Young-Hoo Kwon,
Chris Como, Ki Hoon Han, Sangwoo Lee, & Kunal Singhal
Biomechanics Laboratory, Texas Woman’s University, Denton, TX
6th World Scientific Congress of Golf, Phoenix, AZ
Triple-pendulum model
X-Factor
Stretch-Shortening Cycle
(Cochran & Stobbs, 1968; Hume et al., 2005; Hellstrom, 2009)
2
Motion Planes
L Shoulder
MD
R Shoulder
R Elbow
MF
L Hand
FSP
FSP
(Kwon et al., 2012)
3
Hand Path Determined by:
Projected Clubhead
New Hub
• Trunk motion &
• Arm motions
Trunk Motion:
Projected Hand
•
•
•
•
Flexion/extension
Lateral flexion
Rotation
Elevation/depression
Arm Motions:
• Shoulder motions
• Elbow motions
4
New Kinematic Sequence: Joint Angular Velocities
500
400
P: P/A Tilt
(deg/s)
300
P: R/L Tilt
200
P: L/R Rot
100
T: R/L Lat Fl
0
(deg/s)
-100 0
-200
500
400
300
200
100
0
-100 0
-200
-300
20
40
60
80
100
T: L/R Rot
Normalized Time (%)
S: Fl/Ext
S: Abd/Add
S: E/I Rot
20
40
60
80
100
E: Fl/Ext
Normalized Time (%)
Meaningfulness of the trunk rotation and the X-factor?
5
Trends:
• Comparison among different skill levels (Cheetham et al. 2000; Zheng et al.,
2007; Cole & Grimshaw, 2009)
•
•
•
•
•
Comparison among different ball velocity groups (Myers et al., 2007)
Comparison among different effort levels (Meister et al., 2011)
Correlation/regression (Myers et al., 2007; Chu et al., 2010)
Training effects (Lephart et al., 2007)
Methodology (Joyce et al., 2010)
*p < 0.05
Issues:
•
•
•
•
ANOVA/correlation/regression with heterogenous samples
No direct relationship between CH velocity and X-factor
Influence of the planar swing model / stretch-shorting cycle
Projected to the horizontal plane
6
To assess the contributions of the joint/segment
motions to the clubhead velocity:
• Homogenous sample
• Normalized CH velocity
• Direct relationship between the CH velocity and the trunk
motion
To assess the relationship between the X-factor
parameters and the CH velocity:
• Projected to the functional swing plane
• Homogenous sample
• Normalized CH velocity
7
18 Male Skilled Golfers:
• Recruited from North Texas (Dallas)
area
• Handicap: -0.6 ± 2.1
• Height: 1.81 ± 0.05 m
• Mass: 82.6 ± 10.4 kg
Clubhead Velocity:
• 45.48 ± 2.85 m/s (102.3 ± 6.4 mph; CV = 6.3%)
• 25.21 ± 1.82 BH/s (CV = 7.2%)
8
Motion Capture:
•
•
•
•
•
10-camera VICON system (Centennial, CO)
Captured at 250 Hz
‘TWUGolfer’ marker set (65 markers)
2 AMTI force plates (250 Hz)
4 different types of trials (ball plate, club, static
posture, & motion trials) captured
Laboratory Study:
• Wiffle balls
• Ball mat
• 5 driving trials per golfer collected
9
‘TWUGolfer’ Body Model:
• 89 points
• 13 joints / 24 computed points
• 18 bodies / 6 additional reference frames
Data Processing:
•
•
•
•
C3D importing
Kwon3D (Visol, Seoul, Korea)
Cutoff frequency: 20/10 Hz
Interpolated to 2,000 Hz
10
TB
ED
MD
BI
MF
Top of BS
Early DS
Mid DS
Ball Impact
Mid FT
11
FSP (Kwon et al., 2012):
• Plane formed by the clubhead trajectory
(MD to MF)
• Projected trajectory
Moving FSP Reference Frame:
• Instantaneous rotation centers & arms
• Normal, tangential, & radial axis
X-Factor Computation:
• Shoulder & hip lines
• Projected to the FSP frame
ii
n
ro
ki
ji
12
v1  2  r21
v1
 3  r31
Elbow (1)
 4  r41
Shoulder Joint (3)
 5  r51
Mid-Shoulder (1)
 6  r61
L4/L5 (3)
6
 F  r71
Pelvis Rotation (3)
7
 v7
Mid-Hip Translation
1
A
4
D
C
B
2
5
E
3
F
Wrist (2 + 1 DOFs)

Time Function:
( FSP )
1
v
 TFSP G   v2  v3  v4  v5  v6  v 7   
Max contribution
Contribution at BI
Contribution
13
30
100%
25
(BH/s)
CH
20
Wrist
46.9%
15
Pr/Sup
16.8%
SJ
19.2%
Trunk
15.7%
Pelvis
18.5%
10
5
(5)
(1)
(12)
0
0
20
40
60
80
100
Normalized Time (%)
14
30
vs. Max CH Velocity
(p < 0.05)
25
r = 0.724
(BH/s)
20
Max
15
Change
r = 0.539
10
r = 0.501
r = -0.475
5
0
(3)
-5
CH
Wrist Pr/Sup Elbow
SJ
Trunk Pelvis
Joint/Segment
(1)
MH
15
140
120
100
Hip Line
(deg)
80
60
40
Shoulder
Line
20
X-Factor
0
-20
0
20
40
60
80
100
-40
-60
Normalized Time (%)
16
140
120
100
(deg)
80
Hip Line
X-Factor Stretch
60
Shoulder
Line
1.5 ± 2.2 deg
40
X-Factor
20
0
-20
0
20
40
60
80
100
-40
-60
Normalized Time (%)
17
150
CV = (15, 79, 18)%
CV = (21, 25, 17)%
CV = (10, 31, 11)%
100
r = -0.461*
50
(deg)
vs. Max CH Velocity
(*p < 0.05)
0
Max
-50
Impact
r = -0.486*
-100
r = -0.568*
Change
-150
X-Factor
Hip Line
X-Factor Parameter
Shoulder Line
18
Velocity Contribution:
• Wrist motion: the main source of the CH
velocity
• Pelvis motion: larger contributions than the
trunk motion
• Wrist & pelvis contributions: correlated to the
max CH velocity
• Trunk motion: no notable contribution /
correlation to the max CH velocity
Velocity Decomposition:
• Decomposed velocities  causal relationships
• 3-D modeling studies needed: to establish the causal relationship
19
X-Factor:
• Not the X-factor but the hip & shoulder
parameters were correlated to the max CH
velocity.
• Direct relationship between max CH velocity
and X-factor is questionable.
• Inter-group difference in X-factor may mean
fundamental differences in swing style.
• The X-factor could be an indicator of the
golfer’s skill level.
20
Golf swing:
•  a planar motion around a hub (Cochran & Stobbs, 1968)
• Planar perspective, X-factor, & SSC:
• Popular menus
• Time to reassess their meaningfulness
• Trunk & arms: work together to
achieve a planar CH motion in the
delivery zone
• Future studies: trunk-arm
coordination
21
Velocity decomposition revealed that
contribution of the trunk motion to
the max CH velocity was minor.
Not the X-factor, but the hip and
shoulder line position/ROM showed
significant correlations to the max CH
velocity.
The link between the X-factor/stretch-shortening cycle perspective
and CH velocity generation is questionable.
Future studies need to focus on hip and shoulder line position/ROM
vs. downswing motion patterns.
22
23
Static Posture
Motion Trial
Processed Motion Trial
Club
Ball Plate
24
CH Velocity:
v1   v1  v 2 
v1
  v2  v3 
1
A
4
  v3  v4 
D
C
E
B
2
5
3
6
F
7
  v 4  v5 
  v5  v 6 
  v6  v7 
 v7
Relative Velocity of CH to Wrist:
v1  v 2  A  r21
  2  3  4  5  6  F   r21
25
v1   2  3  4  5  6  F   r21
Segment Perspective:
v1
  3  4  5  6  F   r32
1
  4  5  6  F   r43
A
4
D
C
5
E
B
3
2
F
  6  F   r65
6
 F  r76
7
 v7
Joint Perspective:
 2  r21
v1
 3  r32  r21 
 4  r43  r32  r21 
1
A
4
 5  r54  r43  r32  r21 
D
C
5
E
B
2
  5  6  F   r54
3
6
F
7
 6  r65  r54  r43  r32  r21 
 F  r76  r65  r54  r43  r32  r21 
 v7
26
v1  2  r21
v1
 3  r31
Elbow (1)
 4  r41
Shoulder Joint (3)
 5  r51
Mid-Shoulder (1)
 6  r61
L4/L5 (3)
6
 F  r71
Pelvis Rotation (3)
7
 v7
Mid-Hip Translation
1
A
4
D
C
B
2
5
E
3
F
Wrist (2 + 1 DOFs)

Time Function:
v1  v2  v3  v4  v5  v6  v 7  
 v dt   v dt   v dt   v dt   v dt   v dt   v dt  
1
2
3
4
5
6
7
Max contribution
Contribution at BI
Contribution
27
10
8
6
(BH/s)
4
CH
Up
2
Wrist
0
-2
0
Down
20
40
60
80
100
Pr/Sup
SJ
-4
Pelvis
-6
-8
-10
Normalized Time (%)
28
1.5
1
Toward
CH
(BH/s)
0.5
Wrist
Pr/Sup
0
0
20
40
60
-0.5
80
100
SJ
Trunk
Away
Pelvis
-1
M Hip
-1.5
-2
Normalized Time (%)
29
Goal:
• Accuracy & consistency in distance &
direction
• Maximization of the distance
Impact Conditions:
•
•
•
•
Motion of the clubhead (velocity)
Orientation of the clubface at impact
Location of impact on the clubface
Distance: function of the CH velocity at impact
30
31
Study
Methods
Results
Cheetham et al.
(2000)
10 skilled
9 less skilled ( 15)
Skilled > less skilled (max)
Zheng et al.
(2007)
18 professional (0)
18 low HC (3.22)
18 mid HC (12.5)
18 high HC (21.3)
Pro > high (TB)
Myers et al.
(2007)
21 low ball velocity (15.1)
65 medium ball velocity (7.8)
14 high ball velocity (1.8)
Low, med. < high (TB)
Low < med. < high (max)
Correlation (TB, max)
Lephart et al.
(2007)
15 golfers (12.1)
8-week golf-specific training
Pre < Post (shoulder
rotation, x-factor)
Cole & Grimshaw 7 low HC ( 10)
(2009)
8 high HC (12-18)
None
32
Study
Methods
Results
Chu et al. (2010)
266 males & 42 females (8.4)
Multiple regression (TB)
Joyce et al.
(2010)
Method study
Orientation angle approach
Comparison among
rotation sequences
Meister et al.
(2011)
10 professional (scratch or better)
Within subject correlation
5 amateur (4, 15, 30, two novice)
(professional; max,
3 effort levels (easy, medium, & hard) impact)
Issues:
•
•
•
•
Heterogenous samples
No direct relationship between CH velocity and X-factor
Influence of the planar swing model / stretch-shorting cycle
No normalization of the CH velocity to body size
33
Correlation: vs. Max Clubhead Velocity
Maximum
(BH/s)
At Impact
(BH/s)
Change
(BH/s)
Clubhead
25.21 ± 1.82
24.86 ± 1.85
(r = 0.997*)
-0.35 ± 0.15
Wrist
11.87 ± 2.08
(r = 0.724*)
10.32 ± 2.16
(r = 0.633*)
-1.55 ± 1.05
Pr/Sup
4.17 ± 2.23
4.14 ± 2.24
-0.03 ± 0.08
Elbow
1.94 ± 1.10
0.75 ± 1.93
-1.19 ± 1.20
(r = 0.501*)
SJ
4.82 ± 0.63
2.71 ± 2.24
-2.11 ± 2.14
Trunk
3.95 ± 0.67
3.25 ± 1.30
-0.70 ± 0.88
Pelvis
4.67 ± 0.84
(r = 0.539*)
3.97 ± 0.94
-0.70 ± 0.58
M Hip
0.35 ± 0.15
(r = -0.402; p = 0.10)
-0.04 ± 0.15
-0.39 ± 0.23
(r = -0.475*)
34
Correlation: vs. Max Clubhead Velocity
TB-ED
(BH)
TB-MD
(BH)
TB-BI
(BH)
Clubhead
0.75 ± 0.10
1.60 ± 0.13
2.41 ± 0.36
Wrist
0.02 ± 0.09
0.34 ± 0.10
0.73 ± 0.17
SJ
0.12 ± 0.06
0.31 ± 0.08
0.41 ± 0.11
Trunk
0.24 ± 0.06
0.36 ± 0.08
0.46 ± 0.08
Pelvis
0.28 ± 0.08
(r = 0.544*)
0.47 ± 0.11
(r = 0.420; p = 0.08)
0.62 ± 0.14
(r = 0.468*)
35
Correlation: vs. Max Clubhead Velocity (BH/s)
Maximum
(deg)
At BI
(deg)
Change
(deg)
X-Factor
58.2 ± 8.9
10.7 ± 8.5
-47.5 ± 8.5
Hip Line
Angle
38.4 ± 7.9
-38.7 ± 9.8
(r = -0.486*)
-77.1 ± 13.4
(r = -0.461; p = .05)
Shoulder
Line Angle
95.1 9.4
(r = 0.415; p = 0.08)
-28.0 ± 8.8
(r = -0.400; p = 0.10)
-123.1 ± 13.0
(r = -0.568*)
36
30
vs. Max CH Velocity
(*p < 0.05)
r = 0.997*
25
(BH/s)
20
r = 0.724*
r = 0.633*
15
Max
Impact
r = 0.539*
10
Change
r = 0.501*
r = -0.475*
5
0
-5
CH
Wrist Pr/Sup Elbow
SJ
Trunk Pelvis M Hip
Joint/Segment
37
Inter-Joint/Segment Correlations (p < 0.05)
Pelvis Max
MH
Elbow Max
Wrist Max
-0.471
Pelvis
-0.553
Trunk
-0.536
El/Depr
0.503
Pelvis Max
El/Depr Max
Elbow Max
Wrist Max
0.607
-0.476
Elbow
MH Max
Pr/Sup Max
SJ Max
Wrist Max
-0.631
Pr/Sup Max
0.470
0.497
0.493
-0.674
38
3
2.5
CH
100%
Wrist
29.9%
SJ
17.1%
Trunk
19.3%
Pelvis
25.6%
(BH)
2
1.5
1
0.5
0
0
20
40
60
80
100
Normalized Time (%)
39
3
vs. Max CH Velocity
(*p < 0.05)
2.5
(BH)
2
TB-ED
TB-MD
1.5
r = 0.468*
r = 0.544*
1
TB-BI
0.5
0
CH
Wrist
SJ
Trunk
Joint/Segment
Pelvis
40
(deg/s)
(deg/s)
500
400
300
200
100
0
-100 0
-200
-300
2000
1500
1000
500
0
-500 0
-1000
-1500
P: P/A Tilt
P: R/L Tilt
P: L/R Rot
T: R/L Lat Fl
T: L/R Rot
S: Fl/Ext
20
40
60
80
100
S: Abd/Add
S: E/I Rot
E: Fl/Ext
Normalized Time (%)
F: Sup/Pr
W: Fl/Ext
20
40
60
80
100
W: R/U Dev
Normalized Time (%)
41