# Implications of Rigid Gripping Constraints on Clubhead Dynamics in Steel Golf Shafts
## 2 Materials and Methods
### Experimental Setup  
A 9-iron was chosen as the test club as it represents the shortest iron club of interest (excluding wedges) and therefore the shortest distance for the waves to travel. A steel-shafted blade-style 9-iron was assembled to an un-gripped length of 37.75 in (0.908 m), with loft and lie angles of 42\({}^{\circ}\) (0.733 rad) and 62.5\({}^{\circ}\) (1.091 rad), respectively. The shaft was a commercially available model, featured a tip diameter of 0.355 in (9.017 mm), a butt diameter of 0.600 in (15.24 mm), and was of'stepped' design, i.e., the difference in diameter between the larger butt and smaller tip was achieved using steps, as opposed to a continuous taper. The club was fitted with a commercially available non-corded rubber golf grip. The test club was 'rigidly clamped' using a custom-built vice mechanism and positioned in front of a pneumatic ball cannon so that the clubhead was 600-630 mm from the nearest edge of the light gates, as illustrated in Figure 1. The point at which the club was clamped was representative of the gripping mechanism of the golf robot used at The R&A Equipment Test Centre; the robot gripping mechanism encloses approximately the first 0.23 m of the club as measured from the butt of the grip. The requirement of the gripping mechanism was solely that it needed to hold the club so that it could sustain multiple impacts. An accelerometer was positioned on the back of the clubhead to detect contact between ball and club. Three strain gauges were adhered to the shaft. The first was a gauge measuring torsion positioned on the shaft adjacent to the club's ferrule (approx. 0.1 m from the accelerometer measured parallel to the club shaft) on the 'underside' of the shaft, i.e., it would not have been visible to a golfer at address. A second gauge measuring torsion was located just beneath the grip (0.6 m from the accelerometer) on the same aspect of the shaft as the first gauge. A third gauge measuring longitudinal strain was located diametrically opposite to the second torsion gauge. Given that a fully-compensated circuit could not be achieved with the available resources, this third gauge offered reassurance that torsion was only being measured by the second torsion gauge, and that no cross-talk was occurring. The accelerometer signal was split between two two-channel data acquisition devices to ensure synchronisation (the acceleration signal was used to trigger the measurement). The remaining channel of each device acquired a strain signal from one of the three available gauges. A third device was used independently to capture the signals from the light gates monitoring inbound ball speed. All data acquisition devices sampled at a frequency of 10 MHz. Strain signals were subsequently filtered using a third-order Butterworth filter; a cut-off frequency of 20 kHz was deemed appropriate after inspection of the signals in the frequency domain. It is acknowledged that this cut-off frequency may have been somewhat conservative; this was considered sensible however, given the aims of the study and lack of a fully-compensated strain gauge circuit. Two target inbound speeds were used: 16 and 34 m\(\cdot\)s\({}^{-1}\). The lower speed permitted a fidelity check in that the strains for this speed should be lower than those for the higher speed. The higher speed was selected to represent 9-iron clubhead speeds generated by elite male amateur golfers (approximately 38.9 m\(\cdot\)s\({}^{-1}\)) [19], however it was a slight underrepresentation as pilot tests with inbound speeds above 34 m\(\cdot\)s\({}^{-1}\) risked dislocation of the accelerometer from the back of the clubhead. A digital spirit level was used to quantify (\(\pm\)0.2\({}^{\circ}\)) the orientation of the clubhead relative to the incoming trajectory of the ball. The shaft was angled such that the effective loft and lie of the clubhead were 26\({}^{\circ}\) and 0\({}^{\circ}\) respectively (i.e., the grooves were horizontal).