This is Galileo (Leo to his friends.) He wants to be a good boy, but he needs some work. Unfortunately, winter is coming on, and he demands treats as a price for his studiousness. We live in a northernish climate, and our summertime treat dispenser (a plastic sandwich bag) is not something you can manage with decent gloves or mittens, so I came up with this.

Disclaimers:

This isn't an advanced 'ible, but it will require you to take a little bit of initiative to complete. For example, I won't tell you how long, wide, deep or hard to make something, but I will tell you how to decide that for yourself.
Take appropriate safety measures. I won't tell you when it's okay to take off your safety goggles (never, probably.) Use tools properly and DON'T DO STUPID STUFF. You know how not to do stupid stuff. You wouldn't be at Instructables.com if that was a problem.
Anyone who's used a saw, a drill and a rotary tool should be able to make this. Still, if you have any doubts, ask someone who seems more confident with those tools than you are. If you doubt them, ask them to demonstrate. Keep 911 on speed dial and enjoy the show if they turn out to be a blow-hard.
As with all DIYs, it's a really good idea to read the whole tutorial before you begin. Do it while you're trying to wake up or something before you buy a single piece. That way you'll kind of know what's in store for the day.

Step 1: Gather Your Stuff

The supplies aren't too hard to come by. You'll need:

A length of PVC Pipe ("the tube" from here on out) and a matching cap. The length and diameters aren't critical. You want a piece at least half as long as your arm and wide enough to allow the flow of your (dog's) preferred treats like Santa down a chimney. It's worth dropping a few treats through to test it. They should drop easily down the tube, one at a time.
A small pony clamp (also called an "A" clamp.)
About ¼ sq. foot of PVC sheeting (brand names like Sintra, Komatex, etc.) I use 6 and 3 mil here but it could all be 6 mil I suppose. If you've never worked with this, you should get to know it as a maker. It's durable and easy to cut, sand, form and paint. You can usually find shippable sheets of this on auction websites or locally in 48"x96" sheets at plastic suppliers or at sign shops (ask for a square foot or so of "drop.")
A span of flat aluminum "rod." If you have it laying around, good, but chances are you'll have to buy at least 3' of it from the hardware store. I use 1/16" thick but use whatever you feel confident you'll be able to bend in a fairly small shape. The width should be at least as wide as and not much wider than the diameter of the plastic around the pony clamp's center hinge. You could also use c-channel if it's deep enough and the right width for your clamp, but you'd be on your own calculating the measurements and drilling it.
Two-sided hook-and-loop, the kind with hook on one side and loop on the other, two pieces each long enough to go around your bicep twice. (I'll actually use bicycle toe-clip straps on mine, but those are hard to come by sold separately any more.)

Tools are pretty normal too:

A saw. Chop, mitre, hack, whatever you feel comfortable cutting PVC pipe and Aluminum with.
A good hobby knife.
A ruler at least. (Adding a decent caliper will be advantageous but not strictly necessary.)
A hand drill.
Clamps large enough to lock down around the tube with a little extra room (6" jaw or greater usually.)
A heat gun and a glove. (Alternatively, a wide pot of boiling water and tongs.) This will be used to form the PVC.

Expendables should be stuff you have in your shop or junk tub under the stairs-PVC ("plumbers") glue (or Craftix if you have it), knife blades, electrical or duct tape, maybe a ½" 4-40 nut&bolt, pencil, thread and a needle, etc.

Construction time: An hour or so for a maker who knows the tools and materials.

Step 2: Cut the PVC Pipe

Cut one end of the PVC pipe at a 45 degree angle, as shown. This is the end the treats will come out of.

Step 3: Prepare the Treat Door Clamp

Unscrew the center axle of the clamp. Keep all the parts. Take one of the clamp body halves and cut the tip off (if it has the hinged tip as shown.) Measure the distance of the body half from the new tip to the first elbow and keep this measurement in mind for the next step. (Note:Make sure to keep the spring from the clamp and that the spring is one that you can bend the free ends of. If it isn't, get another clamp.)

Step 4: Trace and Cut the Treat Door Parts.

Draw a line the distance of the clamp section you just measured from and parallel to one edge of a piece of 6mil PVC sheet and trace the cut end of the PVC pipe as it lays flush to the sheet with the short-end apogee of the tube against the line you just drew (First pic.) This will leave you with an oval at a tangent to the line. Draw lines perpendicular to that line at a tangent to the perigees on each side of the outline that extend to the end of the PVC sheet (I flushed one to the side of the sheet so I didn't have to cut as much. You should have a shape that looks kind of like a U with a bar across the top which is the edge of the PVC sheet. Cut this out. (As in the second pic.) This will form the actual treat door.

Cut another piece of 6 mil PVC (pic 3) sheet as wide as the distance you measured in the end of step 3 and as high as the trough of the clamp half is deep. Make sure it sits flush inside the clamp as in the 4th picture, but also that you can pry it out with a small screwdriver or a bent paperclip or something.

Take the treat door and make a mark at half its width (picture 5), then glue the piece of PVC you just fitted into the clamp trough to the treat door on that mark as shown in picture 6.

Step 5: Get Some Measurements and Make a Hinge Mount.

Here's the part where a caliper and the metric system are useful. Before we go to the next step, we need to get some clamp data. Write it down as you go. Measure the width of the the clamp across the hinge holes (record this as "A") and the radius of the hinge (from the center of the hole to the edge of the round part of the plastic around the edge of the hinge) and record that as "B." If you don't know them, measure the wall thickness of the tube ("C") and the thickness of your aluminum rod ("D".)

We need these measurements to make the template for the tube-side of the treat-door hinge. It may be best to draught this first, as in the 3rd image diagram here, but if you're feeling ballsy, cut* a piece of aluminum (A+4B+2C+2D) units long, then drill two holes at the center-width of the rod, B units from either end.

Bend both ends of the centered A units the same direction at right angles so that you have a squared-off "U" shaped aluminum hinge mount that looks sort of like picture 4.

*I assume you'll use a hack or mitre saw here, but my wife was trying to sleep when I did this part so I used a nibbler.

Step 6: Assemble the Treat Door.

Glue the clamp to the treat door so that the clamp trough envelops the PVC piece as it fit in step 4a. (I put a 4-40 screw and nut through the whole assembly because I didn't have confidence in my glue with the clamp.) Allow the glue to dry. You may want to make sure that the whole assembly fits the tube roughly like it appears in the second picture at this point. If it doesn't, you may want to back up and re-assess your choices of materials.

Step 7: Cut the Tube Hinge Mount Holes and Install the Hinge Mount.

This is probably the most dangerous part. You need to cut two parallel slits in the tube for the hinge mount to fit through. First of course, you need to know where to cut.

Determine this by holding the hinge door in place and marking either side of the clamp hinge prongs where they contact the tube as in the first picture. Then, hold the hinge mount so that it straddles those two marks and draw outlines of the hinge sides where they contact the tube as in the second picture. (The result should look like pic 3.)

Here's where it gets a little hairy:you need to cut out PVC within those outlines so that the cuts are straight down as the tube lies with its longest edge down (as opposed to as radii of the tube.) I did this using a drill for the outside edges of the outlines and a rotary tool to remove the chunks between them and a hobby knife for clean-up. Use whatever you feel confident and safe with. The result should look like the 4th pic.

Fit the hinge mount through the inside of the tube as shown in the 5th pic, and push it flush against the inside of the tube so that it looks like the 6th pic from the side.

Step 8: Prepare to Mount the Treat-door Assembly

You kept the spring from the A clamp when you took it apart, didn't you? You need it now. Using pliers, vice grips, a vice or what ever you have handy, bend a short section (about the thickness of the tube wall, or "c") away from the center coil so that it looks something like the 2nd pic. (If your clamp is of a very different design it may not look like this, or the spring may be too thick. Time to back up to step 3 and start over.)

Insert the spring into the hinge mount and put something through the center as shown in pic 3(the original center screw ought to work here) and mark where the end of the spring you bent makes contact with the tube. Drill a hole just big enough for the spring end to fit into through the tube here.

Insert the spring back into the modified clamp half (which is now a permanent part of the treat door) and carefully tape the spring to the clamp arm as shown in the fourth picture with the spring tensioned as tight as you can manage (rendered as though the clamp were being squeezed before you disassembled it.)

Step 9: Attach the Treat Door to the Tube.

This part isn't so much dangerous as tricky, but you've probably guessed how it goes together. Insert the hinge of the treat door clamp into the hinge mount with the spring in the small hole you drilled in the tube as in the first two pictures. You may want to use something (like my small screw driver) to align the spring with all the holes here.

Once aligned, put a small bolt through the center of the clamp holes, hinge mount holes and spring coil and attach a fitted nut to it on he other side (3rd and 4th pics.) If the original clamp nut is too short to allow just a little wiggle, a 4-40 or 6-32 ought to work. Once you're satisfied that the assembly is secure, cut and discard the tape from the treat door. Put the cap on the other end of the tube and set it all aside.

Step 10: Make the Belt Loops

The "Belt loops" are what keep the hook-and-loop in contact with the tube.

Cut a square piece of PVC sheet (I used 3mil for these but 6 will work) about as wide/high as the circumference of the tube (first pic.) Cut that in half so that you have two rectangles as wide as and half as high as that circumference. You may choose to cut and round the corners a little so as not to snag any light winter garments, but that's up to you. I did.

Measure one width (record it as "W") of your hook-and-loop (or toe-clip strap) in from each end of both plastic rectangles and draw a line the height of the rectangle at that width (second photo.) Find the center of each of these marks and make marks one half the width of your hook and loop strips or toe-clip straps to either side of the center mark, then drill out holes at each end (third pic) at least the thickness of your PVC sheet and cut out the drop between the holes (it should look something like the diagram in the fourth image.)

Step 11: Form and Attach the Belt Loops to the Tube.

This part can be a little uncomfortable. Using a heat gun (or the boiling water), soften the belt loops and bend them about half-way around the tube. Allow them to harden in the shapes that the first and fourth pics demonstrate. (The plastic has to get hotter than you'll want to touch with bare hands to become malleable so wear gloves or use tongs or something.)

Measure and mark one width of your hook and loop/toe clip strap from the end of the cap (second pic) and the hole that the bent end of the spring on the treat door assembly fits into. Generously apply plumber's PVC glue or Craftix to the inside elbow of each belt loop, then clamp them to the pipe so that their outside edges are at the marks you just made on the tube and their elbow contact the tube in line with the hinge of the treat door assembly (3rd-5th pics.)

Step 12: Thread the Belt Loops

Run your toe-clip straps or hook and loop through the belt loops as shown in this photo. If you are using the toe clip straps, run the ends of the straps through their clasps and you're done with the construction part.

If you use hook and loop, you have one more step. Center each length of hook and loop with the tube so that a little less then half of each length comes out either side of the belt loops. Put your arm through the channel formed by the area between the tube/belt loop assembly and the hook-and-loop, and estimate about how much hook and loop you'll need to securely strap the hook to the loop so that the assembly is held tightly to your arm without overlapping, and fold this much of each end of the hook-and-loop back on itself at each end of each strip. Sew these loops to themselves so that the hook faces the loop on the inside (see diagram in second image.)

Test it out for fit around your arm. The velcro may take a few tries if you're thin or have big "guns." I really like the toe-clip straps though. They're very easy to tighten and release.

Step 13: Wear and Use

Fill'er up and put the cap on, then strap it to your forearm or bicep once you've put on most of your outerwear (save the mittens or gloves that made this thing necessary.) Take your animal companion for a walk, and when s/he does something right, cup your hand underneath the treat door and push on the clamp arm above the hinge, and a treat should fall right out.

Some treats are moist and can "catch" in the chute or on the inside of the hinge mount, but a shake of your arm should clear that up. If you've chosen treats that are too wide or oddly shaped, this will happen more often and you may want to re-evaluate your choice of training treat and/or the size of pipe that you use.

Step 14: Epilogue

Galileo is learning slowly. He has epilepsy or CECS, and after a particularly horrible day of seizures two months ago he seemed to lose the benefit of most of the training we'd done up to that point. However, we've switched his medicine and haven't had a seizure since. So either the seizures, the medicine or good old Anatolian Karabash stubbornness are making him dumb, so in his honor and at the suggestion of my wife, I"m giving this a "marketable" name (though this is totally creative commons-I'll likely never make another, advertise or sell one, though you may if you wish-just without a patent, like everyone else.)

Ladies and gentlemen, I give you: