Welcome back to the Robotics Lab at Lawrence
Tech, I'm Jim and this will be a short video
on using the right hand rules (or conventions)
for defining the positive directions of the
X, Y, and Z axes and for determining the direction
of a moment using the right hand rules.
Let's start with the axis - if we draw the
typical X, Y, 2 dimensional axis, the convention
is to draw the positive X to the right and
positive Y upwards.
And, if this were three dimensions, the Z
would be coming out and poking you in the
eye.
We can use the right hand rule to figure out
which way is positive in three dimensions
by using our thumb, first finger, and middle
finger for the x, y and z axis respectively.
So, in our 2 dimension case, my middle finger
is pointing out from the board and that's
the direction of the positive Z axis.
I can draw the axis on the board in our typical
orientation - and if I twist my hand around
my fingers match the positive directions on
the board.
We gotta get like that.
So, this is the downside of this rule - you
have to twist around in a really awkward way
to match the way it's typically drawn.
But, to figure out the positive directions
for axis oriented differently it's pretty
easy to use.
Just remember to start counting with the thumb.
Once we have determined the positive directions
for the axis, we can use another right hand
rule to visualize the direction of a moment.
Recall that the magnitude of a moment is equal
to the perpendicular distance between our
axis, here, and the line of our force times
that force.
So, when I turn my fingers in the direction
of the applied moment, my thumb points in
the positive Z direction so I know I have
a positive Z moment.
Or, if we applied a force in the negative
Y direction against the positive X axis, we
would be twisting it around the Z like this.
We would turn our hand this way and find that
our moment is in a negative Z direction.
Of course we could be applying a force in
any direction about any arbitrary axis, and
the right hand rule would tell us the resulting
x, y, and z components; some may be positive,
and some may be negative.
If I have an axis pointed this way, up, to
the right and into the board, and if I apply
a moment about this inclined axis, my thumb
points in the positive Z, positive Y and negative
X directions.
So this rule makes it simple to determine
the directions of the i, j, and k components
of a moment.
So, for the axis directions, thumb, first
finger, middle finger point in the positive
x, y and z directions.
And, for moments, curl you fingers in the
direction you are twisting your system and
your thumb will point in the direction of
the moment.
And, of course, as I have said before, use
you right hand.
If you are writing, you have to put your pen
down and use your right hand.
Using you left hand, just because it is empty
gets you the wrong answer.
This is where left handed people have the
advantage on exams.
I hope that was clear.
Thanks for watching, and I'll catch you on
the flip side.
