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Design Variable Pitch Helix by Equation Curve

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 Design Variable Pitch Helix by Equation Curve
30-08-2013 03:28 . pm | View his/her posts only

A variable pitch helix is often used in product design, especially in [url=app:ds:mechanical]mech[/url]anical products . In ZW3D, designers can easily create various helixes by using the Equation Curve feature.

Here are some existing equations that are used to create helical curves. Firstly, let’s see the simplest helix with constant radius and constant pitch.

The table below shows the general expression, two different methods.


Cylindrical coordinates Cartesian coordinates

r(t) = Radius

theta(t) = 360*Num_turns*t

z(t) = Num_turns*Pitch*t

x(t) = Radius*sin(360*Num_turns*t)

y(t) = Radius*cos(360*Num_turns*t)

z(t) = Num_turns*Pitch*t
10.jpg
2013-8-30 15:11

For example, Radius=3; Num_turns=5; Pitch=2;


spiral helix.jpg
2013-8-30 15:20

To make the variable radius, just replace Radius with Radius*t.

To make the variable pitch, just replace Pitch with Pitch*t.

Take a look at other spiral curves. (R mans radius; P means pitch)


NameEquationSpiral curve
Spiral curve (constant R, variable P)

1.jpg
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2.jpg
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Spiral curve (variable R, constant
P
)

3.jpg
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4.jpg
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Spiral curve (variable R,
variable P)

5.jpg
2013-8-30 15:24

6.jpg
2013-8-30 15:24

In real design, some spiral curves are irregular, meaning designers couldn’t directly use these existing equation curves. Don’t worry! You can now modify the equation to get your required spiral curves.

Firstly,Let’see if it is possible to use a general expression to cover all of the above cases.

(R: Raduius;
N:Num_turns;
P:Pitch)

7.jpg
2013-8-30 15:27

When R2 and P2 are both 0, this sprial curve is a general spiral helix curve. If R1 and P1 are both 0 , this is a variable radius & variable pitch spiral curve.

So by using this general expression, designers can work more productively!

For example, there is a spiral curve with constant radius (50mm),variable pitch (from 20 to 60mm) and length of 200mm.

According to these given conditions and the general expression, we get the following equations:

8.jpg
2013-8-30 15:27


The result of variables:
N= 5;
P1= 15;
P2=25;

So the expression of this spiral curve is

r(t) = 50

thera(t) = 360 * 5 * t

z(t) = 5* 15* t + 5* 25 * t * t

Case- spiral curve with variable pitch.jpg
2013-8-30 15:24

ZW3D provides many different equation curves, including several different types of spiral curve. Comprehensively understanding the meaning of each parameter, designers are able to use the equation to create their desired curves.

See also