"simplest" in the sense of the simplest bill of materials, but definitley not a simple path towards plotting an image. Anyone who's tried to build one of these and actually have it plot reasonably well will know that it's super fiddly to get working.
I'd save my time and just buy a proper axidraw, if you actually want to plot anything.
It's very generally true that, when you have money and a functioning economy, buying a product to do some well-understood task requires less effort than building something to do it yourself. Similarly, it's easier to look up the answer to a well-known math problem than to solve it yourself. The advantage of DIYing existing things is usually just that you build competency you can later use to DIY things that don't exist yet.
I haven't tried this, but I would expect that maintaining precise and steady down-force is especially tough. The axidraw does a lot to make that work well.
Sloppy x/y motion (as you'd also expect here) can just be treated as a "lofi" aesthetic, but sloppy z can mean having whole sections fail to draw or your pen digging into the surface and producing unrecoverable tears and drags of the paper.
I think the AxiDraw has a hard time maintaining precise down-force because it's so good at maintaining precise position. Maintaining a precise position requires either precise negative feedback (which the AxiDraw doesn't have) or high rigidity, and the AxiDraw does have (comparatively) high rigidity.
But the BrachioGraph has very little rigidity, so (I infer) most of the weight of the pen-lifting servo is supported by the point of the pen, and almost none of the weight of anything else. So I don't think that will be a problem, as long as your gravity field is constant. But maybe someone who's built one can comment?
Wouldn’t any spring work for application of downforce? Not that I’m immediately clear on how to attach that to the brachiograph, but for purchasable machinery it seems it should be relatively easy to solve.
The arm from the BrachioGraph shoulder to the elbow is a spring. I mean, not just in the sense that literally every solid object is a spring, but in the sense that it has a large compliance; the derivative of force with respect to equilibrium position is small. But if you want constant downforce, at least at low accelerations, the best thing is a weight, and almost all the downforce on the BrachioGraph end effector appears to be from the weight of the lifter motor.
I'd save my time and just buy a proper axidraw, if you actually want to plot anything.