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

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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

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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

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