The Problem

How can we make a hula hoop automatically go up a straight vertical pole?

The problem sounds simple, people have been playing with hula hoops for many decades making them go up and down their bodies. However, when it is a straight vertical pole instead of a gyrating human body, a whole new method needs to be developed.

This blog demonstrates a fairly non-intuitive solution to this problem - the resulting machine will make a hula hoop go up a straight vertical pole.

This blog is also probably the only place you will learn about the secret sauce that makes this type of hula hoop work.

This technology uses lots of scientific and engineering principles but there is no physics or engineering textbook that describes how such a device works. The problem must be solved from first principles. The main issue of course is how to impart a vertical force to a free-wheeling hoop to overcome the force of gravity which is always tending to pull the hoop down.

This device uses an electric motor to spin everything, so there is lots of power available, but how can we translate that rotary power into vertical force on a hoop that is not connected to the motor.

You may want think up your own theories before reading further and you may want to watch it in action in the first video demo to see if the clues there are sufficient to figure out how this particular device works.

The Secret Sauce

First I want to coin a technical description for this hula hoop. I call it an unconstrained toothless planetary gear, but there are lots of other scientific principles involved.

Lets talk about the key issue of how a hoop can go up a pole.

Lets start by looking at the forces at work.

We have gravity pulling the hoop down, so to go up we need to apply a vertical force larger than the weight of the hoop.

We can assume the energy for the vertical force will come from the motor spinning the pole, but how does this translate into a vertical force on something not even connected to the motor?

Maybe it is aerodynamic lift like a wing or an Aerobie or Frizbee but in fact those cross sectional shapes don't work well in this application, and this design does not use an airfoil shape or aerodynamic lift as its vertical force.

However aerodynamics do play a role.

If you look closely, you can see the hoop is shaped like a conical skirt. As the hoop spins the leading edge has a downward slope and the air it encounters tends to push it down. That doesn't sound like what we want, but the trailing edge of the hoop is tilted up which pushes the back of the hoop up a bit as the hoops spins. These are not large forces, especially at low speed and they tend to cancel out and in fact end up creating more downward force than upward force.

But if we look at the point where the hoop contacts the pole we can see the hoop is touching at an upward angle.

Since the hoop is rolling around the pole, if the hoop does not slip it will roll up the pole in a spiral.

So what is the vertical force imparted to the hoop - well it uses the principle of the inclined plane and the screw to go in an upward direction, but it is simple friction that prevents slipping and provides the actual force for the hoop to go up the pole. If we have a slippery pole, the hoop will not go up. I think this is an extremely neat use of friction.

Okay but how do we get enough friction to overcome gravity? Well we have centrifugal force from the spinning hoop, pulling the center of mass of the hoop in a horizontal direction.

If the coefficient of friction between the pole and the hoop was 1, then when the centrifugal force equals the force of gravity, there should be enough friction to support the weight of the hoop. Of course the coefficient of friction isn't 1, but this illustrates that friction translates horizontal centrifugal force into a vertical force.

The centrifugal force is proportional to the speed of rotation, so how fast we need to spin depends on the coefficient of friction. If we can have high friction, we can spin slower and still go up.

That explains how the hoop goes up, but there are more tricks needed to get the hoop up the pole.

First of all, if the hoop never touches the pole, it cannot go up the pole, so how do we ensure it will make the right contact with the pole?

If we have a flat plate around the pole, also spinning, the hoop will try and slide off the plate, but the pole will stop it, so this ensures the hoop will slide over and contact the pole.

Centrifugal force will naturally force contact between the hoop and pole to the correct side of the pole.

However, if the hoop is on a flat plate, it cannot tilt and will never start rolling up the pole.

But if we make the plate into a cone, when the hoop contacts the pole it will hang down at an angle. Now if we go fast enough, centrifugal force will lift the edge of the hoop off the cone, which now allows the hoop to respond to the air and tilt into its rolling angle.

That isn't the whole story of course - if the cone is too steep, the hoop will not be able to slide up the cone to contact the pole.

So there is a tradeoff between a cone that is too shallow to launch the hoop and a cone that is too steep for the hoop to contact the pole.

There are several other tricks to make the machine work, like how to safely prevent the hoop from flying off the top of the pole, and how to get the hoop to come down the pole, but the principles just described are the primary principles to grasp in making a hoop like this go up a pole.

There are even more principles involved in this machine, some of which are described in the next section.

 

How Can We Apply These Principles to Design a Working Machine?

This segment discusses some of the design process and related issues.
First - here is a picture showing the parts that are visible:


crown, pole, hoop, launch platter, gears and bearings, encoder skirt, optical coupler, motor mount, chassis, electronics case, optical distance sensor, base plate.


Lets talk about how to design a hoop that can go up a pole.
The previous section described the secret sauce or scientific principles that allow the hula hoop to work. But that is a light years from figuring out all the design parameters to make a working system.
How do we decide the diameter of the pole, or the hoop, or the cross-sectional shape of the hoop, or the pole offset from the center of rotation, or the angle of the cone, or the speed of rotation, or the amount of power it will take to run, or how to balance this revolving pole and hoop, or how to stop the hoop from flying off the top, or how strong all the components have to be, or how to make the pole revolve without rotating or a bunch of other details like gear ratios and bearings and of course what electronics are needed.
Since I know all the principles, I could probably calculate all these parameters and eventually come up with a working design, but that is not what I did.
I simply visualized the entire mechanism and every component in the system in full 3D color animation and what each component had to be to make a working system. When people talk about the human brain as being the best computer, it is just a matter of letting it out for a walk once in a while. Anyway, then I just purchased the necessary components, and designed the rest in CAD to be 3D printed. And it all worked..... well not exactly. I ordered a bunch of gears and bearings just as I visualized, but after accepting the orders, several suppliers cancelled due to some virus going around.
So now I had to design both the bearings and gears for 3D printing. So I did all that, but then I decided it would be better to design all the gears and bearings into the other plastic parts.
This all worked out fine except the gears were now going to be plastic, which could wear out quickly. So I decided the gears had to be proper involute spur gears. Involute gears have teeth with curved surfaces such that the meshing teeth roll on each other with essentially no friction to cause wear. The tooth curve is described by the end of a tangent rolling on the surface of a wheel. After researching them, I concluded that whoever invented involute gears was one smart cookie. It turns out the first analysis I could find was done by one of the most amazing intellects of all time. Leonhard Euler. You have the great minds of all time like Einstien, Newton and Maxwell. And then you have minds like Beethoven, Hawking and especially Euler who accomplished spectacular intellectual feats despite incredible handicaps. If you think visualizing this machine was a neat trick, you should explore what Euler could do and did do even after he went blind.
Anyway, back to gears - my CAD system can't do gears and it is pretty tough to design them from scratch. So I loaded up FreeCAD and learned how to use it to make gears - that is the way to go if you need involute gears - really powerful - saved weeks of work.
The gears driving the pole need to allow it to revolve around a main axle without rotating, like keeping your finger vertical while your hand goes in a horizontal circle. This can be done with identical 3 gears, one is fixed to the chassis and it doesn't rotate. One is on the bottom of the pole, and it doesn't rotate. Think of holding a gear in each hand, one hand doesn't move and the other makes its gear go around the first one without touching. Neither gear is rotating, but one is going around the other. If we put a third (idler) gear in between these two non-rotating gears, it will force this relationship to be maintained as the pole revolves.

There are lots of details to design to ensure all parts are strong enough and the axle and pole remain vertical despite all the stresses. When visualizing this, I just made sure they were bigger than needed so no detailed calculations would be needed.

For the hoop I wanted to make it look more like a hoop than a thick donut so this meant the conical surface would not be too large, which in turn implied it would need to spin fairly quickly to achieve a decent spiral angle. This allowed the launch platter to have a nice shallow conical angle so the hoop would slide to the pole easily. Because, at high speed, centrifugal force will lift the hoop off even a shallow launch cone.

 

The Electrics

This is element 14, so the project needs electrics. It has a DC gearmotor driving the main axle via a flexible coupler. Speed of the revolving pole is a crtical parameter is dictating the centrifugal force, vertical friction force, aerodynamic tilt (spiral angle) and vertical speed, so it is appropriate to measure and display the main axle rotational speed. This is accomplished using an optical coupler to sense an encoder skirt with 50 slots. The sensitivity of the light sensor was adjusted using a red plastic sleeve to the sensor would work under normal lighting as well as strong video lights.

The processing of sensor data was accomplished using an arduino Pro Micro with a 5110 LCD to display speed and height.

The height was measured by a Sharp optical distance sensor. These sensors are great for many applications but not great for this application. Since it needs to capture the hoop height as it passes by a high speed, it must somehow ignore the edges of the hoop and be fast enough to capture a correct height when the hoop is actually above the sensor. This is difficult for this sensor because it uses 2 light sensors to detect a reflection and the angle of the reflection is deduced from the ratio of light hitting each sensor. As the hoop cuts through the beam it causes large variations in the beam which play havoc with the ratio of light hitting each sensor. The sensor does get the correct hieight sometimes, but it is not easy to tell which reading is correct. It might be better to use an ultrasonic sensor, but those may have an issue operating at the speed needed for this application.

Another future enhancement would be to drive the DC gearmotor from a PWM speed control. By using feedback from the optical encoder any precise speed profile could be programmed. A second optical distance senor could be added to detect hand height so the height could be controlled with gestures.

 

Summary

This has been a really fun project that stretched my imagination and it definitely demonstrates a nice mix of scientific and engineering principles, including optical sensors, micro controllers, LCDs, and electric motors, involute gears, aerodynamics, planetary gears, and basic physics properties like friction, inclined planes, screws, rotating hoops and centrifugal force.