Take a sheet of paper. That's your wall. Lay it
flat on your desk. Any point on the surface of the paper or your desk top is "in
the same plane".
Pick the paper up, tear it into two pieces, and put the
two pieces back on your desk. Re-align the two pieces so that your paper looks
like one piece again. The tear is your crack. Your wall has a crack but both
pieces are still "in the same plane".
Now for planes of movement. There
are three of them, plus rotation.
Take one of the pieces of paper, and
while keeping it flat on the desk, move it away from the other one slightly, so
that the crack gets gradually wider. Keep the open space between the two pieces
of paper equal along the full length of the crack. That's one plane of
Now, put the paper back together so that it looks like one
piece again. Take a pencil and draw a short straight line from one piece, across
the tear, and on to the other piece. While holding one piece down against the
desk so it doesn't move, take the other piece and slide it slowly along the
crack, so that the pencil lines on each piece remain parallel to each other
while the gap between the lines gets wider. Both pieces are still on your desk.
The two pieces of paper should not have a gap between them; they are sliding
relative to each other. That's your second plane of movement.
paper back together again so it looks like one piece. Leave one piece on your
desk. Take the other piece and raise it slowly off your desk, keeping the
surface of that piece of paper parallel to the surface of the desk. Don't move
it in the direction that you moved it in the first example, and don't slide it
relative to the other one like you did in the second example. If you looked down
on it from straight above, it would still look like one piece of paper, with one
line drawn on it. If you looked at it from the side you would see two pieces of
paper, one laying on the desk and one slightly above the surface of the desk.
That's your third plane of movement.
None of this so far involved
rotation. Let's add it now.
Put the two pieces back on the desk and align
them so that they look like one piece of paper again. Grab one piece at the edge
that is opposite the crack and raise that edge off the desk. There is no gap
between the pieces of paper and the crack is acting like a hinge. That's one
axis of rotation.
Align the two pieces of paper so it looks like it is
one piece again. This time, leave both pieces flat on the desk, but take one and
rotate it slightly, so that the crack becomes wide at one end and narrow at the
other end. There's your second axis of rotation.
Put the paper back so it
looks like one piece again. Leave one piece flat on the desk but grab the other
piece on either one of the two sides that touch the side that is torn. Take the
side you grabbed and raise it up off the table, while leaving the opposite side
against the table. The side against the table is acting like a hinge. If put
your eye down close to the desk and you looked toward the crack from the side,
you would see a gap between the two pieces of paper. The gap would be wide at
the edge raised off the table, and narrow at the edge still on the table. If you
looked down on it from directly above, you would not be able to see any gap
between the two pieces of paper. That's your third axis of rotation.
these examples I've used the piece of paper that I kept flat on the desk the
whole time, and a point on the torn edge of it, as my common frame of reference.
This is because I want an easy way to describe how one piece has moved relative
to the other piece. We could also pick any point on a stationary object anywhere
in the room and use it to describe the motion of each piece of paper in three
planes of motion and along three axes of rotation, relative to that point and
relative to each other.