Ep 2: Kinematics (Rotation matrices)


 

Getting started with Kinematics, the first thing 2 things one needs to remember, are: 

  • Rotations of a rigid body (robot in our case) are determined by rotation matrices.
  • Positions are represented by displacement vectors.
Fig 1: Rotation matrices for rotation along x, y, and z axes respectively.
For simplicity, we shall consider rotation along the z-axis only in this blog.


Upon rotation of an axes, we consider the projection of that (rotated) axis at an angle theta to the original axis (for example: we consider the projection of X1 on X0, Y1 on Y0, and so on).
Fig 2

At the end of the lesson, I calculated the rotation matrices or frames of the respective joints in a 6 DOF (Degree Of Freedom) robotic arm.

Fig 3: I have calculated the first 2 rotation matrices here. 
However, similar processes are repeated when calculating the others, as well.

Note:
  • Always consider the Z-axis as the rotation axis (No matter what, you gotta be doing that!).
  • When marking the axes of successive joints keep the following points in mind.
  1. The X-axis of a joint must be perpendicular to the Z-axis of the joint, as well as its previous joint.
  2. The X-axis of a joint must coincide with the Z-axis of the previous joint upon extension.
It's 3:30AM at the time of writing this blog. In case of any confusion or mistakes in the blog itself, please feel free to comment them down below. Thank you!

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