When I was building my Stapleton/GMProps Mk X medical tricorder, I wanted to add a rechargeable battery, but didn't like the idea of a visible power jack on the exterior. Also I wanted to avoid having to remove the back for charging, as that seemed like a recipe for lost screws or some other disaster. So I went with another option - wireless (induction) charging 
The commonly available product line for this is Powermat, and many perfectly good (discontinued) items can be had rather inexpensively on eBay. There are different ways to go about this, but here's a quick summary of what I did for mine.
DISCLAIMER/WARNING: As far as I know, this is ok to do. HOWEVER I am not an electrical engineer and I make no guarantees that this is safe (especially the alternate methods). Improperly charged lithium batteries can explode and/or cause fires! If you aren't comfortable trying this and/or don't understand it, don't do it! If I did something horribly wrong please speak up :lol
The ingredients:
-Micro-USB LiPo charger board from Jaycon Systems ( Micro-USB Lipo Charger (MCP73831) Jaycon Systems LLC ) - $7
-3.7V Battery w/ JST connector to plug directly into charger board (can be purchased from Jaycon also - need 500mAh or greater for compatibility with unmodified charger) - $8
-Powermat Powercube (this is simply an induction power board connected to a USB cable - set the box on the mat and voltage comes out) -$5 on eBay, or may come with the mat
-Powermat charging mat - there are several different kinds of mats, but one of the folding travel type mats is best. The back of the tricorder must rest flat on the surface of the Powermat and on a larger/wider mat you would not be able to get a good connection if the tricorder's rear scanner hump can't hang over the side (not a problem on a Mk VII though). Can be found for ~$13-$20 on eBay.
-JST power connector - hobby R/C store, $2-3
Connecting everything:
Here's the board that is inside the Powercube. It's very thin so be careful.
The parts are connected together something like this. The power to the tricorder comes from the positive and negative pins at the center of the red board.
There is not enough room inside the tricorder shell for the green USB cable and its adapters, so the cable was snipped and connected directly to the USB pins at the left of the red board (VUSB and GND):
It works!
Before securing this assembly, determine where on the rear panel the power board should go. With the mat unplugged, place the tricorder shell on it and make sure there is room for the rear scanner bump to hang over the edge, so that the back of the tricorder sits flat on the mat surface. Remove the shell, leaving the rear panel in the same spot on the mat. If you set the power board on top of the rear panel, the magnets in the board and mat will attract and the power board will snap into place - mark this location.
You can use a JST connector to make the back panel/power assembly removable for ease of service:
Solder one end of the JST connector to the charger board's +/- pins, and the other JST connector to the tricorder's +/- wires. Be sure to use hot glue to secure the base of the JST extension to the inner side wall of the tricorder shell to protect the delicate wiring from being accidentally pulled. You will also secure the charger and power boards to the tricorder rear panel with hot glue. Insulate the back of the charger board with tape or craft foam before gluing, and cover the power board with the white disc from inside the Powercube shell.
There's definitely a more space-efficient way of arranging the components, so don't take my first attempt as gospel. It does all fit, though just barely.
And that's it! Fairly simple.
Here's a short video of it charging. The mat makes a little chime when a device is connected or disconnected.
Addendum:
As previously mentioned, there are other options for the power board. This is a power board out of an iPhone 3gs case (VERY cheap), which will also fit:
It's a little more bulky and doesn't come with a wire. The power out contacts are the solder pads in the upper right hand corner.
The powercube board would probably work in a phaserang too!
(with only slight modification to the body)
There is also a Powermat device with the battery and charger board built in- "Powermat dual 1200 portable rechargeable battery"
This would be ideal since it runs under $10 on eBay and includes everything. Unfortunately, the board inside is too large to fit in the Mk X medical. But! It will fit in a Mk VII with slight modification (chopping off the USB charge jack). You would need to connect tricorder power directly to the battery to bypass the board's power switch, or use a SPDT reed to simultaneously switch on the powermat board and the tricorder.
Anyway, that's what I did. Hope this is helpful
The commonly available product line for this is Powermat, and many perfectly good (discontinued) items can be had rather inexpensively on eBay. There are different ways to go about this, but here's a quick summary of what I did for mine.
DISCLAIMER/WARNING: As far as I know, this is ok to do. HOWEVER I am not an electrical engineer and I make no guarantees that this is safe (especially the alternate methods). Improperly charged lithium batteries can explode and/or cause fires! If you aren't comfortable trying this and/or don't understand it, don't do it! If I did something horribly wrong please speak up :lol
The ingredients:
-Micro-USB LiPo charger board from Jaycon Systems ( Micro-USB Lipo Charger (MCP73831) Jaycon Systems LLC ) - $7
-3.7V Battery w/ JST connector to plug directly into charger board (can be purchased from Jaycon also - need 500mAh or greater for compatibility with unmodified charger) - $8
-Powermat Powercube (this is simply an induction power board connected to a USB cable - set the box on the mat and voltage comes out) -$5 on eBay, or may come with the mat
-Powermat charging mat - there are several different kinds of mats, but one of the folding travel type mats is best. The back of the tricorder must rest flat on the surface of the Powermat and on a larger/wider mat you would not be able to get a good connection if the tricorder's rear scanner hump can't hang over the side (not a problem on a Mk VII though). Can be found for ~$13-$20 on eBay.
-JST power connector - hobby R/C store, $2-3
Connecting everything:
Here's the board that is inside the Powercube. It's very thin so be careful.
The parts are connected together something like this. The power to the tricorder comes from the positive and negative pins at the center of the red board.
There is not enough room inside the tricorder shell for the green USB cable and its adapters, so the cable was snipped and connected directly to the USB pins at the left of the red board (VUSB and GND):
It works!
Before securing this assembly, determine where on the rear panel the power board should go. With the mat unplugged, place the tricorder shell on it and make sure there is room for the rear scanner bump to hang over the edge, so that the back of the tricorder sits flat on the mat surface. Remove the shell, leaving the rear panel in the same spot on the mat. If you set the power board on top of the rear panel, the magnets in the board and mat will attract and the power board will snap into place - mark this location.
You can use a JST connector to make the back panel/power assembly removable for ease of service:
Solder one end of the JST connector to the charger board's +/- pins, and the other JST connector to the tricorder's +/- wires. Be sure to use hot glue to secure the base of the JST extension to the inner side wall of the tricorder shell to protect the delicate wiring from being accidentally pulled. You will also secure the charger and power boards to the tricorder rear panel with hot glue. Insulate the back of the charger board with tape or craft foam before gluing, and cover the power board with the white disc from inside the Powercube shell.
There's definitely a more space-efficient way of arranging the components, so don't take my first attempt as gospel. It does all fit, though just barely.
And that's it! Fairly simple.
Here's a short video of it charging. The mat makes a little chime when a device is connected or disconnected.
Addendum:
As previously mentioned, there are other options for the power board. This is a power board out of an iPhone 3gs case (VERY cheap), which will also fit:
It's a little more bulky and doesn't come with a wire. The power out contacts are the solder pads in the upper right hand corner.
The powercube board would probably work in a phaserang too!
(with only slight modification to the body)
There is also a Powermat device with the battery and charger board built in- "Powermat dual 1200 portable rechargeable battery"
This would be ideal since it runs under $10 on eBay and includes everything. Unfortunately, the board inside is too large to fit in the Mk X medical. But! It will fit in a Mk VII with slight modification (chopping off the USB charge jack). You would need to connect tricorder power directly to the battery to bypass the board's power switch, or use a SPDT reed to simultaneously switch on the powermat board and the tricorder.
Anyway, that's what I did. Hope this is helpful
