narrower than the axle (1.5mm diameter), so that the gear will bend & clip into place with a bit of pushing, but stay in place when spinning on the axle.

To help the gear spin as freely as possible, we will add in cylindrical bumpers on the inside of the gear sleeve, minimising the contact area and friction between it and the axle. 0.2mm clearance from the bumpers to the axle will give it enough room to spin without catching.

Step 8: The Wind Catcher

(UPDATE - thanks to comments from petercd and Kiteman)
My original turbine design had the vanes orientated flat to the direction of the spin, resulting in a lot of self generated 'eggbeater' drag. I've rotated the vanes to minimize this drag so the turbine spins with less effort. The rounded ends of the vanes doesn't look that bad either!

---

In this step, we will be tackling the last moving component of our design, the turbine.

Wanting to understand how the vertical axis turbine works to catch wind from any direction, I first looked at cup type anemometers. I didn't want to use the cup design for our turbine as it didn't fit aesthetically (with no spherical elements on the Strandbeest). So I took the principle behind the cup anemometer and applied it to something more rectangular. The turbine leaves are angled in such a way that wind from any uniform direction will catch on more surfaces on one side of the turbine than the other, causing it to turn.

The turbine also wants to be as light weight as possible, to minimise load & friction so it can start up with less force, and spin more freely. To do this, the turbine is modelled as an open frame structure, with each turbine vane designed to take a thin paper membrane panel.

Another consideration for the turbine design is how it sits in relation to the Strandbeests. The bottom of our turbine is positioned about 20mm above the top of the Strandbeest frame, giving it enough clearance over the legs to not catch on them when it is spinning. The diameter of the turbine is about 150mm, to match the overall width of the Strandbeest. The turbine vanes are about 40mm wide x 16mm high to provide enough surface area to catch the wind, without being too tall as to unbalance the Strandbeest.

An 8 arm-turbine design is adopted, perhaps from an subconscious bias for the 8 compass directions. Generally, a higher number of turbine leafs gives a smoother spin.

Step 9: And to Hold It All Together

And finally, the clip-on frame that holds everything together. (although it actually only holds the turbine and the small bevel gear in place over the strandbeest!)

Firstly, the small bevel gear needs to be connected to the bottom of the turbine so they act as one component, and the clip-on frame needs to hold this turbine in place while it spins. A 'C' shaped bracket is modelled at the top of our clip-on frame for the turbine to slot into, with the opening of the 'C' is slightly narrower (4.0mm) than the neck of our turbine/gear (5.8mm diameter) so the turbine stays in place once it is clipped in.

A hole (2.4mm diameter) is made at the bottom centre of small bevel gear, for small pin (2.0mm diameter) to slot into. The pin holds the turbine's centre in place on the vertical axis while the turbine spins.

To get the turbine to spin freely, small cylindrical and spherical bumpers are added between the turbine neck and the 'C' bracket to reduce contact area and friction, similar to those used in one of the previous steps.

For our clip-on frame to attach securely to the Strandbeest, small 'c' type clips are used on the 6 corners of the triangular Strandbeest frame.

And to finish it all up, the small 'c' clips, the 'C' bracket and the pin are then connected together to create our clip-on frame. Generally 1.2~1.5mm thick frame members will be sturdy enough for frames of this size.

Step 10: Print, Test, Refine, Print...

There you have it. Now all you have to do is send it off to get it printed (unless you're lucky enough to have access to a SLS machine). Depending on how accurate your reference model is, and how well you have allowed for the right amount of tolerances, your Strandbeest turbine might fit perfectly on first print, or you might need to do a bit of re-modelling. It is not unusual to have to adjust and print a design a several times to get it to the point where you're happy with it.

Once the turbine add-on is working more or less as it should, you can even test out different gear ratios and different turbine designs and configurations.