Frame Rotations
An Introduction
In this page, I will be introducing some of the basic concepts around Frames in a 3D enviroment.
Some of the examples shown in this page were produced using the application Autodesk Fusion 360.
A frame is like a snapshot of a point of space, such as a record of a position. These are used to track and manage positions in the virtual world relative to the axes in use.
In robotics, every joint will have a position in space, managed as frames. Frames can be translated linearly, rotated or a sequence of both. Frames cannot just represent a position of a joint in space, but its rotation too.
Every time a joint moves a new frame can be created, using the axis in relation to the joint itself. This can be later compared to the axis of the origin point of the environment, or to that of other objects when calculating movments.
The image below shows an example of a "Robotic Manipulator", a 3D render of a robot "gripper" made for explanation purposes. In the centre of the object, you can see it's Centre Point and its relation to the axes in use. In this example, the axes of the object are aligned with the axes of the environment.
The next collection of images shows the direction of these axes with varies orientations of the object.
Now let's take the example of a robot arm. In this example, we will be monitoring the rotation of its base.
Below is an image of the side view of the robot, with the frame at the centre of the base of the robot with the Z-axis pointing above.
From the axes may look like this. This will make it easier to monitor a rotation on the Z-axis, turning the base of the robot.
By turning the base, a new frame relative to the original can be created and stored to update the orientation of the robots segments. By comparing the frames its rotation from one frame to another, or the origin point can be calculated.
Changes of orientation, from frames of smaller movements, can be combined into one larger movement.
The animation below shows the various frames that can be taken in one rotation around the Z-Axis.
Note that the axes on the left is used to describe the orientation of the axes in relation to the robot, not of the robot. As well as this, note that the lengths of the Z-axis on the top right would be of the same length, just made smaller for ease of viewing.
In the next page, I will be introducing Rotation Matrices. These will be used to measure and create these changes in orientation mathematically.