Understanding Euler/Cardan Angles?

• posted

I have a question regarding the explaination of Euler/Cardan Angles? I do not really understand them, or really know how to apply this to human movment. I know they are sequence driven and will change with respect to the chosen sequence (i.e, x-y-z), but can not conceptualize this for human movment. For example, when the knee bends, there is motion in three planes...not specifically around one plane of interest. I'll give an example...

Say I have a rigid body defined as my thigh (A), and a rigid body defined as my shin (B) and I would like to describe the motion of B relative to A during jumping (both A and B will be moving simultaneously). This would be very similar to two rods attached by a ball-and-socket joint. In theory we know that most motion will occur in the sagittal pane, but will have some movement in the frontal and transverse planes. How can we use Euler/Cardan Angles to determine the amount of rotation occuring in the three planes, or about the three axes?

Assuming the sequence is x-y-z. My understanding is that B would first rotate about the x-axis of A, then around the "new, prime' " y- axis of A, and finally around the "newest, double prime'' z-axis of A". Is this correct?

How would this work if the initial two rigid bodies are not aligned/ coincident with each other?

How do you chose the appropriate sequence?

Is there a good text/website that can help me to visualize this?

• posted

Hmmmm. Though I am predisposed to try to help answer queries on a few newsgroups, I'm not sure I should be stepping into this question.

Briefly: euler angles are away of accounting for dynamic objects that move and rotate in three axes, so that one set of coordinate measurements can be tracked in another set of co ordinates.

An example: it is helpful to work out lift and drag on aircraft with respect to the local airflow, but navigating them requires an account with respect to ground referenced co ordinates.

Given some arbitrary sequence of applying the nine transforming euler equations, the nuts and bolts of those equations - the arithmetic operators etc., - are specified for that sequence. in terms of sin cos plus minus operators....

It sounds like you have a dynamic system with some rotations and some displacements, where you are tasked with accounting for positions and angles in one ( "body-centered?) coordinate system to the usual ground based framework...

One example that is sometimes used to talk about coordinate transformations is the gyroscope, with its system of gymbal rings.

This shares one particular property of the euler transformations - the gyro can lock in its gymbals at particular points - which can be the arrangement pointing through a north or south pole.

But that's as much as I can reasonably say here. It goes without saying that from this little toe hold, you can dig out plenty of web-based material

Best Wishes

Brian Whatcott Altus OK

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