R. Andries

10-10-1995, 06:35 PM

Dear biomch-L readers,

I'm new to the biomch network. I'm working on a Ph. D. on knee kinematics in

vivo using positional data of markers (measured with Vicon) as input.

I have two problems in calculating knee kinematics:

1. Until now I calculated the rotation matrix using the least squares

method described by Veldpaus e.a. (J. Biomech 21: 45-54). In several

publications (Challis 1995 J. Biomech 28 733-737; Soderkvist and Wedin

1993 J. Biomech. 26: 1473-1477; Woltring in several publications; ...)

the Singular-Value-Decomposition (SVD) theory is proposed to estimate

R, in stead of the polar decomposition theorem proposed by Veldpaus.

Do both procedures give different results? And suppose SVD is better,

(as sometimes is mentioned), can somebody give me some practical

information that can help to program the SVD-calculation in

Borland Pascal (Dos version).

2. When I calculate the instantaneous screw axes parameters I need to

estimate the angular velocity vector omega. I use the formula

published in Woltring e.a. (1994, J. Biomech. 27: 1415-1432) where

the velocity vector is approximated from (R+R'_ - R_R'+)*(1/4T)

where R+ and R_ are the attitude matrix of the next and

previous sampling times and where T is the sampling

interval.

I'd like to know if there is a better way of calculating the velocity

vector using the velocity vector of each marker as input AND

using a least-squares technique.

Thanks in advance for your reply,

**************************************

Kaat Desloovere

Faculty of Physical Education and Physical Therapy K.U.Leuven

Tervuursevest 101

3001 Leuven (Heverlee)

Belgium

tel -- 32 16 32 90 74

fax -- 32 16 32 91 96

email kaat.desloovere@flok.kuleuven.ac.be

*************************************

I'm new to the biomch network. I'm working on a Ph. D. on knee kinematics in

vivo using positional data of markers (measured with Vicon) as input.

I have two problems in calculating knee kinematics:

1. Until now I calculated the rotation matrix using the least squares

method described by Veldpaus e.a. (J. Biomech 21: 45-54). In several

publications (Challis 1995 J. Biomech 28 733-737; Soderkvist and Wedin

1993 J. Biomech. 26: 1473-1477; Woltring in several publications; ...)

the Singular-Value-Decomposition (SVD) theory is proposed to estimate

R, in stead of the polar decomposition theorem proposed by Veldpaus.

Do both procedures give different results? And suppose SVD is better,

(as sometimes is mentioned), can somebody give me some practical

information that can help to program the SVD-calculation in

Borland Pascal (Dos version).

2. When I calculate the instantaneous screw axes parameters I need to

estimate the angular velocity vector omega. I use the formula

published in Woltring e.a. (1994, J. Biomech. 27: 1415-1432) where

the velocity vector is approximated from (R+R'_ - R_R'+)*(1/4T)

where R+ and R_ are the attitude matrix of the next and

previous sampling times and where T is the sampling

interval.

I'd like to know if there is a better way of calculating the velocity

vector using the velocity vector of each marker as input AND

using a least-squares technique.

Thanks in advance for your reply,

**************************************

Kaat Desloovere

Faculty of Physical Education and Physical Therapy K.U.Leuven

Tervuursevest 101

3001 Leuven (Heverlee)

Belgium

tel -- 32 16 32 90 74

fax -- 32 16 32 91 96

email kaat.desloovere@flok.kuleuven.ac.be

*************************************