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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 Z-axes are

along the link lengths. The Xi axis is oriented such that Xi = Zi X Zi+1

and Y-axis such that it completes a right-hand system. For the base frame

of manipulator the Z-axis 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 end-effector 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 hyper-redundant manipulator. The atoms are modelled as joints and

bond-lengths as links. The bond-lengths and bond-angles are constants and

torsion angles are the variable parameters. The frames are attached as

described in the first paragraph. The Z-axes are along the bond-lengths.

The Xi axis is oriented such that Xi = Zi X Zi+1 and Y-axis such that it

completes a right-hand 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 Z-axis), d- distance between X-axis is here

is taken as the bond-length, theta is the torsion angle. All DH parameters

are calculated from atomic positons of atoms.

Initially iam trying to calculate the end-atom position(end-effector)

withrespect to first-atom(base-frame),for some known values of theta. This

iam sucessfully able to do. But Iam not able to calculate end-atom

position withrespect to world frame. So i want to know the transformation

matrix which relates frame attached to first atom(note that the Z-axis of

frame attached to first-atom is oriented along the bond from first-atom to

second-atom but X and Y axis are arbitrary) to the world frame.

Iam assigning frames in a similar manner as given in the lower half of

this page:

frame is different from that described there.

Thank you for your patience reading of my long describtion of my question.

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