We have enough knowledge on rotation mattresses and homogeneous transformation mattresses.
We can find orientation or position of one frame with respect to another, and we can transform one
frame to another.
Perfect.
Now it's time to put these theoretical concepts into practice and get much more interesting results.
We will start with forward kinematics.
Robot kinematics describes motion of robot manipulator without considering forces and talks that create
this motion.
So the conclusions are solid geometrical.
If we can say the robot kinematics, we can split it as forward kinematics and inverse kinematics.
Forward kinematics, which we are interested with for now, helps us to fund in the fact that the position
and orientation in the workspace given joint angles of the robot manipulator.
Indeed, by using forward kinematics, we don't only find position and orientation of the end effector
of later, but also any point in the robot's structure.
How can we calculate forward kinematics, surely using homogeneous transformation mattresses?
Because by using homogeneous transformation mattresses, we can find position and orientation of one
frame with respect to any desired frame.
However, before going deep, we have to understand some basic concepts.
First of all, as you may probably know, robot manipulators consists of joints and links.
More generally, joints are connected with each other through joints.
Excuse me, more generally, links are connected with each other through joints.
Drones are used to provide motion to the links of the robot manipulator.
Here are the joints indicated in this robot arm, which is called scalar robot by the creator.
And here are the links of the robot arm connected through joints.
Jones can be in different types because we want to give the robot as much flexibility as possible in
order to provide a wide range of motions we want or in order to achieve wide range of motions.
We want links to be able to rotate, not only rotate, but also translate.
So let's see the alimentari joints that will provide all these alimentari motions.
This is a joint which has one degree of freedom.
As you know, object in space has six degrees of freedom.
It can translate along x y z and rotate along x y z axis.
But when we add rotational joined, it doesn't let leads to translate or any of the accesses.
So we have lost three degrees of freedom already in terms of rotations.
As you can see from the picture, it only lets rotation around one axis.
This can be X. This can be why this can be depending on the orientation of rural joint.
So we just have one degree of freedom with rotational joint, and this motion can be described by rotation
angle to AI for each joint.
Then we have translation joint, which provides translation and motion over just one axis.
So again, we have one degree of freedom, and its motion can be described by variable.
The eye for our joint and the AI is worrying length of the joint as it comes out or goes back inside.
And that's vertical joint, which has three degrees of freedom because it allows on rotation along three
axis.
But the translation on Motion Spherical Joint can be described by three in the video rotation joints.
So we will represent it always with three rotational joints because it's easier for us and the pictures
inside the red boxes represents different joint tides in robotic pneumatic diagram.
We will see now what is the robot's kinematics diagram, so don't worry, OK?
We have seen different robot joint types and its limbs.
However, we have to consider one another thing that will make our life a bit easier.
We cannot do calculations or robots real image because there are too many unnecessary details on the
real robot.
This is like human and its skeleton.
You can represent humans with only a skeleton, right, because it has the same shape as our body.
But our bodies generally have many unnecessary things that will distract us from means of analyzing
human or main aim of analyzing human.
The same is with the robot manipulators.
We want to draw the skeleton of it, and it can be done using robot kinematic diagram.
You can immediately see how simple is the robot schematic diagram.
It only consists of joints and links.
That's all we can do.
Calculations on that diagram much more easily.
As you can see, we use joint designations that we have seen to represent the joints in the robot kinematics
diagram.
The first joint is rotary, so we use designation of rotational joint.
The second one is also rotational joint.
However, the third one is prismatic one, so its designation is different.
And finally, we have again a rotary joint after we have seen these basic concepts basic concepts.
Let's try to understand what we might explore.
OK, now let's see.
Let's try to understand the forward kinematics more clearly.
OK, what we have see, for example, first of all, let's see what's the forward kinematics?
What we have said in the lecture, we have said that if we are given for the robot manipulator at joint
angles of the robots because this can be a prismatic also doing dito on Dito two, Dito three and four.
So we are given let's throw that given Tito one, Tito two, Tito three Tito fourth.
What's interesting for us output of the forward kinematics is the position and orientation orientation
of either in the vector.
Okay.
And Victor, what is the in the sector in the fifth?
Or is this what you saw with forward given that you're interested?
This one, we are given Tito one, Tito to Tito, three, and Tito for what will be the position and
orientation of in the victor in the past space or work workspace by workspace, we mean this one to
be able to.
About it later moves.
OK, so this is interesting for us.
So, for example, we are given 15 degrees for this one, 30, 20 and, for example, 10 degrees.
What will be the position and orientation, for example, it will be five, six and one in X Y Z.
And for example, with respect to the base frame, surely we get it with respect to the base frame.
For example, 30 degrees for two degrees and then minus 10 degrees.
Okay, why this?
Why this is interesting for us?
For example, we want to get.
For example, we want robot manipulators in the vector to come to the object in order to grab it.
Okay.
So this is interesting for us in if we give, for example, this is certainly 2010 and five degrees.
OK, excuse me for this 10.
OK and five degrees will be end effector near the object.
Or it's far from the object, OK?
Because from the joint angles, we can conclude what will be the end of the position and orientation,
the tusk space or workspace, and we can know that whether it is near the object or not.
And the second we can know the position and orientation of any point, any point in the robot, any
point in the robot, okay, robot structure, for example, we can know the what will be the position
and orientation of this point, what will be the position and orientation of this point or this point
or this point or this point, any point in the robot manipulator?
OK.
Why this is interesting for us.
For example, we we want to grab this object, OK, we want to grab this object, but we have an obstacle
in the workspace and we don't want robot any point to touch to that obstacle.
OK, so we can calculate each of robot manipulators for points.
OK, these points and check that whether they are collided with their coordinate is the same with the
coordinate of the obstacle or it is near the obstacle.
We can calculate this one and we can predict whether it will collide or it has already collided and
try to avoid from the obstacle.
OK, so you can see that the forward kinematics is pretty interesting for us per team.
And this is the let's summarize again.
Excuse me.
Let's summarize again why.
What is the forward kinematics?
So the purpose of everything makes be able to give them joint angles.
We want to calculate position and orientation of either in the vector or any point in the robot manipulator.