Need Math to Rotate XYZ Point Around A-B Rotary Axes

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Randy Rauh
Randy Rauh am 22 Jan. 2020
Kommentiert: Matt J am 22 Jan. 2020
I need help with some CNC Machine Tool logic that has to do with Coordinate Rotation. I have a known XYZ Point that I need to rotate around A(First Rotary) and B(Second Rotary) angles. The A-Axis is Parallel to "Z" and the B-Axis is Parallel to the "Y" Axis.
My logic for "Z" shown here works correctly to give me the pre-rotated Z-Axis value.
Z=(Z*(cos(Rotary B Angle)))-(X*(sin(Rotary B Angle))))
I can't come up with the correct formula for the same X-Y values.
Example:
This is a known value after Coordinate Rotate: X-8.8103 Y6.473 Z4.6117 A= -90 B= -45
I need a formula for the XYZ value BEFORE Coordinate Rotation which is: X6.473 Y9.4908 Z-2.96887
The Z Formula above works to properly convert Z4.6117 to Z-2.96887. I need help with a formula to do the same conversion for X-Y.
The software I am using to write the formula is a proprietary CAM Software with limited Math Operators such as ACS, ATN, COS, SIN, EXP, SQR, SQRT, TAN
  2 Kommentare
Matt J
Matt J am 22 Jan. 2020
The software I am using to write the formula is a proprietary CAM Software with limited Math Operators such as ACS, ATN, COS, SIN, EXP, SQR, SQRT, TAN
Does that mean that you are not working in Matlab? If so, this is probably not the right forum.
Matt J
Matt J am 22 Jan. 2020
Randy's comment moved here:
I am new to Matlab so I appologize for my question which was a plea for general Math help and not something that pertains only to working in Matlab. If you are a Moderator you can delete my non Matlab related question.

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Matt J
Matt J am 22 Jan. 2020
See Rodrigues' formula,
Also, though you are apparently not working in Matlab, you could use Matlab to verify your calculations using this FEX submission,

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