View Full Version : AAA, ICR, and central point

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

(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