I am unable to transfer images from my Canon Rebel XTi to my iMac OS X Yosemite (10.10.5) using the cord provided with the camera. I know my computer recognizes the camera. I can put them on my Windows laptop and get them off and then transfer with a thumb drive but I don't have time to do that every day.
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Read through this thread and see if it helps. If not, report back with the steps you are using and any error messages that pop up.
Is your cable connected directly from camera to computer with no USB hub involved? I have gone through probably three or maybe 4 different USB hubs before I actually found one that works reliable with all devices (there's a lot of junk on the market). But connecting direct to the USB port should work.
You mention that you know the comptuer recognizes the camera. How do you know this? Are you looking at the "System Information" app (it's found in the "Applications" -> "Utilities" folder on your Mac) and reviewing the devices that are attached to the USB bus (note that the app only lists the devices that were attached when it scanned the bus. If you start the app, then connect the camera and power it on, then the camera wont show up in the list unless you re-scan.)
What software are you attempting to use to communicate with the camera? Canon EOS Utility? iPhoto or Photos? Something else?