Variable Pitch Helix by Equation Curve

[glenn-chun]

You can create a variable pitch helix by using the Equation Curve feature introduced in Inventor 2013.

Create a new 3D Sketch. Start the Equation Curve command.

Here are equations that I use to create helical curves. Many other variations exist, but the following should give you some basic ideas.

Cartesian coordinates:

x(t) = radius * sin(360 * num_turns * t) 

y(t) = radius * cos(360 * num_turns * t)

z(t) = height * t

      = num_turns * pitch * t

Cylindrical coordinates:

r(t) = radius

theta(t) = 360 * num_turns * t

z(t) = (same as Cartesian)

• To make the radius variable, replace radius with radius * t.
• To make the pitch variable, replace pitch with pitch * t.

Examples:

radius = 3 or 3*t

num_turns = 5

height = 10

pitch = 2 or 2*t

t ranges from 0 to 1.

1. constant radius, constant pitch:

Cartesian coordinates:

x(t) = 3*sin(360*5*t)

y(t) = 3*cos(360*5*t)

z(t) = 5*2*t

Cylindrical coordinates:

r(t) = 3

theta(t) = 360*5*t

z(t) = 5*2*t

2. constant radius, variable pitch:

Cartesian coordinates:

x(t) = 3*sin(360*5*t)

y(t) = 3*cos(360*5*t)

z(t) = 5*2*t*t

Cylindrical coordinates:

r(t) = 3

theta(t) = 360*5*t

z(t) = 5*2*t*t

3. variable radius, constant pitch:

Cartesian coordinates:

x(t) = 3*t*sin(360*5*t)

y(t) = 3*t*cos(360*5*t)

z(t) = 5*2*t

Cylindrical coordinates:

r(t) = 3*t

theta(t) = 360*5*t

z(t) = 5*2*t

4. variable radius, variable pitch:

Cartesian coordinates:

x(t) = 3*t*sin(360*5*t)

y(t) = 3*t*cos(360*5*t)

z(t) = 5*2*t*t

Cylindrical coordinates:

r(t) = 3*t

theta(t) = 360*5*t

z(t) = 5*2*t*t

Note: You can use t^2 instead of t*t above.

When you sweep a profile along a helical path, use the plane normal sweep (instead of perpendicular sweep) to orient profiles suitable for coil or spring.  In the example below, the sweep path is a constant radius, variable pitch helix.

HTH,

Glenn

[dacruces]

Thank you very much for this explanation, I have come to understand quite a year I have to make, but I still have the following questions:

How I can make the step variable is logarithmic form taking the first step fixed?

If you can see, I have managed to circle geometry of hexagon but it costs me the logarithmic pitch control.

Greetings and thanks for your help!  

[WHolzwarth]

I think, that's a way to go. I'm not sure about the exact formula of the curve.

Walter

[dacruces]

Thank you very much for your help with the equation, which could not raise either. Find out to see if it is correct, if not, you commented to our wisdom.  

Saludos desde Chile... Danilo Cruces 

[jwillieinventor]

Hi Glenn,

I have followed your post with some interest. I do have a screw profile that i want to create in inventor using the helix function. The profile has seven segments and each segment has a different pitch. When i change the pitch there is a sharp change in the profile that is visible in the 3D geometry. Is there any way i can make the transition smooth in Inventor? I have a cross-section of the profile as an excel file that i can input into inventor.

Thannks in advance for your help.

Jimmy

[gilcos28]

Check this Add-In to solve your problems:

https://github.com/gilcos28/HelixGenerator_advanced