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
Glenn Chun
Sr. Principal Engineer
