[python] Re: frame geometry and pivot angle
- From: George Durbridge <gdurbrid@xxxxxxxxxxxxxx>
- To: python@xxxxxxxxxxxxx
- Date: Thu, 29 Mar 2012 15:56:48 +1100
It works, just try it. It's easier to do than to describe. You have to
keep each half of the paper flat, so the only bend or curve in the paper
is the fold you put in it, and keep one half of the paper perpendicular
to the table.
The lower edge of the paper represents a python frame, hinged at the
fold. That edge lies flat on the table when not bent at the fold
(hinge). If bending the paper at the fold causes one end to bite into
the table, then the hinge of a similar real python will rise when the
frame bends, because the ends of the frame (the two dropouts) are always
held at constant height above ground. In that case, the frame has the
inverse pendulum geometry which contributes to stability.
There's an even easier way to see this, since we are just looking at the
hinge angle and the dropouts. If the distances between the dropouts and
the hinge and the hinge angle are the same, a Python frame has the same
inverse pendulum property, whether it is going forwards or backwards.
Patrick's other point is the real worry with a hinge which is angled
down to the rear. The negative trail will be huge. The trail is the
distance along the ground from the contact point of the front tyre to
the point where the projection of the steering axis meets the ground. By
convention it is positive, if the steering axis ends in front of the
contact patch (as on upright bikes) and negative, if the steering axis
is behind the contact patch (as with Pythons). Positive trail tends to
keep the steering stable, and negative trail tends to make the steering
unstable. On an upright bike, you achieve self-correcting steering by
designing in 2-3 inches of positive trail. This is impossible with a
Python, so you make it stable by a) keeping negative trail to a minimum
and b) the inverse pendulum effect.
On Wed, 2012-03-28 at 21:37 -0400, jan wrote:
> lovely looking bike..but don’t really understand your paper example
>
> From: Patrick van Gompel
> Sent: Wednesday, March 28, 2012 7:22 AM
> To: python@xxxxxxxxxxxxx
> Subject: [python] Re: frame geometry and pivot angle
>
> Hey Mike,
>
> I think Pythons are always made this way:
> front / back (the '/' is the pivot angle) So in words that would
> mean you measure the angle from the back and the hinge is leaning
> backwards.
> I think a Python with a pivot angle the other way would be very hard
> to drive, unless you have some very different setup (like a tadpole
> trike).
>
> You could make a very easy simulation if you want: get a piece of
> paper and make a 65 angled fold in the middle. Unfold and put the
> paper with the edge on a table (the fold should be at 65 angle to the
> table). Now, keep one part vertical (fixed) and move the other left
> or right. If the corner of the paper goes down into the able, you will
> have the python setup and the Centre of Gravity will go up. If the
> corner of the paper goes up from the table, you are doing it wrong ;-p
> (the CoG will go down and the bike will be unstable)
>
> I made a few animations to get a better idea about how the CoG is
> affected. See: http://cycle.free-creativity.com (bottom left: CoG
> animations) I consider a setup with a CoG that goes up when you steer,
> a stable one and a CoG that goes down, unstable.
> For the above paper example you could consider the rear of the Python
> as the fixed vertical element. In my eyes this is because when you are
> just sitting (not driving) on a Python the rear is kept upright with
> either your feet or your hands. When you cycle, it is a mix of both
> (both the rear and front will move when steering) but since most of
> the body weight is attached to the rear, the front will move easier.
>
> Hope make rattling makes sense ;-)
>
> Patrick
>
>
>
> > Date: Wed, 28 Mar 2012 03:22:18 -0700
> > From: mpower.lists@xxxxxxxxxxxx
> > To: python@xxxxxxxxxxxxx
> > Subject: [python] frame geometry and pivot angle
> >
> > I assume based on what I have read that the pivot angle is the
> angle
> > from the ground to the axis of the hinge.
> >
> > Does it matter if the pivot angle is measured from the front of the
> bike
> > versus the back? To put it another way does it matter if the hinge
> > leans forward or backward?
> >
> > I see most pythons with the hinge leaning backwards and I had
> designs
> > with the hinge leaning forward. I am concerned that would affect
> the
> > physics of the bike.
> >
> > Mike Power
> > ============================================================
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