Table 1.
Abbreviation of parameters.
Fig 1.
A schematic diagram of an non-deformable oar with a net external force () applied at the free end of the oar and the position of the location at the blade at which the external force is applied at that moment in time (
) (panel A). In panel B and C the free bodies 1 and 2 are presented.
Fig 2.
(A) An overview of the experimental setup, (B) the related schematic overview of the experimental setup in a horizontal plane, and (B) a schematic representation of the bended oar relative to its neutral position with the relevant determined parameters.
The xy-frame of reference represents an earth-bound frame of reference in which the positive x-axis points towards the blade of the oar in an unloaded position. The x’y’-frame of reference represents the blade-bound frame of reference in which the positive x’-axis points towards the end of the blade.Φb/w is the angle of the blade in loaded position relative to the blade in neutral position. ,
, and
refer to the three bending moments measured at location 1,2, and 3 of the oar respectively. T and E are the beginning and the end of the blade respectively.
is the external force vector applied at the blade, while
and
are the perpendicular and parallel force components, respectively.
,
,
, and
are the position vectors of location 1,2, T, and E in the loaded situation relative to their location in the unloaded position. Note that
is not depicted in this figure since it is very small. The
and
represent the x and y-components of the known and measured moment-arms in a blade-bound frame of reference.
is the x’-component of the position vector of the location of the PoA with respect to the beginning of the blade.
Fig 3.
Typical examples of the (1) bending moment at one location of the oar , (2) the orientation of the blade relative to an earth-bound frame of reference (Φb/w), and (3) the displacement of the beginning of the blade in y-direction for one validation trial (
).
Reference values are depicted using a bold grey line, while the values estimated using strain gauges are illustrated as dashed black lines. Note that the missing data refers to data in which the parallel force is lower than -30 N or higher than 20 N.
Fig 4.
Typical examples of (1) the perpendicular force component (), (2) the parallel force component (
), and (3) the x’-component of the location of the point of application
.
The bold grey lines represent the reference values obtained using Optotrak and the force transducer, while the black dashed lines are the values obtained using the presented method. Note that the missing data is data in which the parallel force is lower than -30 N or higher than 20 N.
Table 2.
Correspondence values (i.e. Intra Class Correlation; ICC; and the Standard Error of the Estimate; SEE) between estimated force components and the x’-component of the position vector of the location of the point of application (i.e. ,
,
, respectively) on the one hand, and their reference values on the other hand for the (1) whole data set and a data set that only includes samples of which the displacement of the beginning of the blade was more than (2) 0.58 cm and (3) 2.6 cm.
Fig 5.
Typical examples of (a) the velocity in y’-direction of the location of the blade where the point of application is located (), and (b) the component of Pdefl associated with the perpendicular force.
The bold grey lines represent the reference values obtained using Optotrak and the force transducer, while the black dashed lines are the values obtained using the presented method. Note that the missing data is data in which the parallel force is lower than -30 N and higher than 20 N.