ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

moments of inertia or eigenvalues which map on to perceived object magnitudes (such
as length and weight). The other consists of the principal directions or eigenvectors,
which map on to perceived relations between the hand and the object (such as position
of grasp). The interaction between said processes of “dynamic touch” is acknowledged
to play an important role in the adjustment of movement from the originally conceived
cognitive “framework”.
The main focus of our investigation is the identification and solution of
meaningful eigenvalue problems for spatial inertia tensor(s) that are associated with
proprioceptive invariants during the downswing. The first aim of the present study was
to clarify this issue in terms of a new set of eigenvalue problems. Essentially, we
attempted, a mechanical characterization of the connection between the inertial tensor
and dynamic touch via the spatial (free- and line-) vector components that are engaged
and responsive for such proprioceptive invariants. We then applied both the free-vector
and line-vector eigenvalue problem to the spatial inertia tensor of a golf club with hand
grasping. It has been suggested that the collection of all information variables relevant
to perception and action in some task can be represented on a low-dimensional simple
form or manifold [5]. We deal with manifolds that are coordinate-invariant in Euclidean
space albeit represented in the coordinates that we have chosen. We chose the club’s
Instantaneous Screw Axes (ISA)[6-7] and principal moment of inertia axes (e3) [8] and
used their instantaneous successive locations during swing as generating manifolds for
the perception to action diagram.
The second aim of our study was to apply the perception to action diagram that
we obtained, in the sense of dynamic touch paradigm to the role of perceptual learning
in the golf swing, i.e. movement across the information manifold of perception and
action.
Our working hypothesis was that a more skilled performer would exhibit a
stronger relationship between e3 and ISA. We therefore explored the influence of
perception on skill level, by comparing the perception to action diagrams of—a high
handicap player swing and a low handicap player swing. The implication of these
finding in conjunction with the functioning of the ‘flat left wrist’ are discussed.
3. METHODOLOGY
We developed a representation of spatial vector quantities that are relevant to the
action of the golf swing, using screw theory [9] to represent a directed line in space. It
has long been known that Instantaneous Screw Axes (ISA) are fundamental to the
description of a rigid body motion. The instantaneous motion of the club may be
considered to be rotating about the ISA. It is important that the general motion of the
perceiver’s action towards his/her perceived orientation of the hand-held club be such,
that it can be characterized by the ISA of the club. Said ISA is considered as the sum of
contributions of all the joints and muscles that are involved during the golf swing (i.e.
not only those that influenced by the wrist action). Line coordinates (or Plücker
Coordinates) [10] were extended here to describe screw motion (i.e. rotation with
translation) and thus to locate screw surfaces in terms of the set of ISA.
As we indicated in the introduction of this paper, the eigen structure of the
spatial inertia tensor as a proprioceptive invariant in motor control and learning has not
been fully explained. Since dynamic touch paradigm is based on the detection of
deviation from (normally) established patterns [2], in this study it is thought to be
analogous to the error covariance tensor that is encountered in estimation theory for
linear system[11]. Note that the spatial inertia tensor summarized the inertia and mass