Moment of Inertia Orientation

    Quote from Fabian Munoz

    Tell them to give you a drawing like the attachment
    Check the axis, usually we have to rotate them, Im talking about right and left hand rule

    I have the same problem and i find that solution what you send.

    I have a KUKA robot so maybe its an other thing, but i hope you can help me.

    Which value should i use if the robot says: Center of mass(X,Y,Z), and the Orientation(A,B,C) of the Moment of inertia(JX,JY,JZ)

    Center of mass is obvious, because solid works clearly says which one is that.

    Orientation is not so clear for me, but i think its 0-0-0, because i won't rotate the gripper.


    The most important question, which line says the right moment of inertia?

    If i have to i would choose the first line, which is the principal axes of inertia and principal moments of inertia...etc
    Maybe the JX is the Px value in solid works?

    Thanks for your help in advance!

    I've moved your reply into its own thread in the appropriate forum. Someone here in the Kuka forum should be able to help you better than the Fanuc forum.

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    Thanks 1

    KUKA robots expect load data that is expressed in proper units:

    mass is in kg,

    distance is in mm

    angle is in deg

    and inertia is in kg*m2



    CAD may use different units but in metric system conversion is easy.

    1000g = 1kg


    1000mm = 1m = 100cm


    but note that for inertia values, distance is squared. that too will affect number of decimal places....

    1m*1m = 1m2= 1000mm * 1000mm = 1000000mm2 = 100cm * 100cm = 10000 cm2


    so you just need to move decimal place correct number of places.

    for example if you see in CAD output that load is computed in g*cm2 then

    1 g = 0.001kg

    1 cm = 0.01 m

    1 cm2 = 0.0001 m2


    so 9451234 g*cm2 is 9.451234 kg*m2


    Also note that KUKA expect Inertia values about CoG of the load.

    Orientation depends on place where load is mounted.

    EOAT and shoulder (A3) mounted loads are relative to robot flange.

    A1 and A2 loads are relative to robroot.


    but to figure out correct flange orientation and specify correct CoG of the EOAT, robot need to be moved into correct position. that is when robot is at cannon position {A1 0, A2 -90, A3 90, A4 0, A5 0, A6 0} :

    flange Z axis is pointing out of center of the flange

    flange X axis is pointing down from center of the flange

    flange Y axis is pointing to (robots) left which is same as in robroot.


    btw when robot is candlestick position {A1 0, A2 -90, A3 0, A4 0, A5 0, A6 0} then flange and robroot are parallel...


    Mass and CoG should be obvious.

    The next part is to choose inertia values.


    If you are using load principal moments of inertia, taken at CoG, then inertia values are Px,Py,Pz (do not forget to adjust decimal point if units do not match). Those would be values for KUKA tool EOAT inertia JX, JY and JZ.


    But...


    you also have to determine which rotation angles A,B,C produce rotation matrix shown next to Px,Py,Pz. (Btw SolidWorks representation of the matrix is transposed, not conventional, see here)


    If you are using load principal moments of inertia, taken at output (robot flange), then

    JX = Lxx

    JY = Lyy

    JZ = Lzz

    again do not forget the correct decimal place... (read units!!!). in this case A,B,C values are zero.


    1) read pinned topic: READ FIRST...

    2) if you have an issue with robot, post question in the correct forum section... do NOT contact me directly

    3) read 1 and 2

    Thanks 1

    So, i would have a question:

    What is the difference between taken at COG and taken at output (robotflange)?
    The robot says i need X,Y,Z which give the center of mass(COG). If i choose taken az output(robotflange).This:

    Quote from panic mode

    If you are using load principal moments of inertia, taken at output (robot flange), then

    JX = Lxx

    JY = Lyy

    JZ = Lzz

    Should i write in the COG values?


    And sorry if i don't understand, but i don't know the difference between these.(taken at COG and taken at output (robotflange))

    We have a vacuum gripper, which support by a cantilever.


    Thanks for your help!:)

    well...


    first of all your screenshot is completely useless since it is incomplete - it only shows text output, without the actual 3D view of the tool. in other words there is no way to tell where the origin is or what the tool orientation is. there is no way to tell if the used coordinate system matches up with robot flange or not. maybe the chosen reference coordinate system in CAD is not even centered on flange or parallel with it. maybe the axes are rotated or swapped...


    Quote

    What is the difference between taken at COG and taken at output (robotflange)?

    read our physics book, chapter inertia... there is something called parallel axis theorem (Steiner's Theorem). if you choose to rotate object about another axis that is parallel but away, inertia increases (a lot) since distance has effect that need to be taken into account.


    Quote

    Should i write in the COG values?

    of course but... it needs to be done correctly. your post begs another question: why did commissioning of the robot become your responsibility? also why is CoG so far? if the values are correct this will add significant change to tool inertia. and that is without product that gripper is supposed to hold. did anyone check if selected robot can handle this?

    1) read pinned topic: READ FIRST...

    2) if you have an issue with robot, post question in the correct forum section... do NOT contact me directly

    3) read 1 and 2

    Thumbs Up 1

    So, i attach the CAD with the parameters. i made a coordinate system where the gripper join to the flange. In out first project, we try to make the loading with 1 vacuum gripper.In the future we will have 2. I just wanted to clarify why the location of the gripper was so strange.

    Quote from panic mode

    flange Z axis is pointing out of center of the flange

    flange X axis is pointing down from center of the flange

    flange Y axis is pointing to (robots) left which is same as in robroot.

    I try the place the coordinate system accordingly , but sadly i couldn't place it the right position.

    Z axis is paralell with the flange axis.
    X axis should pointing down!?

    Y axis should pointing to left!?


    What do you think about the parameters?


    Thanks in advance!

    Cannon position:


    how the tool should be mounted (matching tools 'output coordinate system' with the robot flange orientation):

    in that case load should be

    1) read pinned topic: READ FIRST...

    2) if you have an issue with robot, post question in the correct forum section... do NOT contact me directly

    3) read 1 and 2

    Like 2

    Solid works offers several results and export windows show coordinate systems of each. Also user can choose which coordinate system results refer to.


    first result in report is for "Principal axes of inertia" which solidworks takes at the center of the the mass with principal axes of inertia oriented to match eigenvectors of the object. This is the only report result that does not refer to robot frame, but obtaining rotation angles A,B,C can be a problem - this may not be orthonormal (all three vectors perpendicular to each other or orthogonal).



    so it is more practical to use report result that does match robot coordinates...

    One just need to be careful, pay attention, pick the correct one and ensure that orientation of coordinates matches.


    When "output coordinate system" matches robot flange, A,B,C are zeroes.


    When inertia value is taken at the "output coordinate system" that matches robot flange, X,Y,Z of CM are zeroes and inertia values are Ixx,Iyy,Izz


    When inertia value is taken at the center of the mass, X,Y,Z of CM need to be entered (they are not zeroes). In this case inertia values are Lxx,Lxx,Lzz.


    When "output coordinate system" matches robot flange, but order of axes is different, inertia value components need to be swapped accordingly.


    When "output coordinate system" is parallel both does not match robot flange, obtained inertia value must be corrected using parallel axis theorem. This also need to be done when robot has more than one tool that can handle the same object. It does not matter if the different tools are mounted directly or using tool changer.

    1) read pinned topic: READ FIRST...

    2) if you have an issue with robot, post question in the correct forum section... do NOT contact me directly

    3) read 1 and 2

    Thumbs Up 1 Thanks 1

    i am going deeper and deeper. :frowning_face:

    I can't decide if I calculated correctly then :thinking_face:


    First:

    I calculated the robot inertia around palett center of gravity.

    It doesn't matter there i am using the "Taken at the center of mass and aligned with the output coordinate system" OR just "Taken at the output coordinate system", if my coordinate system located in the palett center of gravity.(calculate here the 3 inertia for xx,yy,zz)

    The palett length(b) 1,1m, width(a) 0,8 m, Mass(M): 29,92kg

    These values are:

    JPalett.xx=(M/12) * a2= (29,92/12)*0,82 = 1,5957 kg*m2

    JPalett.yy=(M/12) * b2= (29,92/12)*1,12 = 3,0169 kg*m2

    JPalett.zz=(M*(a2+b2))/12=4,6127 kg*m2 -> Same as in SW, other axis little difference, but it's OK


    Second:

    For the empty gripper if i use "Taken at the output coordinate system."!!:

    Coordinate system located at $NULLFRAME (tool0) coordinate.

    values:

    JTool.xx= 1,8581 kg*m2

    JTool.yy= 3,4674 kg*m2

    JTool.zz= 4,5718 kg*m2


    Third:

    Steiner equation for "shifting": I = ICM + M * r2

    For palett inertia around $NULLFRAME (tool0) coordinate:


    For this we need distances from palett center of gravity coordinates to $nullframe coordinates:

    rx = 0,18m

    ry = ((0,27533)2 + (0,18)2 )1/2= 0,3289m

    rz = 0,27533m


    And now steiner:

    JpalettMod.XX = Jpalett.XX + 29,92 * rx2 = 2,5651 kg*m2

    JpalettMod.YY = Jpalett.YY + 29,92 * ry2 = 6,2535 kg*m2

    JpalettMod.ZZ = Jpalett.ZZ + 29,92 * rz2 = 6,8808 kg*m2


    Fourth:


    Summarize: JTool.ab + JpalettMod.ab

    TAKEN AT THE OUTPUT COORDINATE SYSTEM! ( $NULLFRAME) matches robotflange:

    JTOTAL.XX = JTool.XX + JpalettMod.XX = 1,8581 + 2,5651 = 4,4232 kg*m2

    JTOTAL.YY = JTool.YY + JpalettMod.YY = 3,4674 + 6,2535 = 9,7209 kg*m2

    JTOTAL.ZZ = JTool.ZZ + JpalettMod.ZZ = 4,5718 +6,8808 = 11,4526 kg*m2


    As we see we got back(with a small difference) what solidworks offers us in terms of "Taken at the output coordinate system."


    So since solidworks backs up the calculation for us it should be good right?


    It seems I´ve made an error as my assumption was that JX, JY and JZ that is entered in load data is referring to the flange coordinate system. When examining and reading the SI manual more thoroughly the inertias entered are expected to be around the center of mass. Which then makes very good sense. In good manner I´ve deleted my previous post as it is misleading. The values shown under "taken at the center of mass and aligned with the output coordinate system" in Solidworks then makes sense.

    Quote from panic mode

    When inertia value is taken at the "output coordinate system" that matches robot flange, X,Y,Z of CM are zeroes and inertia values are Ixx,Iyy,Izz


    When inertia value is taken at the center of the mass, X,Y,Z of CM need to be entered (they are not zeroes). In this case inertia values are Lxx,Lxx,Lzz.

    If I´m interpreting this correctly you could use either way. But in case you want to use the inertias calculated around axes matching robot flange coordinate system axes. CM would always be zeros.


    This might be a bit of a stretch but in theory could/should the x, y, z referring to the center of mass in load data actually be named "position of the inertia reference frame" instead?

    you are correct. value of inertia can be observed at different points. but KSS does not have separate data entry for CM for static load (mass M) and dynamic load (inertia J). so from KSS perspective values will always need to be with respect to CM.

    1) read pinned topic: READ FIRST...

    2) if you have an issue with robot, post question in the correct forum section... do NOT contact me directly

    3) read 1 and 2

    Thumbs Up 1

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