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- Re: Variable Pitch Helix by Equation Curve

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5902 Views, 22 Replies

06-20-2012 12:36 AM

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

Autodesk T-Splines Component Development

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06-20-2012 05:37 AM in reply to:
GlennChun

I think you guys just made my day!!

Autodesk Inventor 2012 Certified Assosicate

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Autodesk Inventor 2012 Certified Professional

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06-20-2012 06:18 AM in reply to:
GlennChun

Now if you can flatten that I will be impressed.

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06-20-2012 12:20 PM in reply to:
GlennChun

FINALLY!!!! Thanks for posting this.

<snark>

Maybe we'll be able to do equation surfaces by 2020.

</snark>

Inventor Professional 2014

Windows 7, x64

Dual-core i7, 8GB RAM

NVIDIA Quadro FX 880M

HP Elitebook 8540w

Windows 7, x64

Dual-core i7, 8GB RAM

NVIDIA Quadro FX 880M

HP Elitebook 8540w

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06-26-2013 10:11 AM in reply to:
GlennChun

Glen,

Thanks for the equations. Do you know of equations for compression springs?

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06-26-2013 12:19 PM in reply to:
sention

Hi sention,

When you create a coil, spring, or helix sweep, please use the **Coil** command or **Helical Curve** command in 3D Sketch whenever you can for optimized performance/capacity.

- To create
**constant-pitch**helix, you'd better use the**Coil**or**Helical Curve**command than the**Equation Curve**command. - To create
**variable-pitch**helix, use the**Equation Curve**command since the**Coil**or**Helical Curve**command doesn't offer that functionality.

By looking at your drawing, I see everything as a constant-pitch helix. I would use three **Coil** features in this case.

I defined the following parameters before I designed this model. You can see/edit these in the **Parameters** dialog > **User Parameters**.

helix_radius = 10 mm

wire_radius = 1 mm

wire_diameter = 2 * wire_radius

active_coil_pitch = 4 * wire_diameter

active_coil_num_revolution = 5

active_coil_height = active_coil_pitch * active_coil_num_revolution

dead_coil_pitch = wire_diameter

dead_coil_num_revolution = 3

dead_coil_height = dead_coil_pitch * dead_coil_num_revolution

For the 'dead coils', the pictch is the same as the wire diameter, and this is possible only in Inventor 2014 and later. See **Type 3b** in my recent post called **Demystifying Self-intersecting Sweep**

http://forums.autodesk.com/t5/Autodesk-Inventor/De

Attached is the part that I created in Inventor 2014. Every surface in this model is analytic geometry (rather than NURBS), so you can feel the optimized performance. All planes of the cross-sectional profiles in the three Coil features contain the helical axis (Z-axis in this case).

Hope that helps,

Glenn

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06-26-2013 01:03 PM in reply to:
GlennChun

In my example above, the transition between the active coil and each dead coil is not tangent-continuous. If you want smooth transitions, the above technique is not appropriate.

Glenn

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06-26-2013 04:35 PM in reply to:
GlennChun

If you want smooth transitions between active and dead coils, here's a workflow that you could use.

In the attached *compression_spring_2_glenn.ipt*, I added the following parameters:

*entire_coil_height *= active_coil_height + 2 ul * dead_coil_height

*active_coil_len *= active_coil_num_revolution * sqrt((active_coil_pitch) ^ 2 ul + ( 2 ul * PI * helix_radius ) ^ 2 ul)

*dead_coil_len* = dead_coil_num_revolution * sqrt((dead_coil_pitch) ^ 2 ul + ( 2 ul * PI * helix_radius ) ^ 2 ul)

*entire_coil_height *is used as the height of the cylindrical surface (The first feature in the model). *active_coil_len* and *dead_coil_len *are used in the **Aligned** dimensions for the three lines in the sketch called **curves to project**.

If you project the three lines to the cylinder, using the **Wrap to surface** functionality of the **Project Curve to Surface** command, the sweep path would be the same as *compression_spring_glenn.ipt*, except for performance/capacity. To make the **projected curves** tangent-continuous, I added two sketch fillets as shown below. I randomly chose R=100 mm for fillets. Instead of three lines and two fillets, a spline curve could be used.

For the sweep feature, I used the **plane normal sweep** (aka **pull-direction sweep**). The guide surface is the XY plane since the helical axis is the Z-axis in this model. That makes the planes of all cross-sectional profiles in the sweep body contain the helical axis.

A drawback with using the **Wrap to surface** functionality of the **Project Curve to Surface** command is low performance and huge file size. If you open the *compression_spring_2_glenn.ipt*, move the **End of Part** to the bottom, and save the part, then you will see the file size become ~2,300 KB. The previously attached part, *compression_spring_glenn.ipt*, is only 360 KB. The Inventor development team is aware of the performance/capacity issue with the **Wrap to surface**.

If anyone knows of any equation for the compression spring, please post it. Performance/capacity of using the **Equation Curve** command is somewhere between analytic geometry from the **Helical Curve**/**Coil** command and the NURBS from **Wrap to surface**.

Glenn

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06-26-2013 05:20 PM in reply to:
GlennChun

The above screenshots using the "Right" view do not really show the difference.

Here's the "Top" view that shows the difference between the two models. The red arrow below indicates G0 continuity between the dead coil ad active coil. The second model shows G1 continuity (tangent-continuous).

Glenn

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07-07-2013 06:38 PM in reply to:
GlennChun

When sweeping, can you make it such that the profiles all angle towards a single point, say in the center of the helix at its base? If so, how?? Thanks!

GlennChun wrote:When you sweep a profile along a helical path, use the

plane normal sweep(instead ofperpendicular sweep) to orient profiles suitable for coil or spring. In the example below, the sweep path is a constant radius, variable pitch helix.

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