equations describing the motion of a gauge pointer

Dear Kevin Nolan:

"Kevin Nolan" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
pass
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I'd go for a damped spring mass system. The speedometer cable acts like a
spring, and winds up. The needle has mass. And the cable lube provides
the dampening. So it would be sinusoudal. Now the needle may over shoot a
little on the high end (the k value might be a little smaller for the
higher speed direction).

So the correct "animation" polynomial would be of infinite order... or just
a couple of sine & cosine terms.

equations describing the motion of a gauge pointer

I am trying to simulate the motion of a gauge pointer (a automobile
tachometer, for example). I have real-time sampled data at more or less
regular intervals. In real life, gauge needles do not register the
instantaneous value. They resist movement and therefore seem to possess a
quantity akin to "mass".

It seems to me that the changes in the sampled data with respect to time are
similar to velocity, and the changes in the velocity are acceleration.
Intuitively this seems the work of a cubic spline, however c-splines are
expensive to compute in real-time and I'm not sure I need that kind of
accuracy, and then there's the problem of incorporating the simulated "mass"
of the instrumentation.

What I'm looking for is an algorithm that will take a stream of sample data,
together with a constant mass that can return a stream of interpolated
points resembling the motion that I'm after.

I've tried using a moving average to smooth out the rather erratic motion of
the pointer, but that's not giving me the behavior that I'm looking for.

It's been over twenty years since I took Calculus. The integration of
constant acceleration to give velocity and then position seems fairly
straightforward, however it seems that I'm dealing with a more complex model
than that.

equations describing the motion of a gauge pointer

I've experimented with using a moving average filter, essentially a low pass
filter, to smooth the data with mixed results. It does a very good job at
smoothing, particularly at high orders, but the problem with the filtered
behavior is that it is inherently linear. I suspect that the behavior that
I looking for is a polynomial of the second order which is definitely
non-linear. Somehow I think it has to do with converting my input stream
into a series of accelerations, integrate them and then interpolate between
integrals.

Consider the tachometer of, say a Porsche 911. The tach tends to
"undershoot" and then "overshoot" the instantaneous measurements. The
motion, empirically, looks non-linear, not just smoothed.

I've created animations of gauge motion using the moving averages
(convolutions), but somehow the motions seems "unnatural". That's really the
problem I'm trying to solve.

Am I missing something?

"Greg Neill" <[Only registered users see links. ].netcom.ca> wrote in message
news:EjfUb.15388$[Only registered users see links. ]. ..
a

equations describing the motion of a gauge pointer

"N:dlzc D:aol T:com (dlzc)" <N: dlzc1 D:cox T:[Only registered users see links. ]> wrote in
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<snip>

....OR...

Newton's Law:

m*a - G*v + k*x = Sum[F(i)]

m = mass
a = acceleration
G = drag coefficient
v = velocity
k = spring constant
x = displacement from equilibrium
F(i) are applied forces

It is a simple differential equation, amenable to a wide selection of
numerical solution methods. You *do* have to characterize the F(i) forces
rather explicitly.