No, I'm sorry, but I strongly disagree. OP, you're going to need a workbench to which you can mount a vise. Regardless of which parts you're working on, stock, furniture, barrel (and especially stock and barrel), you need something like a vise to hold the parts rigidly fixed while you work on them with your other two hands. You'll also need some kind of an adjustable light source, like an an articulating arm or gooseneck arm lamp, to closely illuminate your work from different angles, which usually mounts on the workbench (but can be portable). Both these tools require sturdy mount points. Without something sturdy on which to securely mount your vise and your lamp, it just becomes too much of a whole slug of issues working against you, and I suggest you just forget it, if you're dead set against a workbench.If you order a Kibler fowler kit you won't need much more than a small chisel and some sandpaper for the wood,
That being said, I don't see any reason you can't build a small and sturdy workbench even in a one bedroom apartment, unless maybe you've got a Significant Other also occupying the same space who would strenuously object to the egregiously resulting assaults on living space decorating style. It doesn't need to be that big. A small workbench occupying about 3 ft by 4 ft of your living space would be suitable, with a couple small shelves alongside to hold your tools, materials and parts. My main workbench is resting on and attached to a couple of those folding portable sawhorses Home Depot and the like sell, and that's been plenty sturdy enough for many, many projects of all kinds. Your kitchen table is not going to be stable enough. And you're going to ruin it trying. So, don't even think about it. If you assemble the workbench with screws, it can be disassembled easy enough when you move out. Saying you can't have a workbench because you live in an apartment isn't being creative enough.
You can do this, but start by first getting and making the right stuff (tools, materials and workspace environment) to do the job properly, and working for you, not against you, or else you're wasting money, time and energy.
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