Herman J. Woltring

06-06-1991, 11:02 PM

Dear Professor Sommer and other Biomch-L readers/posters,

It is with pleasure that I see others joining the ICR debate. In fact,

Professor Sommers kindly sent me on 2 Jan 1991 a letter with some highly

interesting (p)reprints of his most recent work, to be precise:

(1) H.J. Sommer III, Determination of First and Second Order Instant Screw

Parameters from Landmark Trajectories, Proc. 21st Mechanisms Conference,

American Society of Mechanical Engineers, DE-25:429-437 (1990), also

accepted for publication in the ASME Journal of Mechanisms, Trans-

missions, and Automation in Design (scheduled to appear during Spring

1991);

(2) H.J. Sommer III & F.L. Buckzek, Least Squares Estimation of the Instant

Screw Axis and Angular Acceleration Axis, 1990 ASME Advances in Bio-

engineering, BED-17:339-342 (1990), also to be presented at the Inter-

national Symposium on 3-D Analysis of Human Movement whose programme

was posted onto this list by Ian Stokes some weeks ago.

My main problem with Professor Sommer's zero acceleration pivot (which can

be calculated from the rotation velocity and acceleration vectors and the

acceleration of some base point on the moving body) is the question what it

can be used for: while it is the generally unique point with zero instanta-

neous acceleration on (an extension of) a moving rigid body, it does not in

general have the smallest, instantaneous velocity. Thus, it is -- in my mind

-- less attractive a candidate for (straightforward) generalization from a

fixed to an Instantaneous Centre of Rotation than the Instantaneous Helical

Axis' central point or pivot; it is, however, the generally unique point which

has instantaneous *stationary* movement by virtue of of its vanishing accele-

ration, and this may have some special kine(ma)tic implications hopefully

revealed in future research.

>From Professor Sommer's posting I understand that he claims ASME priority on

what I have chosen to call the `3-D ICR',

"These methods have been combined to also determine the instantaneous

central point of the screw axode ruled surface (the point on the ISA

with minimum acceleration about which the ISA instantaneously changes

direction with time) ...

Mathematical development of these methods has been presented and

published through ASME. Application of these methods to biomechanics

will be presented in July at the Int. Symp. on 3D Analysis of Human

Movement in Montreal".

I must confess not having been aware of prior ASME-published work in this

area (but then, my Nov 1990 postings tried to make clear that I was not

claiming any `inventors' primacy other than believing to have shown that the

IHA's central pivot is that point on the IHA which has the smallest accele-

ration; it is the point with the latter property that I choose to call the

3-D ICR). At any rate, the central point as such is an old notion, having

been used in a finite displacement context by Otto Fischer in 1907, and

proposed as an `instantaneous' centre of rotation by Ed Chao and Kai-Nan An

at the Nijmegen ESB meeting about 10 years ago. Furthermore, the central

point's instantaneous kinematics have been provided by Suh & Radcliffe in

their 1978 book "Kinematics & Mechanisms Design", Chapter 10 (N.B.: Ian

Stokes might think again about encyclopedias, but I must insist on declining

that compliment: Professor Sommer does not only quote Suh & Radcliffe, but

also Everett 1875 with work getting close to the above idea that the central

point coincides with the 3-D ICR defined as the point of smallest accelera-

tion of all points on the IHA).

While the mathematics for assessing all these kinematic movement descriptors

from rigid-body data and their derivatives is straightforward but tedious,

assessing these intermediate rigid-body data from noisy landmark coordinates

is not so easy. For example, optimally transforming noisy landmark data is

a nonlinear least-squares problem under rather conventional noise conditions,

and Professor Sommer has kindly quoted some recent litterature in this area.

While there are certain linear procedures, they are not optimal from a mini-

mum variance point of view; however, it is currently not known how suboptimal

these linear methods are in practice.

Last-but-not-least: obtaining reliable 1st and 2nd derivatives from noisy

data -- especially if they contain genuine transients -- is far from easy;

this is even more difficult for 3rd derivatives, and I look forward to the

Montreal presentations about these and related signal processing challenges.

Finally, I'd like to have some `democratic' feedback from the readership on

whether this kine(ma)tics debate is thought interesting or too esoteric.

Herman J. Woltring, Eindhoven/NL

It is with pleasure that I see others joining the ICR debate. In fact,

Professor Sommers kindly sent me on 2 Jan 1991 a letter with some highly

interesting (p)reprints of his most recent work, to be precise:

(1) H.J. Sommer III, Determination of First and Second Order Instant Screw

Parameters from Landmark Trajectories, Proc. 21st Mechanisms Conference,

American Society of Mechanical Engineers, DE-25:429-437 (1990), also

accepted for publication in the ASME Journal of Mechanisms, Trans-

missions, and Automation in Design (scheduled to appear during Spring

1991);

(2) H.J. Sommer III & F.L. Buckzek, Least Squares Estimation of the Instant

Screw Axis and Angular Acceleration Axis, 1990 ASME Advances in Bio-

engineering, BED-17:339-342 (1990), also to be presented at the Inter-

national Symposium on 3-D Analysis of Human Movement whose programme

was posted onto this list by Ian Stokes some weeks ago.

My main problem with Professor Sommer's zero acceleration pivot (which can

be calculated from the rotation velocity and acceleration vectors and the

acceleration of some base point on the moving body) is the question what it

can be used for: while it is the generally unique point with zero instanta-

neous acceleration on (an extension of) a moving rigid body, it does not in

general have the smallest, instantaneous velocity. Thus, it is -- in my mind

-- less attractive a candidate for (straightforward) generalization from a

fixed to an Instantaneous Centre of Rotation than the Instantaneous Helical

Axis' central point or pivot; it is, however, the generally unique point which

has instantaneous *stationary* movement by virtue of of its vanishing accele-

ration, and this may have some special kine(ma)tic implications hopefully

revealed in future research.

>From Professor Sommer's posting I understand that he claims ASME priority on

what I have chosen to call the `3-D ICR',

"These methods have been combined to also determine the instantaneous

central point of the screw axode ruled surface (the point on the ISA

with minimum acceleration about which the ISA instantaneously changes

direction with time) ...

Mathematical development of these methods has been presented and

published through ASME. Application of these methods to biomechanics

will be presented in July at the Int. Symp. on 3D Analysis of Human

Movement in Montreal".

I must confess not having been aware of prior ASME-published work in this

area (but then, my Nov 1990 postings tried to make clear that I was not

claiming any `inventors' primacy other than believing to have shown that the

IHA's central pivot is that point on the IHA which has the smallest accele-

ration; it is the point with the latter property that I choose to call the

3-D ICR). At any rate, the central point as such is an old notion, having

been used in a finite displacement context by Otto Fischer in 1907, and

proposed as an `instantaneous' centre of rotation by Ed Chao and Kai-Nan An

at the Nijmegen ESB meeting about 10 years ago. Furthermore, the central

point's instantaneous kinematics have been provided by Suh & Radcliffe in

their 1978 book "Kinematics & Mechanisms Design", Chapter 10 (N.B.: Ian

Stokes might think again about encyclopedias, but I must insist on declining

that compliment: Professor Sommer does not only quote Suh & Radcliffe, but

also Everett 1875 with work getting close to the above idea that the central

point coincides with the 3-D ICR defined as the point of smallest accelera-

tion of all points on the IHA).

While the mathematics for assessing all these kinematic movement descriptors

from rigid-body data and their derivatives is straightforward but tedious,

assessing these intermediate rigid-body data from noisy landmark coordinates

is not so easy. For example, optimally transforming noisy landmark data is

a nonlinear least-squares problem under rather conventional noise conditions,

and Professor Sommer has kindly quoted some recent litterature in this area.

While there are certain linear procedures, they are not optimal from a mini-

mum variance point of view; however, it is currently not known how suboptimal

these linear methods are in practice.

Last-but-not-least: obtaining reliable 1st and 2nd derivatives from noisy

data -- especially if they contain genuine transients -- is far from easy;

this is even more difficult for 3rd derivatives, and I look forward to the

Montreal presentations about these and related signal processing challenges.

Finally, I'd like to have some `democratic' feedback from the readership on

whether this kine(ma)tics debate is thought interesting or too esoteric.

Herman J. Woltring, Eindhoven/NL