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Spiral around a helix


Spiral around a helix

I am wondering how to create a spiral around a helical curve. I have no problems creating the helix itself, but I don't know how to iterate it with the spiral along the helical path.

I found the general equations to use, but without definition of the variables.

x = [1+r*cos(wt)]cos(t)
y = [1+r*cos(wt)]sin(t)
z = ht + r*sin(wt)

From what I can tell, h is the height of the helix, r is the radius of the helix, t is the number revolutions in radians.

I gathered these from the helix equations

x = r*cos(t)
y = r*sin(t)
z = ct where c is the pitch of the helix.

What is w and how do I time step the spiral around each time step of the helix?



Does it help ?

We can use for helix-plot a cylinder coordinate of the 3DPlot too.
Valery Ochkov

Try this.



How would it work as car suspension ?
If you like DE ... here is a nice exercise !


Actually, it's for a bimetallic temperature element. In short, a very complex thermostat spring.

Imagine a thin, narrow, and very long piece of sheet metal. Now that that strip of metal and coil it into what looks like a drinking straw. Then take that drinking straw and bend it into a helix. As temperature increases, helix expands axially; as temperature decreases, helix contracts axially.

I need these XYZ data points to create a curve in my CAD package that I can create the solid model from to throw into our FEA package to size the original piece of sheet metal.

Although using it in car suspension would be fun. Could you imagine the maintenance?

Thanks all,


>>Actually, it's for a bimetallic temperature element. In short, a very complex thermostat spring.<<

I know those things ( as an Instrumentation man ).
Then you just need the blue line from Xavier.
Or the one posted last night, conical spring.

The best car suspension (smooth) is the hydraulic, like in the french Citro�n (the old ID, DS ... now: don't know ?)


Huh! They were also very prone to low frequency oscillation that made them wallow like barges - the old Citroen's were the only vehicle of any kind (so far) to make me ill - and vehicles includes boats, subs, light aircraft(+/- g!), gliders and fast cars.


Thanks, Xavier

That's exactly what I'm looking for. If I may ask, though, what are your graph settings. I've been having a few problems with mine looking correct even when I know the data is correct. Needless to say, my graph is just a garbled bunch of lines and I would like to clean it up.

Thanks again.


On 10/9/2003 10:49:24 AM, swertel wrote:
>That's exactly what I'm
>looking for. If I may ask,
>though, what are your graph
>settings. I've been having a
>few problems with mine looking
>correct even when I know the
>data is correct. Needless to
>say, my graph is just a
>garbled bunch of lines and I
>would like to clean it up.

You need to set the type of the second plot to "Scatter plot". It comes up as "Surface plot" by default. Also, in the appearance section check "Lines" and uncheck "Draw points".


The solution proposed above assumes that the plane of the spiral is vertical, which is not quite as satisfactory as having the plane of the spiral being perpendicular to the helix axis. This second case is illustrated below.


Another comment on my graphing problem. Even when I open your file, the graph looks nothing like your picture.

I'm running SP1 for 2001 Pro.

Never mind, sorry about all the extra posts. My computer froze at generating the first graph of Xavier's file. I didn't realize that there was a second section. All is well.

I saved the file from Mathcad11. I've had problems in the past with 3D plots when saving to Mathcad versions predating 2001i.


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