Help: How to make spiral/helix along truncated cone?

rhino
(Joycevkim) #1

Hi all,

I’ve been trying to make these spiral stairs that decrease in width as it goes up in height.
It’s important that the spiral stay consistent.
The stairs takes 11 turns with 360 steps.

I’ve tried to flowalongsrf a helix onto a truncated cone which does create a spiral that is correct in the x-y direction but not consistent in the z direction.

(my attempt)

(reference) - I would like to recreate these steps. What is the best way to do this? Thank you!!

(Diego Krause) #2

Have you tried with _Pull instead of _Flow?

(Joycevkim) #3

I get the same result from using the pull command. It seems that the spiral gets more spaced out near the top and more compressed at the bottom. Where as in the reference photo the spiral seems to become more compressed at the top.

#4

That is correct, due to the decreasing length of the path of a single turn, but with a constant climbing angle, you will get less height gain on every turn.

This looks like a simple proposition, but it is actually difficult to construct. I did try it before, but ended with an approximation where I literally took it step by step, more or less, creating successive points on the cone surface, and creating the path with a curve through points command.

Max.

#5

I gave it another shot:

create a flat spiral:


extrude it into a vertical surface:

command Squish

draw a diagonal to represent a continuous rise angle of your staircase:

create a step pattern by dividing the diagonal in the required number of steps, create a single step and use ArrayLinear to create all steps, then join into one curve (for convenience only, selecting all steps for the next action will also work):

select the squished surface together with the line representing the step pattern, and SquishBack:

delete the surface and hey presto!:

side view, check the decreasing height of each turn:

Now to create the actual steps…:sweat_smile:

Max.

1 Like
#6

The subject intrigued me, so I kept experimenting a bit. I now made a staircase more or less to your reference example. The dimensioning is a bit sketchy, so I guessed the inner (1 meter) and outer (5 meter) radius of the spiral.
Creating the steps is actually far less sweat than I expected. I used the command Fin, which creates a surface from a curve on a base surface, with a given width, perpendicular to that base surface. So, before deleting the extruded spiral surface, I typed Fin, picked the steps pattern and hit enter, typed the width value at -100 cm, picked the spiral surface and the entire staircase was created in one go. Magic.
Btw, you have to be patient after typing the Squish command, at takes a while for Rhino to calculate it (at least om my ageing Mac (10 years)), but it gets there in the end.

As you can see in my pictures, the shape of the steps changes from near rectangular at the bottom to a triangle shape at the top (because I selected a top radius of 1 m, and the same for the width). When you are doing a real design intended for construction, you will have to look into the building regulations governing stair design. It will most likely give you a maximum step height, the minimum width and also the restrictions to the minimum depth of each step as a dependant of the turning radius.

Good luck with your design,

Max.

SpiralStaircase.3dm (9.8 MB)

Edit: I noted that some of my pictures are curtailed, so not all gyrations are shown…:frowning:
Edit 2: Rhino file attached.
Edit 3: Oops! There is a major flaw to all of the above, it is not cone-shaped! And I was so happy thinking I cracked it…What happened is, as the basis is a flat spiral, every consecutive pass is at an even distance to the previous. This was raised to the outer edge of the spiral staircase, and the same is true there, each consecutive pass of a particular station is further inward by an equal amount. But because of the phenomena I discussed in my first reply above, the vertical distance becomes ever smaller the higher you get, and for it to be a true cone, also that should be constant!

Alas…:disappointed_relieved:

3 Likes
(Diego Krause) #7

just… wow

#8

Also have a look at this topic:

#9

Could not help myself, just had to build one:

1 Like
Non planar circular surface