Until though, we try to establish a relation between joint position, orientation and end effector
position orientation and also a relation between joint velocities and in the fact velocity.
What about the relation between joint forces talks and and the vector force talks?
Let's see more clearly.
In one of these two pictures, a robot manipulator grabs an object and manipulates it.
And in the second one, the robot manipulators manipulator tries to polish the wood.
As you know, in both of these cases, the robot manipulators in the factory and the objects exchange
forces.
Otherwise, the robot cannot do any of these tasks.
For example, in the first case, Gravity Force affects the robot's end effector, and in the second
case, a range of W, which is nothing but a vector of forces and talks that are fixed robots and the.
Surely, these forces also creates forces and talks in joints.
Otherwise, the robot would be slack and couldn't keep itself in up position or couldn't force on the
polishing tool on its end effector.
We are interested in the relation between external forces talks and Joint Force talks.
This will be useful for us during control of robot manipulators, additional impulse control techniques
that you will see later.
We will use virtual work principle in order to get this relation.
I will not introduce virtual work principle here because we will see it when we will try to establish
inverse dynamics of the robot manipulator based on virtual work principle.
We can write these here if these external forces and talks that affect robot manipulators.
End eFFECTOR Delta X is the virtual displacement in the task space of the robots.
Manipulator Toe is the joint forces and Pollux built a theater.
Is the virtual displacement in joint space?
What is virtual displacement?
Virtual displacement is infinitesimal displacement that obeys any constraints imposed on this system
here.
F Delta X is virtual work in Tusk's space, while total delta TITA is virtual work in the joint space
and they have to be equal.
So you know that we can get tasks based virtual display.
We can also write the same equation in this way.
You know that we can get tasks based virtual displacement from Joint Space Virtual Displacement using
Jacobean matrix.
Let's plug that equation and we will get this equation.
This equation has to be valid for each Delta Q so we can write this, and if we transpose both sides,
we will get the relation between external forces, ports and joint forces talks.
Be careful here.
The forces and Jacobean are with respect to the base frame.
So the joint forces talks are related with external forces talked with Jacobean matrix or the transpose
of Jacobean Matrix.
Let's switch to MATLAB and apply these.
Now let's see the application in MATLAB.
So what we are doing, we are first importing model of Puma five six robot.
OK, then let's try to apply 20 meters of force in y direction.
OK.
This is our external force on our robots and the vector.
Let's see what will happen in our joints so the forces and the forces and the talks are created in our
robot manipulators joints.
So here I want to write or not one thing that I forgot to mention in our lesson or tutorial that, um,
the joint forces the joint, OK, the applied applied external force external force will create talks
in joints if joints are revolted and forces in joints if joints are prismatic.
Prismatic OK.
Why talks in the joints?
Because the forces will rotate the level of joints so it will create only talks.
How prismatic joints don't rotate.
They are moving in the plane.
OK.
So that's why, um, the the forces external forces are very clear will create forces in prismatic robots
manipulator.
OK, so let's.
See what will happen if we apply 20 Newtons of force in white direction, as you can see, this is over.
Let me just first press F9, OK, let me first clear the screen and then press F9 and also make this
in this way so we can see the output.
Press F9, OK?
As you can see, these are the joint forces that should be applied in order to get that force in white
direction.
Let's see.
As you can see, the force that is needed is only in joint one in order to create that force in the
one y direction that lets you know for the force in its direction.
20 Newtons of force in acceleration As you can see in the first three joints have applied this force
in order to get force in X direction.
As you can see, in both of these cases, we don't need any force in the fourth, fifth and sixth because
they are level of joints.
And then, you know, they are only released, so they will need only to create some, you know, torque
for or rotation.
For example, if we need 10 Newtons better torque, then we will need to also utilize these joints in
order to get that torque.
OK.
And because they are wrist joints and they control the rotation of the end effector.
OK, so if we need torque, we have to surely also manipulate the one of these joints or three of these
joints, depending on the situation and also the other joints.
OK.
See you on the next.
Listen.