Project Scribble - The theory craft
Many many years ago (we're talking circa 2000) I read an article in a book about a V plotter used to make mammoth pictures - sheets of cloth hung on the side of a building, spray can dangled between two wires. It used Autocad to generate the path, and then well, worked.
At the start of the year, the Norwich Hackspace started a challenge to Lockdown Challenge to 'build something in 8 weeks', and whilst I made a long list of potential projects, I decided to go with this. This also coincided with taking some leave from work (because of Covid I had stacked a whole heap up), so this isn't going to be a step by step guide to how to build one yourself, instead it's a story about my own journey.
The general plan for a V plotter is to have two motors (stepper motors usually), or motors with rotary encoders etc, in the top two corners, and then stretching either a ball-chain or a timing belt (as timing belts for CAM machines are now so cheap) to a gondola. At the gondola end, some kind of third motor or servo will drive the pen up/down functions.
At this point it's just a matter of powering the motors accurately. With the massive amount of 3d printers and home CAM machines, theres a lot of knowledge and software for driving motors accurately, but these usually work on an X-Y axis, and at a glance, you would be forgiven to think this would work here - but it doesn't. So a very brief look at Y shaped movement is important.
Whats important to realise, is that pulling on a wire, pulls the gondola towards that motor by a fixed distance - but as the second wire is pulled, that angle changes. So because of this, the standard open source grbl doesn't work.
As a quick side note, there are about 3 main open source routes that support these. Makelangelo sell a kit, and their software works perfectly and they support it. If you want one of these, I would recommend that route. It's a little more money, but you know it will work.
I also noted there is a grbl-mega-wall-plotter, but I did not have success in making this work. Whilst I got some movement, it seemed to crash a lot for me. One of the challenges with these projects is that they are very locked into the hardware and wiring that the developer had, and as its a very niche project, they might not be updated (For instance, that one only works with the mega board, and if you've bought an arduino uno or anything new, it won't work out of the box). In the end I decided to homebrew all the software, and I'll go into a bit more detail of the software later.
The home brew decision was a little tricky: I wanted to use grbl so I could use G-code, which meant I could spend my time writing code that produced g-code, rather then having to work on motion. I'ld also benefit from the grbl's acceleration control, and accurate controls, rather then having to duplicate some of that work. In reality, I didn't have to do as much code to control its as I thought, and I didn't loose that much time. However it meant that I couldn't tap into all the software that can generate g-code.
Back on to the angles: This has two important side effects: Because the wires are flexible, and have weight, there are areas of the surface that just don't work well because theres either not enough tension or too much tension. (consider at the top, the wires pull against each other to lift the gondola up - the vector weights mean a lot of force - and at a certain tension level, the belt slips).
The second side effect is to look important things for the maths is to look at the construction - there are two important things to note about where the lines go from. They don't go from the centre of the motor, but instead from the edge of the sprocket / gear. As the angle changes, the position of the intersection changes too. Similarly, on the gondola, it does not attach to the centre of the pen - either you've nailed it to the corners, or to a point offset from the pen. There are some fancy designs which allow for a movable attachment, meaning that the wire is always inline with the pen/cutter.
As a mechanical note, it also means that shallower angles on the motors also mean less grip, Which at higher tensions means more chance of slippage. This can be fixed by adding a second rolling line like on a bike gear, to wrap the belt around the gear more.
If accuracy of the final plot is important, then the size of the wheel, and the offset of the pen is an important calculation. But if you care a lot, then a V plotter is not for you, and instead go for a rigid attachment, because at some point the weight of the cabling will affect your drawing. If you only care about art, then hey, the inaccuracy is part of the fun.