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Transformation matrix from global to loca frame 
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#1
May1012, 11:12 PM

P: 1

Hello friends
Iam naveen and new to this forum.I have a question regarding the transformation matrix from world frame to the base frame of a Spatial serial manipulator. The frames are attached like this. The Zaxes are along the link lengths. The Xi axis is oriented such that Xi = Zi X Zi+1 and Yaxis such that it completes a righthand system. For the base frame of manipulator the Zaxis is along the First link but the X and Y axes are arbitrary. My world frame is at (0,0,0) at some distance and different orientation to that of robot base frame. World frame orientation is along unit vectors xo = [1 0 0],yo = [0 1 0] and zo = [0 0 1]. I want to know how to calculate the Transformation matrix from world frame to manipulator base frame.To make it clear further the First link is located at some distance and oriented differently with respect to world frame.Iam sucessfully able to calculate the endeffector position withrespect to base frame.But iam not able to transform it withrespect to world frame. I tried in many ways but could not succeed.I will describe the context of the problem below. Actually iam modelling the backbone atoms of a RNA molecule as a serial chain hyperredundant manipulator. The atoms are modelled as joints and bondlengths as links. The bondlengths and bondangles are constants and torsion angles are the variable parameters. The frames are attached as described in the first paragraph. The Zaxes are along the bondlengths. The Xi axis is oriented such that Xi = Zi X Zi+1 and Yaxis such that it completes a righthand system.For the first bond the Z axis is along the bond but the X and Y axes can be taken arbitrary. The DH parameters are defined as follows. a =0 always for this problem as the bonds intersect(hence the Zaxis), d distance between Xaxis is here is taken as the bondlength, theta is the torsion angle. All DH parameters are calculated from atomic positons of atoms. Initially iam trying to calculate the endatom position(endeffector) withrespect to firstatom(baseframe),for some known values of theta. This iam sucessfully able to do. But Iam not able to calculate endatom position withrespect to world frame. So i want to know the transformation matrix which relates frame attached to first atom(note that the Zaxis of frame attached to firstatom is oriented along the bond from firstatom to secondatom but X and Y axis are arbitrary) to the world frame. Thank you for your patience reading of my long describtion of my question. 


#2
May1512, 10:22 AM

P: 18

Do you have the transform matrix for the first atom to the world frame?
I would have thought that if you have the end atoms position in terms of the first atom's coordinate system, then you could just apply the transformation matrix for the first atom to the world frame. 


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