PDA

View Full Version : Re: Angular velocity vector



Richard Baker
02-05-2004, 07:39 AM
Ton, Young-Hoo and everyone else

At 10:37 AM 04/02/2004 -0600, you wrote:
>I still think intuitively that total power should be the same, whether
>we use dot product of the w and M vectors:
>
> P = w.M
>
>or sum the three "motor-equivalent" powers from a joint coordinate
>system:
> P = da/dt*Mi + db/dt*Mj + dc/dt*Mk.

I haven't worked through all of Young-Hoo's equations looking at this but
think it is instructive to look at what happens at the gimbal lock point.
At this point (regardless of "true" angular velocity or moment) a and c are
not defined and thus neither are da/dt or dc/dt. Neither can any component
of M which is perpendicular to the plane in which the three (co-planar)
axes lie be represented within the equations. The second equation thus
breaks down at this point.

Gimbal lock doesn't affect moments and angular velocities represented
conventionally about orthogonal axis system so the first equation is still
valid.

If one expression is undefined at a point at which another is valid then
the two expressions cannot be equivalent.

Richard


Richard Baker

Gait Analysis Service Manager, Royal Children's Hospital
Flemington Road, Parkville, Victoria 3052
Tel: +613 9345 5354, Fax +613 9345 5447

Adjunct Associate Professor, Physiotherapy, La Trobe University
Honorary Senior Fellow, Mecahnical and Manufacturing Engineering, Melbourne
University

-----------------------------------------------------------------
To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl
For information and archives: http://isb.ri.ccf.org/biomch-l
Please consider posting your message to the Biomch-L Web-based
Discussion Forum: http://movement-analysis.com/biomch_l
-----------------------------------------------------------------