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part picking/stuffing routine

I have a robot with four vacuum fingers. Each finger is used to stuff parts into a tray with twenty four holes arranged into four rows. The parts are picked up from 19 different tray drawers(four layers, 5 wide, one for empty trays) and each tray holds 88 parts. Has anyone written a labview application to handle any kind of a part picking and loading routine?? How to coordinate which vacuum finger to pickup with and what tray position to pick?? How to remember what parts have been picked after rebooting the computer??
 
I have three ABB robot cells setup like this on a conveyor loop with a Telemecanique Premium plc using PL7 programming. There are several custom FIFO function blocks that can get out of sync and disrupt production. There are eleven devices connected to a CISCO 2955 switch sending data around. We don't have much info on how the whole setup works, so it is kind of hard to know how to fix/improve it. I'm wondering if labview could be a substitute. I use labview 7.0 and DSC right now.
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Is there always going to be a part in every nest that you pick from?  I have done something similar, but not as complex.  I used machine vision to determine which nests had parts in them, then only picked those parts.  Each tray was numbered and a file for each tray was used to keep track of parts in that tray.  I just "numbered" the nests in each tray and treated them as a boolean array.  That array could be converted to a number and that is what to store in the file.  I will think about the rest of your situation.
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There should be as long as it keeps track of what it has already picked when starting a new tray. The algorithm to determine where to pick from the tray and which finger to use has got to be ridiculous. Somehow the system needs to know how many fingers to pickup with and which fingers to lower.
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I found a pdf file on a cd from the vendor that shows the layout of the robot cells. This will give you an idea what everything looks like.
It is a 2 Meg download.
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