Platform-Based Methods for Other Movement Analyses

Other researchers have estimated CM kinematics for activities other than stance or gait using IA methods. Papa and Cappozzo (1999) used the IA for sit-to-stand movements. However, they determined S0 by SK analysis, thus defeating the

purpose somewhat of using an IA method in order to avoid an SK analysis. Kerwin (1986) calculated CM kinematics as part of his method to determine H′CM

at take-off for gymnasts performing flic-flacs (reverse handsprings) by calculating the torque about the CM. S0 was estimated by a full SK analysis because absolute

CM(t) was required to calculate H′CM. As SK analysis was required, albeit only

cumulative drift error to H′CM calculations that may have been practically

significant by the time take-off was reached.

Hatze (1998) and Kibele (1998) used IA methods to determine relative vertical

CM(t) for jumping activities. These approaches were completely independent of SK analyses. Hatze (1998) assumed V0 = 0 for the countermovement jumps he

analysed. He also analysed series of rebound jumps, for which V0 was assumed to

be zero at the commencement of such jump series. The initial velocity (at the time of impact) for each subsequent rebound jump in a series was determined from the time elapsed whilst airborne prior to impact and the calculated final velocity (at take-off) of the previous jump in that series. This approach is dependent on the accuracy of the assumption that V0 = 0 prior to the first jump and

the accuracy of estimates of the airborne phase durations. Although not stated explicitly, it appears that Kibele (1998) also assumed that V0 = 0. Once again, the

discrepancy between V0 = 0 and the actual value of V0 may introduce a practically

significant drift error to CM(t) calculations, particularly for the longer duration series of rebound jumps.

Kibele’s approach was different to Hatze’s in that he determined a specific body weight for each trial. He described the vertical GRF as “constant” during both the aerial phase and the quasi-static phase prior to countermovement jump commencement (minimum duration 0.3 s). The body weight was defined as the difference between these two readings for each trial. The advantage of this approach is that it negates the need to consider the possibility of a force calibration factor error (FC) in the GRF signal (i.e. the error in the calibration

factor which is used to convert force platform voltage signals into units of force, usually from mV into N). Because FC would also be present in the GRF readings

used for determining mWB, this error factor would be present in both the numerator

and the denominator of the first term in Eq. (3), and would therefore cancel out and play no role in CM(t) determination. However, the fundamental disadvantage of this approach is that subject mass does not change from trial-to-trial in reality. Further, vertical GRF is not constant during quiet stance and 0.3 s is arguably an insufficient time period over which to average this signal in order to estimate body mass accurately. Kibele stated that the “body weight value does not vary significantly (less than 1%) between trials.” The effect on CM(t) calculations of the different body mass values observed in his study were not reported by Kibele (1998). Whether or not body mass variations of 1% introduce CM(t) errors of practical significance for activities as transient as countermovement jumps, the effect on longer duration activities is more likely to be practically significant.

Vanrenterghem et al. (2001) also determined trial-specific body mass values when they applied the IA to ten simulated countermovement jump trials. They reported using an “optimising loop” to find the body mass value that resulted in no net vertical displacement of the CM during the two-second stance phase prior to jump initiation. They also assumed vertical V0 to be zero. Vanrenterghem et al.

advocated trial-specific selection of body weight and claimed that this “results in the best possible correct jump height parameters.”

method also required a full body SK analysis to be conducted. They assessed jumping, bending and kneeling activities. Importantly, they attempted to account for another potential source of error by introducing a GRF offset error term (FO)

into the equation for calculating CM(t):

0 0 2 1 1 _⎜⎛ FO _⎟⎞ 2 ) ( g t V t S m Fdt m t CM WB WB + + ⎟ ⎠ ⎜ ⎝ + + =

∫∫

he values of S0, V0 and FO that minimised, in a least squares sense,

e function:

In addition to trial-specific body mass values, Rabuffetti and Baroni (1999) also searched for t th ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + + −

∫∫

where CM(t)SK is the whole body CM determined by a full body SK analysis.

Necessary BSP estimates were derived from Zatsiorsky and Seluyanov (1983). The results they presented for one trial indicated a value of 0.079 ms-1 for medio-lateral V0, which is arguably non-feasible for this parameter for a normal

subject during quiet stance3, particularly considering that stance is more stable in the medio-lateral dimension than the antero-posterior dimension (Winter et al., 1996a). Indeed, even for an eyes-closed condition, Masani et al. (2003) reported maximum antero-posterior CM velocity values less than 0.03 ms-1. The

ta and BSP estimates ontributed to the derivation of a non-feasible value of V0.

buffetti and Baroni (1999) was that a full body SK analysis was ot necessary.

apparently unrealistic V0 value might have been caused by shortcomings in the

optimisation algorithm’s searching performance near the minimum. It is also possible that errors inherent in the joint coordinate da

c

Jaffrey et al. (2003) questioned the validity of the trial-specific body mass determinations proposed by Kibele (1998), Vanrenterghem et al. (2001) and Rabuffetti and Baroni (1999), based on the fact that body mass does not change from trial-to-trial. Jaffrey et al. (2003) also used an IA optimisation method to determine relative CM(t) for a countermovement jump. Their objective was similar, though not identical, to that of Vanrenterghem et al. (2001). They minimised an objective function representing the sum of squared relative CM(t) values during the two-second quasi-static stance phase prior to jump initiation. The advantage of this approach (and that of Vanrenterghem et al., 2001) over the approach of Ra

n

To support the theoretical argument against varying body mass, Jaffrey et al. (2003) demonstrated the different effects of varying body mass versus holding body mass constant when minimising their objective function. Three parameters in Eq. (7) were addressed in their assessment: mWB, V0 and FO (S0 was omitted

m less than the jump amplitude r the constant (accurate) body mass condition.

roposal of abuffetti and Baroni (1999) to include a GRF offset error parameter.

constant value obtained from accurate mass measurement on precision scales (64.21 kg), and only FO and V0 were allowed to vary. The resultant value of V0

was 0.00352 ms-1. Although no values for vertical CM velocity during quiet stance were retrieved from the literature, this value for V0 does not appear to be

excessive for the vertical dimension during quiet stance. When mWB was also

allowed to vary, the resultant value of mWB was unrealistically 1.1 kg greater than

the accurately measured value; the value of V0 only changed by 0.00006 ms-1; and

FO increased by 10.75 N, apparently compensating quite well for the mass error

(1.15 kg × 9.8 ms-2 _{= 10.78 N). However, the calculated jump amplitude in the} variable body mass condition was more than 0.01

fo

The major limitation of the work presented by Jaffrey et al. (2003) was that only a single trial was assessed. However, they demonstrated that accurate mass determination and the use of a force offset error variable produced different CM(t) results to those produced by allowing body mass alone to vary. Coupled with the knowledge that mWB does not vary from trial-to-trial in reality, they concluded that

body mass should be determined accurately on precision scales and included in the objective function as a constant. Further, they supported the p

R

For movement analyses commencing with quasi-static phases, V0 will not usually

be precisely zero. This supports the inclusion of this parameter in any IA optimisation method. The realistic values obtained for V0 by Jaffrey et al. (2003)

ented optimisation search algorithm and e formulation of the objective function.

e to K determination of CM kinematics for a wide range of movement activities.