Calculation of angular joint displacements

In order to quantify the body movement throughout the swing, the players wore a pelvis belt, a vest, a humerus arm band, a wrist arm band, and a golf glove, all of which had markers attached to them (see Figure 32). The marker diameter was 12 mm for the arm markers and 19 mm for the trunk markers, with the smaller markers chosen for the arms to keep the size of the marker clusters as small as possible. The items holding the markers were designed so that at least three non-collinear markers could be attached to the corresponding body segment whilst keeping restrictions to the range of movement of the player to a

minimum. It was felt that this solution, although expected to be potentially less accurate than attaching the markers directly to the skin (Milner, 2008), was more appropriate for the golfers in this particular study because the golf swings were performed in an open hitting bay.

(a) (b)

Figure 32: Placement of (a) posterior and (b) anterior markers.

The software Visual3D (C-Motion, USA) was used to process the marker data, first by using its gap-fill algorithm to fill gaps in the marker trajectories of up to five samples, then by filtering the data with a low pass filter at a cut-off frequency of 15 Hz. The choice of this cut-off frequency was based on visual inspection of the frequency spectrum of selected markers. A similar level of cut- off frequency has been used in previous golf studies (Coleman & Rankin, 2005; Wheat, Vernon, & Milner, 2007). It is possible that data were not always smoothed sufficiently at this cut-off rate, but this was accepted as the derivates of the marker trajectories were not required. Following this, Visual 3D was used to associate local coordinate systems (Cappozzo, Della Croce, Leardini, & Chiari, 2005) with each of the following body segments:

- pelvis - thorax

- left humerus - left forearm - left hand

Assuming each of these segments to be rigid, the three-dimensional position and orientation of the associated local coordinate system could be determined at any given time using the marker coordinates. A detailed definition of the local coordinate systems can be found in Appendix E (p. 211) and a general discussion of this topic can be found in Section 4.5 (p.81). Using a calibration procedure, the local coordinate system for each segment was defined so that its axes corresponded with the anatomical axes of the corresponding segment (Figure 33). When the golfer was in the anatomical position, each segment coordinate system had its z-axis pointing along the distal to proximal segment axis, its y-axis to the front and its x-axis to the right (medially for the arm segments).

Figure 33: Definition of segment coordinate systems. For each segment, the x-axis points medially, the y-axis frontally and the z-axis proximally

when the player is in the anatomical position.

Catani, Della Croce, & Leardini, 1995). Furthermore, the rotation centres of the glenohumeral, elbow and wrist joint were identified using a dynamic calibration. For this, golfers were requested to move the distal body segment according to the instructions of the experimenter whilst the camera system was tracking the movement in real-time. The calibration movements applied included approximately 10 cycles of all applicable joint movements (e.g. pronation/supination and flexion/extension for the elbow), following recommendations available for the hip joint (Begon, Monnet, & Lacouture, 2007). An algorithm supplied by the Visual3D software was then used to estimate the joint centre position (Schwartz & Rozumalski, 2005). It has been shown with simulated data that, whilst being computational demanding and relatively slow, this algorithm is one of the most accurate for determining joint centre positions (Ehrig, Taylor, Duda, & Heller, 2006).

Whilst the functional joint centre method has been used extensively for the lower leg, use of functional methods for determining the joint centres of the upper limbs is still in its infancy. Recent validation studies showed that accuracy may be as low as 20 mm when using one simple marker triad per segment (Roosen, Pain, & Begon, in press). Therefore, additional digitisation points were placed close to the expected joint centre position so that it was possible to perform a visual check after the algorithm calculated the functional joint centres. For instance, the position of the medial and lateral epicondyles of the elbow were marked relative to the forearm marker triad and the functional joint calibration was repeated in case the functional joint centre did not fall approximately on a line connecting the two epicondyles.

After the local coordinate systems were established, angular joint displacement was calculated using the Euler/Cardan-sequences listed below. Each sequence consists of three coordinate system transformations (e1, e2, e3), whose

interpretation is given below and illustrated in Appendix E (p. 211). The sequences are based on recommendations given by Wu et al. (2005) whenever possible:

- Pelvis relative to global coordinate system: X-Y-Z (not provided by Wu et al. but consistent with their sequence proposed for global thorax orientation):

 e1: forward / backward tilt (not reported)  e2: lateral obliquity (left/right tilt) (not reported)  e3: axial rotation

- Thorax relative to global coordinate system: X-Y-Z

 e1: flexion / extension (not reported).

 e2: lateral flexion / extension (not reported).  e3: axial rotation.

- Humerus relative to thorax: Z-Y-Z

 e1: Sets the position of the plane of humerus elevation. With

e1=0°, elevation will be in the plane of abduction; with e1=90°,

elevation will be in the plane of forward flexion.

 e2: Elevation of the humerus relative to the thorax.

 e3: Axial rotation of the humerus (internal/external rotation).

- Forearm relative to humerus: X-Y-Z

 e1: Elbow flexion/extension.  e2: Carrying angle (not reported).

 e3: Pronation and supination of the forearm.

- Hand relative to forearm: X-Y-Z (was not defined by Wu et al. but was chosen so that it was consistent with the elbow sequence.)

 e2: Adduction and abduction, or ulnar and radial deviation.  e3: Circumduction (not reported).