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Science Forum Index » Mechanics Forum » Two vectors, Two coordinate systems...
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 Posted: Thu May 29, 2008 6:23 am |
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Guest
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I have a question that I would like to ask the group given I am not an
engineer. This is not a homework problem, but I am trying to figure
out how to determine the angle between two cables attached to two
rigid structures. Please let me explain what I am talking about. I
have two vectors (2 cables attached to a fixed beam - they will always
have tension and will never deform out of shape of a line) and the
other end they both are attached to a non-fixed box (I guess you can
think of it as rubber cords on the wall attached to a box). I will
always know the orientation of one cable (CABLE A) that is, the angle
relative to the box (coordinate system of the box). I know the
INITIAL angle of the second cable (CABLE B), however, the angle is the
angle relative to the beam. I would like to know if there is a way to
solve the angle of CABLE B in the boxes coordinate system at 1) the
initial position and 2) if the box is moved to a new location. This
seems like it would be simple, but I don't know how to solve this.
So, I started it by trying to transform the vector of CABLE B into the
coordinate system of the box (going from the fixed beam to the box).
I think that would give me the initial position/angle of CABLE B in
the boxes coordinate system. I really do not know how to write the
transformation matrix to do this, but think it would be something
CABLE B
X
Y * [Rotation Matrix] = CABLE B's new XYZ coordinates
Z
Then how would I need to get the angels with respect to the boxes
coordinate system.
Then if the box moves, how would this all work as well? Please help! |
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| dlzc... |
| Posted: Thu May 29, 2008 7:54 am |
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Guest
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Dear animalov...:
On May 29, 9:23 am, animalov... at (no spam) live.com wrote:
...
Quote: I am trying to figure out how to determine the
angle between two cables attached to two rigid
structures. ... I have two vectors (2 cables
attached to a fixed beam - they will always
have tension and will never deform out of shape
of a line) and at the other end they both are
attached to a non-fixed box
...
Then how would I need to get the [angles] with
respect to the boxes coordinate system.
Then if the box moves, how would this all
work as well? Please help!
Treat the two cables as rigid members, the points where they connect
as pin (swivel) joints, the two tie points on the box as a single
rigid member, and the two tie points "in the world" or "on the crane"
as a rigid member.
Then your problem simplifies to a classical "four bar mechanism" or
"four bar linkage".
http://en.wikipedia.org/wiki/Four_bar_linkage
http://iel.ucdavis.edu/chhtml/toolkit/mechanism/fourbar/
David A. Smith |
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