@EdChamberlain and @dc42 - I've been back at researching this variable arm-length delta format and have found that it's called a tripod or hexapod-tripod. LinuxCNC and MachineKit (a variant of LinuxCNC) call the kinematics for it "tripodkins".

See: https://github.com/LinuxCNC/linuxcnc/blob/master/src/emc/kinematics/tripodkins.c

I've also located a video of a proof-of-concept model on YouTube
https://www.youtube.com/watch?v=LJYhz5aTMnA

I'm still very-much interested in building this one.

Any thoughts?
Thanks,
Todd.

Hello @EdChamberlain ,
Sounds good. My concept is pretty simple and uses 3 pairs of steppers, each pair is in lock-step. By mounting the steppers in gimbals, allowing them to move freely about a fixed point, the rods stay in parallel and act the same as in a standard, linear delta -- only varying the length of the rods instead of the height of each carriage. This also limits the number of degrees of freedom to 3 (x, y, z) as the effector stays horizontal.

The Stewart platform concept would work as well and would have about the same parts count. Its kinematics are already part of LinuxCNC and are relatively well known -- just not part of the available kinematics for our 3D printers. A 6DOF Stewart platform as a 3D printer has been done at least experimentally. https://www.youtube.com/watch?v=qGyiXFGvkqE#t=23

Here's the same concept as a 6 DOF milling machine. https://www.youtube.com/watch?v=G_UmhUjZhNo

My interest is in simplifying the linear delta by getting rid of carriages and belts and by stiffening the overall machine by using an octahedral frame.

Here's some more info on hexapods.
Enjoy!
Todd.

@dc42, for the version I've been working on, I'm planning to use end-switches at the gimbal-mounted steppers along with an adjustable, locking collar on the screws.
Thanks,
Todd.

@EdChamberlain, as an engineer who's been studying this "alternate" delta format for a few years, I'm happy to help with your endeavor.
Todd.

@edchamberlain said in Custom Kinematics on Duet?:

Essentially the design in based on a delta style but uses linear motors that push / pull in and out. Three linear motors attach to the top of the machine (where the top of each rail would be on a kossel) and extend / retract to move the print head. I guess you could imagine it like a delta but instead of moving the arms up and down they are statically attached to the top of the machine and are telescopic.

@EdChamberlain, this sounds very similar to the design I've been working on off&on over the last several years. The concept I've been working on is an amalgamation of the linear delta and the inverted Stewart-Gough platform found on an Octahedral Hexapod-style milling machine. By limiting the hexapod geometry to 3DOF instead of the usual 6 and aligning the arms to be in 3 parallel sets (as is done with a linear delta printer), the basic delta printer becomes much simpler. My current concept uses 3 pairs of linear steppers with each stepper mounted in its own gimbal at the upper corners of an octahedron. Ultimately, this results in a very rigid printer with no belts and no slides. By utilizing non-captive stepper motor linear actuators rather than typical steppers, the rods and screws are combined. While I've spent a good deal of time on the mechanics, I'm at a loss for coming up with the firmware to match. From the sounds of @dc42's response, and my understanding of the mechanisms involved, the standard delta kinematics, aren't too far off. Sound like fun?