In my last post I described the math for creating a catenary. Now it's time to get down and dirty and create a family that does this.

The plan is:

• Create a family with a line with a dot at the end that I can hang my line onto - we'll call it "catenary line".
• This family will move the dot horizontally and vertically depending on user input.
• The height of the line will be computed in this family.
• We then create a family "catenary", into which we nest the "catenary line" and which does computing for c.

So let's get cracking.

I start by creating a new Conceptual Mass ( R > New > Conceputual Mass ). And since I want the catenary to be vertical, I set the work plane to the Center(Front/Back) - Reference Plane. On this plane I draw a vertical Line and place a Reference Point at the end.

I then add Dimensions to it and give these dimensions Parameters: x and y.

Now for the "fun" part: the math. I open the Family Types dialogue and enter the following parameters and formulas:

A quick runthrough:

Parameter	Explanation
nr	number of this line (segment)
nr_of_segs	number of segments the catenary will have
x	The distance of the line from (0,0) calculated by multiplying half the length of the arch with the position of the line (segment number divided by total number of segments)
xn	conversion of the distance from (0,0) to a pure number (as opposed to the length x)
y	height of the line at this point (this is where the catenary-formula comes in)
tlen	half the length of the arch
u	number calculated with Newton's Method to get to a
a	constant to put into the catenary formula
e	Euler's Number

Armed with this I can now load this family into the catenary family and start creating the catenary. (Which I'll discuss in the next post).