# Dynamic stability of a tricycle

I'm currently designing the "electric bike of my dream" (please do not laugh! it's for fun, nothing serious), and I came up after some though with a tricycle, where 2 rear wheels are supporting the battery and cargo weight, and a suspended front part for the rider.

The simplified kinematic of the bike is the following:

The link between the front part (in blue and red) and the rear part (in orange and green) would be made by two rotations: R1 for suspension, R2 to be able to move the front part sideways when making a turn. The rear part is supposed to stay vertical (well, more or less perpendicular to the road anyway).

My question is about the suspension part, and its influence on the "rideability" of the bike. I was thinking of putting two suspensions (SL and SR) to provide some positive "feedback" on R2 when making a turn, and to make the front part stay vertical when parked. On paper this looks nice, but I was thinking that this may be a problem when:

1. the road has potholes, or when crossing some curb sideways: the front part (and the rider) will experience some disturbing force sideways;
2. when making a turn the behavior will not be exactly the one of a normal bike as you need a stronger push to tilt the front part.

The feedback force and behavior would depend on the choice of d and h as seen on the diagram (h can be made negative if needed).

Another (probably simpler) solution is to only have one suspension in place of SL and SR, w/o any "feedback" couple.

What would be better in your opinion? Does a small feedback for R2 would render the bike not rideable?

As a bonus some "artist" views to get the whole picture (on the rear view you see only one suspension):

• The amount that we lean a bicycle when turning a corner depends upon the radius of the corner and our speed. I don't see in this design how such variable amounts (angles) of lean are achieved. Commented Aug 18, 2016 at 22:32
• 3-wheeled vehicles with a single wheel in front are notoriously unstable. Commented Aug 18, 2016 at 22:37
• The leaning design gets around the lack of stability, and as long as there's enough suspension travel 20-30 degrees of tilt each way should be possible. I'm also guessing from the sketches that it's not really intended for high speed use - I'm guessing 30kph or less. The battery between the rear wheels will help keep the back end stable too. I would model it as a two wheeler with the actual weight distribution, then work out an approximate point at which the inside rear wheel will lift. But I expect loss of traction to occur before then. Get a bike and replace the back end with the trike.
– Móż
Commented Aug 19, 2016 at 0:42
• Side note about the chain and gears: if you twist the front part including the BB, i would expect your chain do come off or get tangled a lot. And if you instead keep the BB and twist the rest, the feeling on the pedals will most likely be very awkward. I guess this design would work best with a shaft drive. Although that would still create some feedback from leaning. Commented Oct 25, 2023 at 7:00
• Similar project has already been done here contest.techbriefs.com/2014/entries/automotive-transportation/… Maybe you can contact author for questions Commented Oct 25, 2023 at 8:17

The bicycle is a deceptively simple machine. The physics behind bicycles is actually quite complex, with multiple forces interacting to produce self-stabilizing behaviour (i.e., ghost ride a regular bike then run along and strike it, the bike will deviate from its current trajectory and self right). For a good rundown of the main physics principles behind this behaviour, see this short "MinutePhysics" video.

The take home is there isn't a single optimal bicycle handling archetype, but rather there are multiple optimal solutions that are "better" at different use cases. To start to be able to answer which of your designs might be "better" we also need a clear use case and bicycle dynamics we wish to mimic.

To further confuse the matter the reason bicycles are a intuitive to ride as they are (after an initial training/learning phase) is that balance on a bike also co-ops neural pathways in our brain dedicated to walking (i.e., when we walk we step into the direction we are falling and in the same way we turn into a fall on a bike). Coming up with a functional design that is "intuitive" to the end user will be somewhat complicated, as we must also understand how people walk.

Taken together you may find an empirical approach (i.e., trial and error) may be the most effective. I would suggest creating a modular design that would allow you to easily switch between a single suspension beam without any "feedback" coupling, or a design with suspension beams. Ideally, you would also be able to dynamically adjust the level of feedback so you can vary it until it becomes more "natural."

Finally, you mentioned

1. when making a turn the behavior will not be exactly the one of a normal bike as you need a stronger push to tilt the front part.

In this case you may want to consider a lower trail front end as it is my understanding that having less caster makes it is easier to initiate a lean. Also a higher bottom bracket height may also assist in this department (think of balancing a broom on you hand, keeping the weight up high makes corrections easier). [NOTE: I am really outside my area of expertise in this last paragraph, if my understanding is wrong please feel free to add a correction in the comments.]

• Thanks a lot. For the latter part, I'm not found of increasing the bracket height, as in my design this would raise the cargo (for the chain passage), also IMHO this would render the bike more difficult to mount/unmount, I did not mentioned this, but I'm focusing on a "urban bike". Commented Aug 19, 2016 at 7:24

Static conditions This may be looked upon as being simple, but it is not as the level of the road can take any pitching or lateral angle and so the high three dimensional centre of gravity will add a lot of complications , even if the forces are to be considered to be vertical in a static situation. In a dynamic situation forces in other directions do come in including a possible wind and turbulence, centrifugal forces and the pitching and rolling of the road. I would not dare to discuss the general situation in a dynamic condition including acceleration from rest or braking and each situation would better be taken on its own merit. One priority is sure..........It is not easy to balance a tricycle as the centre of gravity cannot be kept on the line of motion and the torque effect due to any reason will give any rider a bit of a headache. A solid structure of a trike is not easy to handle . A trike with suspension has its own difficult consideration. No trike is advised for a beginner as while it looks stable, well there are hidden force and condition which will give any trike the capacity to surprise any rider including the suspension and any twist of the frame.