[python] Wheel movement numbers for four-bar-linkage python (was Re: Sketches of...)

  • From: Michael Rienstra <ageless@xxxxxxxxxxxxx>
  • To: python@xxxxxxxxxxxxx
  • Date: Wed, 25 Aug 2004 23:33:52 -0700

Dirk,

You raise an excellent point, which I have put some thought into, although my ideas are still a bit raw!

First off, I should say (mostly to myself because I tend to get very excited by my own ideas) that it is possible that this idea is a 'dead end', at least in regards to steering a FWD moving BB lowracer. It may turn out that the bearings need to be so heavy and strong that it would be better to stick with the Python design, or with Tom Traylor's design. It might also be unstable for several reasons. But hopefully we will soon know if this idea has merit!

In regards to overall size / movement of the four bar linkage:

First off, what one considers an acceptable turning radius varies widely. Those who commute on lowracers (a small group to be sure) must choose to accept a rather large turning radius. We are all discussing the Python design, which if I am not mistaken, has a rather large turning radius (I have yet to build/learn to ride my own, so forgive me if this is not the case). Right now, I ride a BikeE, which has a fantastic turning radius -- not just the maximum possible turning radius (such as when walking the bike) but the actual practical turning radius is fabulous, which I will surely miss if I choose to ride almost any sort of lowracer (I might be generalizing too much by thinking that all lowracers have a poor turning radius).

Second, the wheelbase will of course affect the turning radius. Tom Traylor's website doesn't specifically mention the turning radius of his design(s), but I measured the wheelbase of his older design as roughly 117 cm / 46" (although it might be different on his newer bike(s)), which is respectably shorter than the Python (130 cm / 51"). Also, because it pivots around the front wheel, it should have a better turning radius than the Python. For comparison, my BikeE has the same wheelbase as the Python, and if I turn the handlebars 45 degrees, my turning radius is 208 cm / 82", which allows me to make a U-turn on my one-way street (with cars parked on both sides). What I'm saying is that with a shorter wheelbase (than the Python/my BikeE), although 60 degrees would be better than 45 degrees, it's not absolutely necessary. Perhaps others (any lowracer riders out there?) could comment on how much they turn their front wheel, what the wheelbase of their bike is, etc. There is probably a simple equation to calculate the turning radius of a given setup but I don't know what it is...

So far I've been avoiding the question! Time for some hard numbers, eh? OK...

The distance between the pivots under the seat is called the ground link, or 'G' (in the formulas below). The two connecting linkages are called side links, or 'S'. The distance between the two pivots points on the front frame is called the coupler link, or 'C' (these terms seem to be popular when discussing a four bar linkage).

Here is one possible geometry, but hardly the only possibility -- we can all play with these numbers -- I can't wait! I wish I didn't have to go to bed so soon...

ground link = G = 30 cm = ~12"
side links = S = 15 cm = ~6"
coupler link = C = 21 cm = ~8"

When the front wheel is in the neutral position, the distance 'D' from the midpoint of the coupler link 'G' to the virtual pivot point 'V' is given by (attached image of formula may be at end of file depending upon your email program:

GIF image



Plugging in the values of G, S and C from above we get:

D = 33.4 cm

Which gives us room for a wheel with an OD of around 62 cm / 24", allowing for the width of 'C', the coupler linkage, along with a small gap, assuming that the virtual rake is zero (it will increase as the wheel rotates).

Some crude observations from a crude cardboard model:

When the wheel is turned 40 degrees to the left, the right-hand 'S' side link will be parallel to the long axis of the bike, while the left-hand 'S' side link will be perpendicular to the long axis of the bike. Which means that the virtual pivot will be located at the right-side 'G' ground link pivot, meaning that during a sharp turn it would behave somewhat like a Python! Just like a Python the wheel axis would actually be far to the left of the centerline during a sharp turn.

When the wheel is turned 25 degrees to the left, the left-hand 'S' side link will be parallel to the 'C' coupler link, which means that the virtual pivot will be located at the right-side 'C' coupler link pivot, and again, the wheel axis be be rather far to the left of the centerline.

In other words, the geometry given above (i.e. specific values of G, S and C) might be difficult to keep centered, since the virtual pivot moves back rather sharply as the steering angle increases. On the other hand, a Python-esque weight-centering effect will occur as the virtual pivot drops back and down! Very interesting!

I really want to stay up for a little longer and try a few more geometries!

But, alas, I must go to bed since it is nearing 11:30 pm, and I must get up at 4:30 am. I was going to take a nap since I got up at 4:30 am today as well, but I was too excited to sleep!

More to come!

Michael

PS: Sorry about the slightly confusing system. We could use a slightly better coordinate system, and it would probably be best to ditch G, S and C and replace them with four points and four line segments, but that's for another day! Everyone, feel free to re-conceptualize it in a way that makes sense to you!

PPS: Chris Broome has a page on Tom Traylor: http://home.earthlink.net/~ccbroome/traylor.html


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