frame transformation with interpolation change

check pinned topic READ FIRST and get key manuals. one of them is system variables manual.

$IPO_MODE = #BASE ; normal case, robot guided tool

$IPO_MODE = #TCP ; using fixed tool

post your attempt and reasoning along with some sketch. are you familiar with geometric operator and INV_POS?

Quote from mmilo31

as far as INV_POS, I am dabbling with them, still unsure or its been unclear to me how they fully work and to what extent.

INV_POS performs a matrix inversion on a FRAME or POS type variable. This basically "reverses" the variable.

For example, in KRL, any POS variable is defined relative to a frame of reference, usually $BASE. The POS can be considered as a sequence of instructions:

1. Start at the position and orientation of $BASE

2. Move along $BASE X by POS.X

3. Move along $BASE Y by POS.Y

4. Move along $BASE Z by POS.Z

5. Rotate in place around your Z axis by POS.A

6. Rotate in place around your new Y axis by POS.B

7 Rotate in place around your new X axis by POS.C

The order of 2-4 is not really important, but the order of 5-7 is critical.

Performing an INV_POS of the POS variable would give a FRAME-type variable that is, basically, the same directions but in reverse -- starting from POS, how to get to $BASE. Given the way Euler angles (the ABC values) work, it's not possible to invert a 6DOF variable by simple arithmetic -- matrix algebra is required. INV_POS performs the conversion from FRAME to matrix, performs the matrix inversion, then converts the resultant matrix back to FRAME.

INV_POS can be used, in addition with the Geometric Operator, to calculate the 6DOF relationship between any point in space and any other point in space. If one were only concerned about 3DOF (XYZ), then simple arithmetic would suffice, but to accurately handle the rotation angles and their effects on the XYZ values, these system functions are necessary.

you were asked but never provided info you promised. all you shared was cropped screenshot of couple of inline forms. this tells us nothing. where are the actual values? where is your attempt to calculate it?

for some arbitrary choice of coordinate systems (lets call the cases X and Y) we can write TCP equations:

robot_position_x:tool_x=base_x:point_x

robot_position_y:tool_y=base_y:point_y

the ":" is called geometric operator. despite appearance, this is not a division operator, it is essentially a matrix multiplication operator (there is no division when working with matrices).

everyone learned about algebra, vectors, matrices. .. and 3D math is matrix based math

in algebra if you have dealt with simpler constructs and this worked:

5*w=w*5=5w

and

a*b=c*d

you can express c as

c=a*b/d

and since matrix multiplication is not commutative

A:B is not the same as B:A

because with matrices it MATTERS from WHICH side multiplication is performed, operands cannot arbitrarily switch sides (they can but this is no longer an equation, so bummer...).

learning and retaining are two different worlds which is why all the smarts come from few clever kids that ate all their vegetables.

since there is no division with matrices, we just use multiplication by inverse of the matrix (fortunately, frames and rotation matrices are type of matrices that are always invertible).

and sometimes we need to look at the robot and notice that robot did not move but the tool was changed. in that case the above TCP equations are not very useful, we need to transform them into more suitable form and look at thing from perspective of the robot flange (the part that did not move).

so from

robot_position_x:tool_x=base_x:point_x

robot_position_y:tool_y=base_y:point_y

we get

robot_position_x=base_x:point_x:INV_POS(tool_x)

robot_position_y=base_y:point_y:INV_POS(tool_y)

notice that in TCP equations, robot position was multiplied by tool position from the RIGHT.

so during transform, tool position moves to the other side of equation but it still MUST be one the RIGHT side of the expression - but inverted.

and if robot arm did not move, then robot_position_x=robot_position_y

in that case we can write

base_x:point_x:INV_POS(tool_x)=base_y:point_y:INV_POS(tool_y)

and you can calculate any term knowing the others.

to determine value for point_y by using suitable matrix operations we need to remove everything around it.

point_y is multiplied by base_y from the LEFT.

to get rid of it, move it to the other side equation and multiply in inverse value also from the LEFT.

so you get

INV_POS(base_y):base_x:point_x:INV_POS(tool_x)=point_y:INV_POS(tool_y)

but point_y is still not alone, it is multiplied by another factor from the RIGHT. we just repeat the process:

INV_POS(base_y):base_x:point_x:INV_POS(tool_x):INV_POS(INV_POS(tool_y))=point_y

note that double INV_POS matrix multiplication simply returns same thing (just like double multiplication by negative one in algebra)

so we get

INV_POS(base_y):base_x:point_x:INV_POS(tool_x):tool_y=point_y

or if we switch sides:

point_y = INV_POS(base_y):base_x:point_x:INV_POS(tool_x):tool_y

that works for any set of frames.

now about that "fixed tool"...

note that in case of fixed tool, things are the same, only terminology changes.

tool and base are swapped in name. so if in case Y you have external tool then

base_Y is your fixed tool frame and tool_Y is the workpiece frame.

and since reference coordinate system is "on the other end", you may need to INV_POS obtained result. this is comparable to multiplying scalar or vector by -1 to flip it over.

no idea what you are really doing there. things do not make sense, for example 'workpiece' is meant to be used with external tool but but then you are using "workpiece2" with all points, inclding P1-P3. also you did not post actual code, just the "user impression" of what appears on smartPad. that is not code, that is just façade. and finally you did not include any values to check what you are getting (DAT file is important part of the program).

Do you want us just guessing?

Give us real numbers for your probem and what you expect and you've got!

Anything elses is just wasting our time

...why the sudden replies to a post from February?

I replied to post #12 and panic mode to post #11.

Quote from mmilo31

Here is the code I currently have gotten to be successful to achieve my end goal

The goal of this forum is to help!

And to my opion post #11 did not help at all.

mmilo31 just picked the rosins and did not have left any for all the others

Quote from SkyeFire

...why the sudden replies to a post from February?

good question...

not sure how it showed up on my radar. most of me responses are reactions to various notifications but there does not seem to be any in this case. i do use multiple devices and some of them may have something open for quite a while.