Kjartan Halvorsen

01-13-2003, 10:10 PM

Dear Colleagues,

In Biomechanics, Euler angles is the dominant representation of joint

motion, as

exemplified by the standardization proposal referred to by Dr. Veeger.

(http://www.wbmt.tudelft.nl/mms/dsg/intersg/ISGproposal.pdf)

The strength of the representation lies primarily in the close connection

to anatomical nomenclature, which is valuable when interpreting 3D joint

motion. The weakness of the representation is mathematical; see van den

Bogert and Kwon's recent discussion. Herman Woltring fought for the

acceptance of the "attitude vector" as the standard for representing 3D

attitude (and rotations). See [1] and contemporary discussions on

biomech-l.

I would like to direct this forum's attention to a different representation

of 3D rotation [2], proposed in the computer graphics literature as a

convenient representation for ball-and-socket type of joints with large

range of motion. The representation is sometimes called "swing-and-twist",

and it has a straightforward interpretation and nice mathematical

properties (no gimbal lock, singularity only for rotations ("swings") of

180 degrees from the reference orientation).

A brief introduction to swing-and-twist: Consider the motion of the

shoulder joint. The motion is decomposed in

two rotations: a swing of the arm, which causes NO axial rotation of the

humerus, followed by an axial rotation of the humerus (the

twist part). The swing of the arm is represented by a rotation vector

that is constrained to lie in the plane normal to the longitudinal axis of

the humerus. The idea of a rotation vector may seem to imply that the

swing-and-twist representation is as difficult to envision (interpret) as

the attitude vector of Woltring. However, the swing axis lies in a fixed

plane, and 2D geometry is a lot easier to visualize and understand than 3D

(at least for most of us, it is).

Take a look at Grassia's paper [2], online at

http://www.cs.cmu.edu/~spiff/moedit99/expmap.pdf

I think it offers a nice compromise between the ease of interpretation of

Euler angles and the nice mathematical properties of the attitude vector.

Yours sincerely,

Kjartan Halvorsen

[1]

@article{biomech_woltring_94,

author = {H.J. Woltring},

title = {3-{D} attitude representation of human joints: A

standardization proposal},

journal = {Journal of Biomechanics},

year = {1994},

month = {},

volume = {27},

pages = {1399--1414},

}

[2]

@article{biomech_grassia_98,

author = {F.S. Grassia},

title = {Practical parameterization of rotations using the exponential

map},

journal = {Journal of Graphics Tools},

year = {1998},

month = {},

volume = {3},

pages = {29--48},

url = {http://www.cs.cmu.edu/~spiff/moedit99/expmap.pdf}

}

--

The Department of Systems and Control

Uppsala University

http://www.syscon.uu.se/

+ 46 18 471 3150

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------

In Biomechanics, Euler angles is the dominant representation of joint

motion, as

exemplified by the standardization proposal referred to by Dr. Veeger.

(http://www.wbmt.tudelft.nl/mms/dsg/intersg/ISGproposal.pdf)

The strength of the representation lies primarily in the close connection

to anatomical nomenclature, which is valuable when interpreting 3D joint

motion. The weakness of the representation is mathematical; see van den

Bogert and Kwon's recent discussion. Herman Woltring fought for the

acceptance of the "attitude vector" as the standard for representing 3D

attitude (and rotations). See [1] and contemporary discussions on

biomech-l.

I would like to direct this forum's attention to a different representation

of 3D rotation [2], proposed in the computer graphics literature as a

convenient representation for ball-and-socket type of joints with large

range of motion. The representation is sometimes called "swing-and-twist",

and it has a straightforward interpretation and nice mathematical

properties (no gimbal lock, singularity only for rotations ("swings") of

180 degrees from the reference orientation).

A brief introduction to swing-and-twist: Consider the motion of the

shoulder joint. The motion is decomposed in

two rotations: a swing of the arm, which causes NO axial rotation of the

humerus, followed by an axial rotation of the humerus (the

twist part). The swing of the arm is represented by a rotation vector

that is constrained to lie in the plane normal to the longitudinal axis of

the humerus. The idea of a rotation vector may seem to imply that the

swing-and-twist representation is as difficult to envision (interpret) as

the attitude vector of Woltring. However, the swing axis lies in a fixed

plane, and 2D geometry is a lot easier to visualize and understand than 3D

(at least for most of us, it is).

Take a look at Grassia's paper [2], online at

http://www.cs.cmu.edu/~spiff/moedit99/expmap.pdf

I think it offers a nice compromise between the ease of interpretation of

Euler angles and the nice mathematical properties of the attitude vector.

Yours sincerely,

Kjartan Halvorsen

[1]

@article{biomech_woltring_94,

author = {H.J. Woltring},

title = {3-{D} attitude representation of human joints: A

standardization proposal},

journal = {Journal of Biomechanics},

year = {1994},

month = {},

volume = {27},

pages = {1399--1414},

}

[2]

@article{biomech_grassia_98,

author = {F.S. Grassia},

title = {Practical parameterization of rotations using the exponential

map},

journal = {Journal of Graphics Tools},

year = {1998},

month = {},

volume = {3},

pages = {29--48},

url = {http://www.cs.cmu.edu/~spiff/moedit99/expmap.pdf}

}

--

The Department of Systems and Control

Uppsala University

http://www.syscon.uu.se/

+ 46 18 471 3150

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------