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Until though, we try to establish a relation between joint position, orientation and end effector

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position orientation and also a relation between joint velocities and in the fact velocity.

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What about the relation between joint forces talks and and the vector force talks?

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Let's see more clearly.

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In one of these two pictures, a robot manipulator grabs an object and manipulates it.

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And in the second one, the robot manipulators manipulator tries to polish the wood.

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As you know, in both of these cases, the robot manipulators in the factory and the objects exchange

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forces.

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Otherwise, the robot cannot do any of these tasks.

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For example, in the first case, Gravity Force affects the robot's end effector, and in the second

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case, a range of W, which is nothing but a vector of forces and talks that are fixed robots and the.

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Surely, these forces also creates forces and talks in joints.

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Otherwise, the robot would be slack and couldn't keep itself in up position or couldn't force on the

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polishing tool on its end effector.

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We are interested in the relation between external forces talks and Joint Force talks.

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This will be useful for us during control of robot manipulators, additional impulse control techniques

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that you will see later.

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We will use virtual work principle in order to get this relation.

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I will not introduce virtual work principle here because we will see it when we will try to establish

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inverse dynamics of the robot manipulator based on virtual work principle.

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We can write these here if these external forces and talks that affect robot manipulators.

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End eFFECTOR Delta X is the virtual displacement in the task space of the robots.

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Manipulator Toe is the joint forces and Pollux built a theater.

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Is the virtual displacement in joint space?

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What is virtual displacement?

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Virtual displacement is infinitesimal displacement that obeys any constraints imposed on this system

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here.

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F Delta X is virtual work in Tusk's space, while total delta TITA is virtual work in the joint space

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and they have to be equal.

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So you know that we can get tasks based virtual display.

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We can also write the same equation in this way.

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You know that we can get tasks based virtual displacement from Joint Space Virtual Displacement using

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Jacobean matrix.

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Let's plug that equation and we will get this equation.

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This equation has to be valid for each Delta Q so we can write this, and if we transpose both sides,

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we will get the relation between external forces, ports and joint forces talks.

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Be careful here.

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The forces and Jacobean are with respect to the base frame.

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So the joint forces talks are related with external forces talked with Jacobean matrix or the transpose

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of Jacobean Matrix.

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Let's switch to MATLAB and apply these.

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Now let's see the application in MATLAB.

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So what we are doing, we are first importing model of Puma five six robot.

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OK, then let's try to apply 20 meters of force in y direction.

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OK.

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This is our external force on our robots and the vector.

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Let's see what will happen in our joints so the forces and the forces and the talks are created in our

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robot manipulators joints.

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So here I want to write or not one thing that I forgot to mention in our lesson or tutorial that, um,

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the joint forces the joint, OK, the applied applied external force external force will create talks

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in joints if joints are revolted and forces in joints if joints are prismatic.

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Prismatic OK.

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Why talks in the joints?

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Because the forces will rotate the level of joints so it will create only talks.

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How prismatic joints don't rotate.

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They are moving in the plane.

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OK.

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So that's why, um, the the forces external forces are very clear will create forces in prismatic robots

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manipulator.

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OK, so let's.

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See what will happen if we apply 20 Newtons of force in white direction, as you can see, this is over.

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Let me just first press F9, OK, let me first clear the screen and then press F9 and also make this

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in this way so we can see the output.

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Press F9, OK?

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As you can see, these are the joint forces that should be applied in order to get that force in white

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direction.

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Let's see.

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As you can see, the force that is needed is only in joint one in order to create that force in the

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one y direction that lets you know for the force in its direction.

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20 Newtons of force in acceleration As you can see in the first three joints have applied this force

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in order to get force in X direction.

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As you can see, in both of these cases, we don't need any force in the fourth, fifth and sixth because

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they are level of joints.

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And then, you know, they are only released, so they will need only to create some, you know, torque

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for or rotation.

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For example, if we need 10 Newtons better torque, then we will need to also utilize these joints in

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order to get that torque.

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OK.

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And because they are wrist joints and they control the rotation of the end effector.

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OK, so if we need torque, we have to surely also manipulate the one of these joints or three of these

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joints, depending on the situation and also the other joints.

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OK.

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See you on the next.

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Listen.