Gimble based math programming program

I am an artist who creates various types of computer-controlled computers. I started prototyping a gimble-based XY machine and realized that the necessary math data was not available. I am a pretty decent programmer, but not very good at math. 3D math.

To understand what I need to do, it would be helpful to look at the rig:

Early prototype:

http://roypardi.com/gimble/IMG_2803.JPG

http://roypardi.com/gimble/IMG_2805.JPG

http://roypardi.com/gimble/IMG_2806.JPG

http://roypardi.com/gimble/gimbleSmall.MOV (short video)

http://roypardi.com/gimble/gimbleLarge.mov (larger video)

The two inner rings represent the X / Y axis and are controlled by stepper motors. I want to be able to use both bitmap images and vector data (gcode). Therefore, I need to be able to address a point in two-dimensional space on paper / from my data and find out what orientation it should be in order to get there (that is, how much for each engine step).

I was looking for 2D> 3D projection, Euler angles, etc., but I'm not in my depth. Any pointers, clicking in the right direction, or code snippets will be most welcome. I can understand most programming languages.

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3 answers

, , , . , .

, , , , , , , .

tan, 0, . Z .

YAxis = arcsin (X/sqrt (X² + Z²))

XAxis = arcsin (Y/sqrt (Y² + X² + Z²))

XAxis = arcsin (Y/sqrt (Y² + Z²))

YAxis = arcsin (X/sqrt (X² + Y² + Z²))

, , .

Edit: , , , , . YAxis Xaxis?

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, http://en.wikipedia.org/wiki/Trigonometry

, ( "O" "" ) - X.

P O, O Y.

, alpha, tan (alpha) = Y/X, , "arctan (Y/X)" [arctan atan]. Arctan - , , , , , API .

.

, , , P . , , , Y1 , Y2 - . ( ), "arctan (Y1/X)", "arctan (Y2/X)".

0

, , , , . , . , , , , . , , ; , .

, plotter, .

0

Source: https://habr.com/ru/post/1708035/


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