Page 167 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

144 BIOMECHANICS OF THE HUMAN BODY

There are essentially two approaches that are used for estimating BSP values. The more exact
approach is to measure the BSP values experimentally. In practice, this is rarely done because the
process is tedious, subject to error, and certainly not practical to perform for every subject. Because
the BSP values are difficult to measure accurately, they are generally estimated using anthropometric
lookup tables and/or regression equations (e.g., Dempster, 1955; Winter, 1990; Zatsiorsky and
Seluyanov, 1985).
For the case of a two-dimensional analysis, when motion is assumed planar, the moment of
inertia in Eq. (6.18) takes on a single value. In the case of a three-dimensional analysis, I becomes
a 3 × 3 inertia tensor. The main diagonal of the inertia tensor is constant and the off-diagonal
elements vanish when the principal axis of inertia is aligned with the axes of the ACS. The
diagonal matrix in Eq. (6.38) reflects this alignment and is the form used in Eq. (6.18) for a
three-dimensional analysis in which the moments are expressed in the ACS of the segment.

⎡ I xx 0 0 ⎤
⎢ ⎥
Ι= ⎢ 0 I yy 0 ⎥ (6.38)
⎢ 0 0 I zz ⎥ ⎦
⎣
If we assume that each segment is a homogeneous solid of known geometry, we can use standard
formulas for calculating mass moment of inertia about the X, Y, and Z axes.

6.4.5 Force Transducers
The role of a force transducer is to record external forces acting on the body. Force plates used in
gait and postural studies to measure ground reaction forces are perhaps the most familiar type of
force transducer used in biomechanics. A force platform is sensitive to the load a subject applies to
the plate, with the plate exerting an equal and opposite load on the subject (hence the term ground
reaction forces). Although we will limit our discussion to force plates, we wish to point out that other
types of force transducers are used in the study of human movement. For example, multiaxial load
cells are used to investigate the motor control of arm movements (e.g., Buchanan et al., 1993, 1998).
Commercially available force platforms use one of the two different measuring principles to
determine the applied load. The first type of force plates use strain gauge technology to indirectly
measure the force applied to the plate (e.g., AMTI and Bertec), while the second type uses piezo-
electric quartz (e.g., Kistler). Piezoelectric materials produce an electrical charge directly propor-
tional to the magnitude of the applied load. In this section, we focus on how the output of a force
platform is used in an inverse dynamics analysis, without considering how the forces and moments
detected by the plate are calculated.
Force platforms are used to resolve the load a subject applies to the ground. These forces and
moments are measured about X, Y, and Z axes specific to the force platform. In general, the
orientation of the force platform axes will differ from the orientation of the reference axes of the
object-space. This is illustrated schematically in Fig. 6.14. Thus, it is necessary that the ground reaction
forces be transformed into the appropriate reference system before they are used in subsequent
calculations. For example, the ground reaction forces acting on the foot should be transformed into
the foot coordinate system, if ankle joint forces and moments are expressed in an anatomically
meaningful reference system (i.e., about axes of the ACS ).
foot
Another variable that must be considered is the location of the external force acting on the
system. For the case of a subject stepping on a force platform, the location of the applied load is
assumed to act at the center of pressure (COP). The term is aptly named since the subject really
applies a distributed pressure to the top surface of the force plate that is treated as an equivalent point
force. As with the forces and moments, the location of the COP in the force platform system should
be transformed into the appropriate reference system. Other devices such as pressure insoles and
mats can measure pressure distributions, but are not suitable for three-dimensional motion analysis
because they do not provide a complete 6° of freedom history of the applied load. If the data from a