What are motion axes?

What is a rotational motion axis (aka axis of rotation)?

Before figuring out how your knees move, you'll first need to understand the concept of motion axes. Motion axes can be used to describe any two objects moving relative to one another. Imagine for example, two objects commonly seen moving relative to one another: a cat and a mouse.

A mouse moving around a cat along a circular path (indicated in red).

If the mouse is moving a circle around the cat, you could say that the mouse is rotating around the cat (you could also describe the mouse as orbiting around the cat like a planet around a sun, but with a circular orbit). Below is the same motion in video form.

If youNow, take your righthand, handhold it up to the image or video of the rotating mouse and curl your fingers insto follow the mouse's path of motion (for this activity, it doesn't matter which hand you use or which direction you curl your fingers, as long as they follow the path).

Curl the fingers of your hand to follow the mouse's path and your thumb will indicate the location and orientation of the mouse's axis of rotation.

With your fingers following the mouse's path, your thumb is now showing you the mouse's axis of rotation relative to the cat. For a circular path, the axis of rotation is a 3D vector that is perpendicular (orthogonal) to the circular path. This is the "central axis" around which the mouse is spinning/rotating.

Using your hand to find the mouse's axis of rotation (straight line) relative to the cat.

Identifying the axis of rotation for circular or spinning motions is powerful because once you know the position and orientation of the axis of rotation, you know everything you need to know about the rotational movement.

How to describe 3D rotations in 2D

If two 3D objects are rotating relative to one another in 3D, it's challenging to describe that motion in a 2D form. One way is to project the 3D axis of rotation as a 2D line on images of the object from multiple views. For example, the figure below shows the motion of the mouse around the stationary cat in 2D.

The 3D motion of one object relative to another (a) can be represented in 2D by projecting the axis onto images of the stationary object from multiple perspectives (b-d). If the axis is oriented directly into and out of the page, it can be represented by a dot (c).

To give you another example, here is the same mouse rotating around the same cat but about a different axis of rotation (along a different