Algebraic functions obviously.... for variable geometry.

[Acevalefor]

I have a cad program at work that I can insert variables into in order to create drawings that will scale with the overall dimensions. So if I tell it that the overall dimension on the sheet (it's a cardboard cad program) is L=45" x W=30.25" and tell it that it has 5 slots cut out of it at evenly spaced intervals on the X axis, it will place those slots when I tell it what the slot size is.

Here's the problem; I can't figure out the correct algebraic function to get it to space the slots evenly. Can anyone help?

I need it to offset the first slot 3" from the edge and the last slot 3" from the opposite edge. The remaining slots need to be evenly spaced. Let's say the slots are A, the spacing is B, and the offset is C.

I feel like I am missing something incredibly simple here to make this work.

Edit: We are working with a 2D drawing.

Edit: 2 Confound it! The title is supposed to say functions

[solanis]

at the risk of doing your homework for you

A = width of a slot
C = offset = 3
x = width of cardboard
n = # of slots more than the first two
B = space between slots <-- desired variable

(y-6-2A-nA)/(n+1) = B

[Orden]

Mathematical!

[Acevalefor]

at the risk of doing your homework for you

A = width of a slot
C = offset = 3
x = width of cardboard
n = # of slots more than the first two
B = space between slots <-- desired variable

(y-6-2A-nA)/(n+1) = B

It's not homework, but it is something I have been trying to do to make my job easier. I'll plug that in when I get to work in the morning. Thanks for the help. It's been too many years and I am forgetting more than I am remembering.

[Acevalefor]

Hmm, that one doesn't want to work. It won't let me set the offset from both sides. so I have to work from left to right or right to left. Here are the variables I can work with;

W=Width of cardboard = 44.6875"
F=Offset from left edge = 3"(It will be the same for the right edge, but I can't tell the program to set both offsets...it gets angry with me.)
S=Slot width = 3.375"(I can't use A because it is already used for the caliper of the paper)
n=number of slots = 4
D=Distance between slots (unknown)


I was trying to do it as follows: [(W-(2F)-(nS)]/(n-1)=D, which is pretty close to what you showed me solanis, but that equation still spreads the slots out like it's ignoring the paper width. Like the program just spreads everything equally after the first offset.

[Teorem]

How does your CAD software calculate the actual location to put the left edge of each slot? Solving for D won't be enough if you need to get the exact position of each slot along the width; you still have to add the offset and a component for the spacing and the width of the slot itself. Assuming the left edge of the cardboard is along the y-axis (x=0):

x position of slot number y = F + y(S + D)

[Acevalefor]

How does your CAD software calculate the actual location to put the left edge of each slot? Solving for D won't be enough if you need to get the exact position of each slot along the width; you still have to add the offset and a component for the spacing and the width of the slot itself. Assuming the left edge of the cardboard is along the y-axis (x=0):

x position of slot number y = F + y(S + D)

The only slots that I need to have an exact position for are the ones on the outside edges. The rest just need to be evenly spaced. the program runs on centerline calculations based on where I set the pick-up point. So if I set the pick-up point at the left edge, it will tell each line based off of that edge to space evenly across the length. I want it to space evenly across the length minus the offset from each edge. I think this might not be possible because it won't set 2 different constants in a variable equation. I was hoping to find a way to force a calculation even if I have to design the board in 4 different quadrants.