MASTERCLASS

# Robotic arms and forward kinematics

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In this lecture, we are going to talk about robot arms. In particular, we are going to talk about the relationship between the joints in a robot's arm and the pose of the robot end effector. So as I've moved the various joints in my own arm we can say that the pose of the end of my arm changes, right?

So what we're going to do is how this works for a robot arm which typically comprises a number of joints. In a robot's arm, they vary, they have different numbers of joints, some robot arms might have only 3 joints, some robot arms might have 6 joints and some might have 10 joints, could have a 100 joints.

There are also two different sorts of joints that robot arms have. There are joints that are called Prismatic joints. These are joints that slide or elongate. And there are joints that are rotating joints, like the joints that I have in my own arm. So we call these sort of rotating joints Revolute joints and the sliding or telescoping joints we called Prismatic joints.

So here are some pictures of a number of different types of robot arms that exist. This is just a very small sample of a very very large number of robot arms that exist within the world.

We are going to work through some of these examples, look at them, look at the number of joints that they have, the different types of joints that they have and then work on the mathematical description, the mathematical relationship between the joint angles and the robot end effector pose.

We introduce serial-link robot manipulators, the sort of robot arms you might have seen working in factories doing tasks like welding, spray painting or material transfer. We will learn how we can compute the pose of the robot’s end-effector given knowledge of the robot’s joint angles and the dimensions of its links.

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p1.teach and p2.teach give an error message:

Error using SerialLink/teach (line 94)

No graphical robot of this name found

Could you take this question to the support forum at http://tiny.cc/rvcforum

p2.teach gives me “Error using SerialLink/teach (line 93) No joint coordinates provided”

How do i add joint coordinates?

Try giving joint coordinates, say

>> p2.teach([0 0])

which sets the joint angles both to 0.

p1.teach

Error using SerialLink/teach (line 94)

No graphical robot of this name found

What is wrong in this?

best to take toolbox issues to the discussion forum tiny.cc/rvcforum, you’d also need to provide a lot more information like version of MATLAB, RTB, and the commands you executed up to the point the error occurred.

As per your lectures, a Homogenous Transformation Matrix represents a translation followed by a rotation, which I completely agree with. But in most of the online resources on the web, I have seen people saying that it represents a rotation followed by a translation. When I try to do as such i.e. Rotation Matrix * Translation Matrix, I don’t get the Homogenous Matrix. So I believe its a translation followed by a rotation. Is my belief true?

With respect to the current coordinate frame a homogeneous transformation matrix will rotate a point about the origin and then translate it. You can see this by expanding out the matrix equation, p’ = Rp + t, where p is the original point and p’ is the transformed one. However if you think in terms of coordinate frames, a homogeneous transformation matrix represents a motion from the current frame to the new one, which is a translation t in the current frame, followed by a rotation R. Can you give me a link to one or two of the other “online resources” you mention.