Sure. It'll have to be done over the analog outputs, though.
If you have a VCR, just plug the 510's output to the VCR's input of the same type - S-Video, composite, or RF, depending on what the VCR has. If you use S-Video or composite, you'll also need to connect L & R audio. Set the VCR up to record from that input, cue up the show you want to capture and pause the PVR, hit the record button on the VCR then play on the PVR once the tape starts to move.
You can buy standalone DVD recorders and do exactly the same thing, I think. Better quality than VHS and not obsolete.
Does the 510 have component video output (Red-Green-Blue cables)? If so, and your recorder does, too, use that.
If you want to use your computer to burn DVDs, you'll have to find a way to get the material into the computer. You can't simply copy the contents of the internal HDD to the computer because it is in a proprietary format, and possibly encrypted, to avoid just this sort of thing. You will again have to go through the analog outputs. A Video Capture card or device may work to digitize and store the video output from your 510, but these are (or at least used to be... it's been a while since I've looked) somewhat complex and tempermental, and a bit spendy for a good one.
I have used a Mini-DV camcorder to record the analog output of my old Dish 501 PVR (an hour at a time - the length of a mini-DV tape), then import the camcorder's digital output into my laptop using the laptop's built-in Firewire port. Splice the sections of shows longer than an hour together using video editing software (came with the laptop), trim, then burn a DVD. This is time consuming because the recording and dump of the DV tape are done in real-time, so each hour of material takes more than two hours to transfer, plus time for editing and burning, but I could do it with equipment I had on hand.
Buying a DVD recorder may be your best bet overall in terms of quality, obsolescence, and convenience. I've never used one, though, so take that advice with a few grains of salt, but I've heard that they're pretty much like VCRs to use, and you don't have to rewind. If they're too expensive, maybe you can borrow one?