Delta Roboter

[default.user]

Jamison,

looks very impressive and with the right ambition behind.

Was is just a proof-of-concept, something you're planning to sell or is it something you want to share with the community ?

[JamisonBruch]

I'm not sure...
Just sent this one to a ASME conference in Montreal... maybe professors will buy the mechanism for their grad student projects or robotics labs.
It has a lot of really cool development steps... just the calibration is a significant software/hardware task... the minimal time between points can be optimized with dynamics modeling and can result in fast but bizarre routes from PointA to PointB.

So cool to develop all these little pieces... maybe I'll develop a kit and sell.

It already outperforms $30-$60k robots for less than half the cost.

[theodleif]

Hallo allerseits,

denkt Ihr, man kann davon die Kinematik berechnen?

http://builders.reprap.org/search?q=assembling+tripod

Die Jungs im deutschen Reprap-Forum stecken da etwas fest. Die wesentliche Frage wäre auch, wie genau sich das ansteuern lässt. Repraps drucken Kunststoff mit einer Genauigkeit von 0.2 mm. Für das Ausfüllen von Flächen braucht man hohe x-y Geschwindigkeiten.

Es wäre natürlich super, wenn man das mit einem Delta könnte, weil man viel Mechanik einsparen könnte und das Ziel der Reprap-Bewegung ja ist, dass sich der Drucker irgendwann selbst nachdrucken kann.

[JamisonBruch]

Nice!
I've used magnet ball joints on a hexapod with great results.

Kinematics are found using trig and the law of cosines. Find an old high school text regarding solving triangles angles and side lengths.

Calibration and error mapping is very important to accuracy on mechanisms like these because link lengths are never perfect. Renishaw has a tripod/delta for dental milling and they get 10 micron accuracy through a painful calibration process.
http://www.renishaw.com/en/incise-sc...oftware--10249

To get motion accurately in X,Y,Z directions is more difficult than in a cartesian machine (even after you've applied the kinematic transforms) because tiny length differences in the fixed-length struts cause 'dishing' in the motion and divergence from linearity. To correct for this we do 3D volumetric error mapping, i.e. we use the machine to probe the locations of a large array of accurately mapped balls (previously measured on a CMM). Depending on the accuracy you are looking for, you may not have to do this. Our machine is tiny (roughly spherical working envelope about 90mm diameter) and without error mapping can be out by 0.3mm or more. With error mapping it is accurate to sub 10 microns.

SO either take special care in "perfect" mechanical geometry, or you will need to calibrate and error map for accuracy.

I haven't used error mapping yet on the deltas I make... I will soon.


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[theodleif]

Is the error mapping done by an artificial neural network? Years ago in a book of Ritter, Schulten, and Martinez about Self Organizing Neural Maps there was an account to solve the Mapping of angles in a robot arm to the yielded x-y positions. At least I remember to have that book in my office. I will look it up.

ADDED: As I see, the master of Self Organizing Maps himself, Teuvo Kohonen, has written about it:

http://books.google.de/books?id=e4ig...page&q&f=false

This seems to be a more contemporary article:

http://mhrg.if.uidaho.edu/papers/201...ic_SOFAMAP.pdf

[JamisonBruch]

Nothing that complex. Calibration takes care of reference frame translations and rotations. Error mapping is a recorded error data table.

Put the tool at a known XYZ location (known either by cmm or calibration tooling) and compare the results given by the mechanism encoders after inverse kinematics. You know it is at point A, but the mechanism says it thinks its at point A PLUS some error in X,Y,Z. If you do this enough times all throughout the workspace you will find error patterns (not necessarily linear).

Now with software, you can error correct by calculating (interpolating from the error mapping results) how much error the robot would probably have at that position and then adding in error correcting offsets.

Very crude, painful procedure, but needs to be done only once per machine.

Jamison

[theodleif]

Are the error vectors just interpolated form the measured errors on nearby positions?

[JamisonBruch]

yes.
Depending on the data..., there are many ways to map error.
Hardcode it in 1mm intervals to interpolate, or if there is a pattern, one could extrapolate. It totally depends on the patterns... I'm looking forward to finding out how link length (and other) error propagates to the tool tip. Perhaps it is a simple equation for each coordinate, or a simple offset constant within certain regions...