Trey Crisco

10-23-1995, 11:30 PM

Greetings,

I do not have a recommendation for a standardized coordinates

systems (CS). I do however have a concern over some recommendations of

Euler/Bryant sequences (i.e. the six sequences of [X][Y][Z], [X][Z][Y],

etc.) that appear to be finding their way into the standardization of CS.

If there is a concensus for a standard CS, fine, but I strongly disagree

with a standard for the sequence of rotations.

When rotation occurs about an axis of the defined CS, there are

negligible differences between the six sequences. Thus, there is not a

problem. However, as the axis of rotation deviates from the axes of the

CS, the differences between the sequences can easily reach factors of 2

(100% difference) or greater. Which sequence is best? NONE. When the

rotations are highly coupled (i.e. the axis of rotation has significant

components in each direction), each of the sequences gives rotations that

are non-intuitive. In these cases, I believe that the helical axis of

motion is the best choice for describing complex coupled motions.

In summary, if there is a concensus to standarized CS, fine (my

vote is one is not needed), but do not attempt to include a standard

sequence for calulating the rotations in that standard.

Sincerely,

Trey Crisco, Ph.D.

joseph_crisco_iii@brown.edu

I do not have a recommendation for a standardized coordinates

systems (CS). I do however have a concern over some recommendations of

Euler/Bryant sequences (i.e. the six sequences of [X][Y][Z], [X][Z][Y],

etc.) that appear to be finding their way into the standardization of CS.

If there is a concensus for a standard CS, fine, but I strongly disagree

with a standard for the sequence of rotations.

When rotation occurs about an axis of the defined CS, there are

negligible differences between the six sequences. Thus, there is not a

problem. However, as the axis of rotation deviates from the axes of the

CS, the differences between the sequences can easily reach factors of 2

(100% difference) or greater. Which sequence is best? NONE. When the

rotations are highly coupled (i.e. the axis of rotation has significant

components in each direction), each of the sequences gives rotations that

are non-intuitive. In these cases, I believe that the helical axis of

motion is the best choice for describing complex coupled motions.

In summary, if there is a concensus to standarized CS, fine (my

vote is one is not needed), but do not attempt to include a standard

sequence for calulating the rotations in that standard.

Sincerely,

Trey Crisco, Ph.D.

joseph_crisco_iii@brown.edu