How to Derive the Grasp Transformation Matrix for a Three-Finger Robot Hand?

[lwcjoseph]

Hello everyone, i am now working on a problem with three fingers robot hand to grab a cube to undergo some motion
however i face some difficulties on deriving the grasp transformation matrix which help to switching the local coordinate frame
at first i was given three point vectors [0 1 0]^T, [1 0.5 0]^T, [0 -1 0]^T (T means transpose)
then to calculate a Grasp transformation matrix
i would like to know the step to achieve the result and any general method for deriving the matrix?
thanks very much for your help !

 

[maajdl]

Read some of these introductions:

http://commons.bcit.ca/math/examples/robotics/linear_algebra/

http://elvis.rowan.edu/~kay/papers/kinematics.pdf

http://en.wikipedia.org/wiki/Transformation_matrix#Affine_transformations
http://en.wikipedia.org/wiki/Transformation_matrixI guess you are familiar with matrices to represent linear transformations like rotations.
The only special thing in these "robotic transformation matrices" is the use of a fourth "homogeneous" coordinate.
This allows to represent the group of rotations and translations at the same time, with matrices.

 

[lwcjoseph]

i have read through the materials ,however, the angle of rotation and any other information concerning the transformation has not been given, that's why i have been stucked for so long
the result is as the pic attached
any help?

 

[Inner_Peace]

at first i was given three point vectors [0 1 0]^T, [1 0.5 0]^T, [0 -1 0]^T (T means transpose)

Could you please answer these so that I can understand your question better?
Are these vectors the points on the cube that you need to grasp?
Do you have any information about the base frame and the position/ orientation of the hand?

 

[lwcjoseph]

yes they are the point that i need to grasp, however no other information are povided
that's why i have been stucked so long