Homogeneous coordinates

[Ricochet]

Hello,
I need help for this assignment.

I have her two local coordinate system
K1 = | 0 1 0 1 |
        | 1 0 0 1 |
        | 0 0 1 0 |
        | 0 0 0 1 |

and
K2 = | 0 0 1 0 |
        | 0 1 0 0 |
        | 1 0 0 2 |
        | 0 0 0 1 |

and a point PK1 in the coordinate system K1.
I need to transform the point into the globale coordinate system and in the coordinate system K2.
How exactly does this work. Does it work with denavit-hartenberg? And how exactly does the globale
coordinate system look like? Thanks in advance.

[SkyeFire]

Well, you came to the right sub-forum.  If you look here: http://www.robot-forum.com/robotforum/kuka_robots/krl_undocumented_features-t1174.0.html, there's a discussion of using the INV_POS and Geometric Operator in KUKA robots to change a point from one base frame to another.  The case should apply generally, because IIRC the INV_POS command is simply a matrix inversion, and the Geometric Operator is simply a matrix multiplication command. 

But we've got some much more adept mathematicians here who can probably help you far better.  And will probably tell you that I'm all wet, heh....

 

[CrossConnect]

Hello,
I need help for this assignment.

I have her two local coordinate system
K1 = | 0 1 0 1 |
        | 1 0 0 1 |
        | 0 0 1 0 |
        | 0 0 0 1 |

and
K2 = | 0 0 1 0 |
        | 0 1 0 0 |
        | 1 0 0 2 |
        | 0 0 0 1 |

and a point PK1 in the coordinate system K1.
I need to transform the point into the globale coordinate system and in the coordinate system K2.
How exactly does this work. Does it work with denavit-hartenberg? And how exactly does the globale
coordinate system look like? Thanks in advance.

Fine
I make this following assumptions that K1 and K2 transformation matrix are w.r.t the global co-ord sys.
Then K1 Matrix defines two things
1> The orientation and location of K1 co-ordinate sys w.r.t the Global
2> the transformation matrix ... which can convert vector expressed in K1 system ito the global system
So if PK1 is in K1 cordinate sys defined by say [a1 a2 a3 1] (we r using ho-moginious representation so the extra 1 at the end) then to express the point in global coordinate sys just pre multiply KP1 with K1 matrix
ie
=K1*PK1
where PK1=[ a1 a2 a3 1]'

Regarding your second question
If K2 transform any vector  from K2 sys to global  then inv(K2) transfers any vector defined in global to K2
then to get transformation from K1 to K2 system we adopt the following path
transfer pk1 to global ie     PG=K1*KP1
transfer PG  from global to K2     ie  PK2 = inv(K2) * PG = inv(k2)*K1*KP1

therefore    inv(k2)*K1 is the transformation matrix from K1 to K2
 
DH system is a special way to assign co-ordinate system to the manipulator arm . The above discussion is general . So of course it applies to DH system of coordinates. Remember DH system is only one of the  way ot assigining cordinate system.

what do u men how the global system looks like