Tilting effector kinematics possible?

o_lampe

Hi gents,
@CNCModeller recently posted a printer with a 4th axis. In the video, they have also introduced a way of slicing for four axis printers. Which is a huge step forward IMHO.
Now my question is: Could I run a Delta printer with a tilting effector by RRF kinematics?

My idea is to use one motor for each rod and modify the kinematics accordingly. Maybe @JoergS5 could help me out with his robot-arm kinematics?

Compared to the rotating nozzle from the video, which can only print at 45°, a tilting effector could print at any angle. That's a huge benefit for first layer adhesion and parts without overhangs.

JoergS5

@o_lampe hello, your idea is what is comparable to what is used for CNC 5 axis with a head configuration, i. e. the rotating axis is not located at the table, but at the endpoint (the hotend).

You may find interesting what @xyzdims developed here: https://xyzdims.com/2021/02/08/3d-printing-penta-axis-pax-5-axis-printing-option/
which is rotating at the head.

The robot kinematics supports the head/head 5 axis CNC, but delta is a closed chain (3 parallel arms), this is not included. I started adding specific parallel arm solutions like 4 axis palletized and 5 bar parallel scara, but don't plan to add delta (at leat not yet), because there is a dedicated kinematics for it. Maybe I combine both when I start developing Stewart platform, but this will take a while.

One reason for the tilting is to print overhangs without support. Tilting the bed instead of the head is imho better suited for this application.

o_lampe

@JoergS5
Thanks for responding.
The PAX5 toolhead is quite heavy and bulky.
Six stationary motors moving a Delta effector will not allow the same angles, but it would be enough to print 90° overhangs.
A Steward platform for the bed was their first attempt too, but to me it's a step backwards, like building a bed slinger...

At least you say, the kinematics are solveable. That's a silver lining...

dc42

@o_lampe said in Tilting effector kinematics possible?:

My idea is to use one motor for each rod and modify the kinematics accordingly.

Google "Stewart platform". The kinematics are unfortunately rather complicated.

o_lampe

I found an interesting instructables project about a servo driven stewart platform, where they explained: the inverse kinematics was easier than the forward kinematics.
I studied the paper of the Wokingham U3A math group and it was overwhelming at first. But they boiled down the monster math to some understandable equations.
StewartPlatformKinematics.pdf
It all starts with solving a rotary matrix which includes "yaw" rotation around Z-axis. Maybe we could skip that part or replace it with constants, since we don't want to build a flight simulator
@dc42 I wonder if that's a method which is already implemented in RRF for the rotary Delta kinematics? Where could I find it?

dc42

@o_lampe the tilting effector isn't quite the same as the traditional Stewart platform, because instead of variable length legs you have fixed length legs with attachment points that move in the Z direction; but the principles should be similar.

I don't think you will find the rotary delta kinematics much help. The code is in src/Movement/Kinematics/RotaryDelta{.h,.cpp}.

o_lampe

@dc42
the math they use calculates the leg(s) length first and then replace that by the required servo angle and even the microseconds for PWM duty cycle.
That's the point where it gets specific and needs new formulas. Either for industrial servos or for Deltastyle tower arrangement with steppers.

Beside that difference it's quite the same: both systems have a fixed base/frame and a moving platform connected by six rods.