Foo -S ike Fo ce Analysis
S e en Wo hing on
2025-09-26
Table o con en s
1 Co ela ion o MLR and IPF 2
1.1 Be ween-subjec s ........................................ 2
1.2 Wi hin-subjec s ......................................... 3
2 Di e ence be ween bipedal pos u es in chimpanzees 5
2.1 MLR................................................ 5
2.2 IPF ................................................ 8
2.3 MVF ............................................... 11
3 Hip angle in chimpanzees 14
3.1 MLR................................................ 14
3.2 IPF ................................................ 17
3.3 MVF ............................................... 20
4 Knee angle in chimpanzees 23
4.1 MLR................................................ 23
4.2 IPF ................................................ 26
4.3 MVF ............................................... 29
5 Ankle angle in chimpanzees 32
5.1 MLR................................................ 32
5.2 IPF ................................................ 35
5.3 MVF ............................................... 38
6 FSA in chimpanzees 41
6.1 MLR................................................ 41
6.2 IPF ................................................ 45
6.3 MVF ............................................... 49
7 Di e ences be ween species and pos u es 53
7.1 MLR................................................ 53
Table o con en s
2
7.2 IPF ................................................ 57
7.3 MVF ............................................... 61
8 Di e ence in CoT be ween pos u es in humans 65
9 Co ela ion o FSA and Ankle Angle 68
9.1 Be ween-subjec s ........................................ 68
9.2 Wi hin-subjec s ......................................... 69
10 Di e ence in FSA be ween species and gai s 71
10.1 FSA................................................ 71
11 Di e ence be ween pos u es in humans 75
11.1 MLR................................................ 75
11.2 IPF ................................................ 78
11.3 MVF ............................................... 81
1 CORRELATION OF MLR AND IPF
3
1 Co ela ion o MLR and IPF
−2
−1
0
1
2
−2 −1 0 1 2
MLR (s anda dized)
IPF (s anda dized)
Chimp Human
Figu e 1: Co ela ion be ween MLR and IPF. Dashed line indica es an iden i y ela ionship. Polygon el-
lipses encompass 50% and 95% o he da a, espec i ely.
1.1 Be ween-subjec s
(MLR𝑖𝑗 |𝑏MLR
0𝑗 )∼No mal(𝜇MLR
𝑖𝑗 ,𝜎MLR)
𝜇MLR
𝑖𝑗 =𝑏MLR
0𝑗
𝑏MLR
0𝑗 ∼No mal(0,𝜏MLR)
(IPF𝑖𝑗 |𝑏IPF
0𝑗 )∼No mal(𝜇IPF
𝑖𝑗 ,𝜎IPF)
𝜇IPF
𝑖𝑗 =𝑏IPF
0𝑗
𝑏IPF
0𝑗 ∼No mal(0,𝜏IPF)
log 𝜎MLR,log 𝜎IPF ∼S uden (3,0,2.5)
log 𝜏MLR,log 𝜏IPF ∼S uden (3,0,2.5)
Be ween-subjec co ela ion:
𝜌𝑏=co (𝑏MLR
0𝑗 ,𝑏IPF
0𝑗 )
1 CORRELATION OF MLR AND IPF
4
0.00
0.25
0.50
0.75
1.00
0.900 0.925 0.950 0.975 1.000
Be ween−subjec s co ela ion
o MLR and IPF
Pos e io Densi y
Figu e 2: Be ween-subjec s co ela ion be ween MLR and IPF.
Table 1: Be ween-subjec s co ela ion
coe icien o MLR e sus
IPF
lowe _95_HPDI uppe _95_HPDI
0.928 0.985
1.2 Wi hin-subjec s
(MLR𝑖𝑗,IPF𝑖𝑗 |𝑏0𝑗)∼Mul i a ia e No mal ((𝜇MLR
𝑖𝑗
𝜇IPF
𝑖𝑗 ),(𝜎2
MLR 𝜌𝜖𝜎MLR𝜎IPF
𝜌𝜖𝜎MLR𝜎IPF 𝜎2
IPF ))
𝜇MLR
𝑖𝑗 =𝑏MLR
0𝑗
𝜇IPF
𝑖𝑗 =𝑏IPF
0𝑗
𝑏MLR
0𝑗 ,𝑏IPF
0𝑗 ∼Mul i a ia e No mal ((0
0),(𝜏2
MLR 𝜌𝑏𝜏MLR𝜏IPF
𝜌𝑏𝜏MLR𝜏IPF 𝜏2
IPF ))
log 𝜎MLR,log 𝜎IPF ∼S uden (3,0,2.5)
log 𝜏MLR,log 𝜏IPF ∼S uden (3,0,2.5)
Wi hin-subjec co ela ion:
𝜌𝜖=co (𝜖MLR
𝑖𝑗 ,𝜖IPF
𝑖𝑗 )
1 CORRELATION OF MLR AND IPF
5
0.00
0.25
0.50
0.75
1.00
0.70 0.75 0.80 0.85
Wi hin−subjec s co ela ion
o MLR and IPF
Pos e io Densi y
Figu e 3: Wi hin-subjec s co ela ion be ween MLR and IPF.
Table 2: Wi hin-subjec s co ela ion
coe icien o MLR e sus
IPF
lowe _95_HPDI uppe _95_HPDI
0.737 0.844
2 DIFFERENCE BETWEEN BIPEDAL POSTURES IN CHIMPANZEES
6
2 Di e ence be ween bipedal pos u es in chimpanzees
2.1 MLR
Di e ence in MLR be ween pos u es in chimps.
MLR𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(pos u e𝑖𝑗)+𝛽2( oude𝑖𝑗)+𝛽3(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−3 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
0.00
0.25
0.50
0.75
1.00
5k 20k 35k 50k
MLR
Pos e io densi y
Mid oo Heel
Figu e 4: P edic ed MLR by pos u e o chimpanzees.
2 DIFFERENCE BETWEEN BIPEDAL POSTURES IN CHIMPANZEES
7
0.00
0.25
0.50
0.75
1.00
10k 15k 20k 25k
MLR Geome ic Mean
Pos e io densi y
Mid oo Heel
Figu e 5: P edic ed MLR by pos u e o chimpanzees.
Table 3: Geome ic mean MLR by pos u e o
chimpanzees.
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 10,383 12,410
Heel 18,033 25,346
0.00
0.25
0.50
0.75
1.00
50% 100% 150%
∆% MLR (geome ic mean)
Mid oo o Heel
Pos e io Densi y
Figu e 6: Pe cen change in pos u e e ec o chimpanzees.
2 DIFFERENCE BETWEEN BIPEDAL POSTURES IN CHIMPANZEES
8
Table 4: Pe cen change (%) in geo-
me ic mean MLR be ween
pos u es (mid oo o heel)
lowe _95_HPDI uppe _95_HPDI
52.3% 131.1%
0.00
0.25
0.50
0.75
1.00
±0% ±50% ±100% ±150%
ROPE h eshold (% change in MLR
geome ic mean: Mid oo −> Heel)
Pos e io p obabili y
ou side ROPE
Figu e 7: Pos e io p obabili ies o pos u e e ec o chimpanzees.
2 DIFFERENCE BETWEEN BIPEDAL POSTURES IN CHIMPANZEES
9
2.2 IPF
Di e ence in IPF be ween pos u es in chimps.
IPF𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(pos u e𝑖𝑗)+𝛽2( oude𝑖𝑗)+𝛽3(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−3 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
0.00
0.25
0.50
0.75
1.00
20 120 220 320
IPF
Pos e io densi y
Mid oo Heel
Figu e 8: P edic ed IPF by pos u e o chimpanzees.
0.00
0.25
0.50
0.75
1.00
130 150 170 190
IPF Geome ic Mean
Pos e io densi y
Mid oo Heel
Figu e 9: P edic ed IPF by pos u e o chimpanzees.
3 HIP ANGLE IN CHIMPANZEES
16
Table 9: Geome ic mean MLR by pos u e o
chimpanzees (a e aged o e hip angle).
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 7,636 11,031
Heel 20,800 35,588
0.00
0.25
0.50
0.75
1.00
−2% −1% 0% 1% 2% 3%
Ins an aneous % change in MLR
(geome ic mean) pe ° hip angle
Pos e io Densi y
Figu e 17: Pe cen change in hip angle e ec o chimpanzees.
Table 10: Ins an aneous % change in
MLR (geome ic mean) pe °
hip angle.
lowe _95_HPDI uppe _95_HPDI
-1.2% 2.1%
3 HIP ANGLE IN CHIMPANZEES
17
0.00
0.25
0.50
0.75
1.00
±0% ±1% ±2% ±3%
ROPE h eshold (% change in MLR
geome ic mean pe ° hip angle)
Pos e io p obabili y
ou side ROPE
Figu e 18: Pos e io p obabili ies o hip angle e ec o chimpanzees.
Mid oo
Heel
−500 0 500 1k −500 0 500 1k
0.00
0.25
0.50
0.75
1.00
Ins an aneous change in MLR
(geome ic mean) pe ° hip angle
Pos e io Densi y
Hip Angle
50° o 60°
60° o 70°
>70°
Figu e 19: Change in hip angle g oups e ec o chimpanzees.
3 HIP ANGLE IN CHIMPANZEES
18
3.2 IPF
Change in IPF o change in hip angle in chimps (bipedal gai ).
IPF𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(hip angle𝑖𝑗)+𝛽2(pos u e𝑖𝑗)
+𝛽3( oude𝑖𝑗)+𝛽4(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−4 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
100
150
200
250
50° 60° 70° 80°
Hip Angle
IPF (geome ic mean)
Mid oo HPDI 0.95 0.8 0.5
Heel HPDI 0.95 0.8 0.5
Figu e 20: P edic ed IPF by hip angle and pos u e o chimpanzees.
3 HIP ANGLE IN CHIMPANZEES
19
Table 11: Geome ic mean IPF by pos u e o
chimpanzees (a e aged o e hip an-
gle).
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 106 157
Heel 179 259
0.00
0.25
0.50
0.75
1.00
−2% −1% 0% 1% 2% 3%
Ins an aneous % change in IPF
(geome ic mean) pe ° hip angle
Pos e io Densi y
Figu e 21: Pe cen change in hip angle e ec o chimpanzees.
Table 12: Ins an aneous % change in
IPF (geome ic mean) pe °
hip angle.
lowe _95_HPDI uppe _95_HPDI
-1.1% 1.9%
3 HIP ANGLE IN CHIMPANZEES
20
0.00
0.25
0.50
0.75
1.00
±0% ±1% ±2% ±3%
ROPE h eshold (% change in IPF
geome ic mean pe ° hip angle)
Pos e io p obabili y
ou side ROPE
Figu e 22: Pos e io p obabili ies o hip angle e ec e ec o chimpanzees.
Mid oo
Heel
−5 0 5 10 −5 0 5 10
0.00
0.25
0.50
0.75
1.00
Ins an aneous change in IPF
(geome ic mean) pe ° hip angle
Pos e io Densi y
Hip Angle
50° o 60°
60° o 70°
>70°
Figu e 23: Change in hip angle g oups e ec o chimpanzees.
3 HIP ANGLE IN CHIMPANZEES
21
3.3 MVF
Change in MVF o change in hip angle in chimps (bipedal gai ).
MVF𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(hip angle𝑖𝑗)+𝛽2(pos u e𝑖𝑗)
+𝛽3( oude𝑖𝑗)+𝛽4(bm𝑗)
log 𝜎=𝛾0
𝑏0𝑗 ∼No mal(0,𝜏0)
𝛽1−4 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
280
300
320
340
360
380
50° 60° 70° 80°
Hip Angle
MVF (geome ic mean)
Mid oo HPDI 0.95 0.8 0.5
Heel HPDI 0.95 0.8 0.5
Figu e 24: P edic ed MVF by hip angle and pos u e o chimpanzees.
Table 13: Geome ic mean MVF by pos u e o
chimpanzees (a e aged o e hip an-
gle).
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 274 305
Heel 340 382
3 HIP ANGLE IN CHIMPANZEES
22
0.00
0.25
0.50
0.75
1.00
0% 0.2% 0.4% 0.6% 0.8%
Ins an aneous % change in MVF
(geome ic mean) pe ° hip angle
Pos e io Densi y
Figu e 25: Pe cen change in hip angle e ec o chimpanzees.
Table 14: Ins an aneous % change in
MVF (geome ic mean) pe °
hip angle.
lowe _95_HPDI uppe _95_HPDI
0.1% 0.6%
0.00
0.25
0.50
0.75
1.00
±0.0% ±0.2% ±0.4% ±0.6% ±0.8%
ROPE h eshold (% change in MVF
geome ic mean pe ° hip angle)
Pos e io p obabili y
ou side ROPE
Figu e 26: Pos e io p obabili ies o hip angle e ec o chimpanzees.
3 HIP ANGLE IN CHIMPANZEES
23
Mid oo
Heel
024024
0.00
0.25
0.50
0.75
1.00
Ins an aneous change in MVF
(geome ic mean) pe ° hip angle
Pos e io Densi y
Hip Angle
50° o 60°
60° o 70°
>70°
Figu e 27: Change in hip angle g oups e ec o chimpanzees.
4 KNEE ANGLE IN CHIMPANZEES
24
4 Knee angle in chimpanzees
4.1 MLR
Change in MLR o change in knee angle in chimps (bipedal gai ).
MLR𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(knee angle𝑖𝑗)+𝛽2(pos u e𝑖𝑗)
+𝛽3( oude𝑖𝑗)+𝛽4(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−4 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
10k
20k
30k
40k
15° 20° 25° 30° 35°
Knee Angle
MLR (geome ic mean)
Mid oo HPDI 0.95 0.8 0.5
Heel HPDI 0.95 0.8 0.5
Figu e 28: P edic ed MLR by knee angle and pos u e o chimpanzees.
4 KNEE ANGLE IN CHIMPANZEES
25
Table 15: Geome ic mean MLR by pos u e o
chimpanzees (a e aged o e knee an-
gle).
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 8,734 11,353
Heel 23,661 36,052
0.00
0.25
0.50
0.75
1.00
−2% 0% 2%
Ins an aneous % change in MLR
(geome ic mean) pe ° knee angle
Pos e io Densi y
Figu e 29: Pe cen change in knee angle e ec o chimpanzees.
Table 16: Ins an aneous % change in
MLR (geome ic mean) pe °
knee angle.
lowe _95_HPDI uppe _95_HPDI
-2.1% 1.2%
4 KNEE ANGLE IN CHIMPANZEES
32
0.00
0.25
0.50
0.75
1.00
±0.0% ±0.2% ±0.4% ±0.6%
ROPE h eshold (% change in MVF
geome ic mean pe ° knee angle)
Pos e io p obabili y
ou side ROPE
Figu e 38: Pos e io p obabili ies o knee angle e ec o chimpanzees.
Mid oo
Heel
−2 −1 0 1 2 −2 −1 0 1 2
0.00
0.25
0.50
0.75
1.00
Ins an aneous change in MVF
(geome ic mean) pe ° knee angle
Pos e io Densi y
Knee Angle
10° o 20°
20° o 30°
30° o 40°
Figu e 39: Change in knee angle g oups e ec o chimpanzees.
5 ANKLE ANGLE IN CHIMPANZEES
33
5 Ankle angle in chimpanzees
5.1 MLR
Change in MLR o change in ankle angle in chimps (bipedal gai ).
MLR𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(ankle angle𝑖𝑗)+𝛽2(pos u e𝑖𝑗)
+𝛽3( oude𝑖𝑗)+𝛽4(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−4 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
10k
20k
30k
40k
90° 100° 110° 120°
Ankle Angle
MLR (geome ic mean)
Mid oo HPDI 0.95 0.8 0.5
Heel HPDI 0.95 0.8 0.5
Figu e 40: P edic ed MLR by ankle angle and pos u e o chimpanzees.
5 ANKLE ANGLE IN CHIMPANZEES
34
Table 21: Geome ic mean MLR by pos u e o
chimpanzees (a e aged o e ankle an-
gle).
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 8,618 12,249
Heel 26,692 38,277
0.00
0.25
0.50
0.75
1.00
−1% 0% 1% 2%
Ins an aneous % change in MLR
(geome ic mean) pe ° ankle angle
Pos e io Densi y
Figu e 41: Pe cen change in ankle angle e ec o chimpanzees.
Table 22: Ins an aneous % change in
MLR (geome ic mean) pe °
ankle angle.
lowe _95_HPDI uppe _95_HPDI
-0.5% 1.6%
5 ANKLE ANGLE IN CHIMPANZEES
35
0.00
0.25
0.50
0.75
1.00
±0.0% ±0.5% ±1.0% ±1.5% ±2.0% ±2.5%
ROPE h eshold (% change in MLR
geome ic mean pe ° ankle angle)
Pos e io p obabili y
ou side ROPE
Figu e 42: Pos e io p obabili ies o ankle angle e ec o chimpanzees.
Mid oo
Heel
−300 0 300 600 −300 0 300 600
0.00
0.25
0.50
0.75
1.00
Ins an aneous change in MLR
(geome ic mean) pe ° ankle angle
Pos e io Densi y
Ankle Angle
<100°
100° o 110°
110° o 120°
>120°
Figu e 43: Change in ankle angle g oups e ec o chimpanzees.
5 ANKLE ANGLE IN CHIMPANZEES
36
5.2 IPF
Change in IPF o change in ankle angle in chimps (bipedal gai ).
IPF𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(ankle angle𝑖𝑗)+𝛽2(pos u e𝑖𝑗)
+𝛽3( oude𝑖𝑗)+𝛽4(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−4 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
100
150
200
250
90° 100° 110° 120°
Ankle Angle
IPF (geome ic mean)
Mid oo HPDI 0.95 0.8 0.5
Heel HPDI 0.95 0.8 0.5
Figu e 44: P edic ed IPF by ankle angle and pos u e o chimpanzees.
5 ANKLE ANGLE IN CHIMPANZEES
37
Table 23: Geome ic mean IPF by pos u e o
chimpanzees (a e aged o e ankle an-
gle).
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 115 165
Heel 216 273
0.00
0.25
0.50
0.75
1.00
0% 1% 2%
Ins an aneous % change in IPF
(geome ic mean) pe ° ankle angle
Pos e io Densi y
Figu e 45: Pe cen change in ankle angle e ec o chimpanzees.
Table 24: Ins an aneous % change in
IPF (geome ic mean) pe °
ankle angle.
lowe _95_HPDI uppe _95_HPDI
-0.2% 1.5%
5 ANKLE ANGLE IN CHIMPANZEES
38
0.00
0.25
0.50
0.75
1.00
±0.0% ±0.5% ±1.0% ±1.5% ±2.0%
ROPE h eshold (% change in IPF
geome ic mean pe ° ankle angle)
Pos e io p obabili y
ou side ROPE
Figu e 46: Pos e io p obabili ies o ankle angle e ec o chimpanzees.
Mid oo
Heel
−2 0 2 4 −2 0 2 4
0.00
0.25
0.50
0.75
1.00
Ins an aneous change in IPF
(geome ic mean) pe ° ankle angle
Pos e io Densi y
Ankle Angle
<100°
100° o 110°
110° o 120°
>120°
Figu e 47: Change in ankle angle g oups e ec o chimpanzees.
5 ANKLE ANGLE IN CHIMPANZEES
39
5.3 MVF
Change in MVF o change in ankle angle in chimps (bipedal gai ).
MVF𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(ankle angle𝑖𝑗)+𝛽2(pos u e𝑖𝑗)
+𝛽3( oude𝑖𝑗)+𝛽4(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−4 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
300
325
350
375
90° 100° 110° 120°
Ankle Angle
MVF (geome ic mean)
Mid oo HPDI 0.95 0.8 0.5
Heel HPDI 0.95 0.8 0.5
Figu e 48: P edic ed MVF by ankle angle and pos u e o chimpanzees.
5 ANKLE ANGLE IN CHIMPANZEES
40
Table 25: Geome ic mean MVF by pos u e o
chimpanzees (a e aged o e ankle an-
gle).
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 290 315
Heel 364 388
0.00
0.25
0.50
0.75
1.00
0% 0.2% 0.4%
Ins an aneous % change in MVF
(geome ic mean) pe ° ankle angle
Pos e io Densi y
Figu e 49: Pe cen change in ankle angle e ec o chimpanzees.
Table 26: Ins an aneous % change in
MVF (geome ic mean) pe °
ankle angle.
lowe _95_HPDI uppe _95_HPDI
0% 0.4%
5 ANKLE ANGLE IN CHIMPANZEES
41
0.00
0.25
0.50
0.75
1.00
±0.0% ±0.1% ±0.2% ±0.3% ±0.4% ±0.5%
ROPE h eshold (% change in MVF
geome ic mean pe ° ankle angle)
Pos e io p obabili y
ou side ROPE
Figu e 50: Pos e io p obabili ies o ankle angle e ec o chimpanzees.
Mid oo
Heel
012012
0.00
0.25
0.50
0.75
1.00
Ins an aneous change in MVF
(geome ic mean) pe ° ankle angle
Pos e io Densi y
Ankle Angle
<100°
100° o 110°
110° o 120°
>120°
Figu e 51: Change in ankle angle g oups e ec o chimpanzees.
6 FSA IN CHIMPANZEES
48
Quad uped
Biped
0% 1% 2%
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
Ins an aneous % change in IPF
(geome ic mean) pe ° FSA
Pos e io Densi y
Figu e 57: Pos e io densi ies o he ins an aneous a e o change in geome ic-mean IPF wi h espec o
FSA (IPF uni s pe deg ee).
Table 35: Ins an aneous % change in IPF (geome ic
mean) pe ° FSA.
gai lowe _95_HPDI uppe _95_HPDI
Biped -0.1% 1.4%
Quad uped 0.1% 2.1%
Table 36:
Pos e io p obabili ies ha he ins an aneous a e o change in
geome ic-mean IPF wi h espec o FSA (IPF uni s pe deg ee) is
g ea e han 0
Gai ℙ(>0)
Biped 0.952
Quad uped 0.980
6 FSA IN CHIMPANZEES
49
0.00
0.25
0.50
0.75
1.00
±0% ±1% ±2%
ROPE h eshold (% change in IPF
geome ic mean pe ° FSA)
Pos e io p obabili y
ou side ROPE
Biped Quad uped
Figu e 58: Pos e io p obabili ies o he ins an aneous a e o change in geome ic-mean IPF wi h espec
o FSA (IPF uni s pe deg ee).
Biped
Quad uped
−2 0 2 4 6 −2 0 2 4 6
0.00
0.25
0.50
0.75
1.00
Ins an aneous change in IPF (geome ic mean) pe ° FSA
Pos e io Densi y
FSA
−10° o 0°
0° o 10°
10° o 20°
>20°
Figu e 59: Pos e io densi ies o he ins an aneous a e o change in geome ic-mean IPF wi h espec o
g ouped FSA (IPF uni s pe deg ee).
6 FSA IN CHIMPANZEES
50
6.3 MVF
Change in MVF o change in FSA in chimps, by gai .
MVF𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(FSA𝑖𝑗)+𝛽2(gai 𝑖𝑗)+𝛽3(FSA𝑖𝑗 ×gai 𝑖𝑗)
+𝛽4( oude𝑖𝑗)+𝛽5(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−5 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
200
250
300
350
−10° 0° 10° 20° 30°
FSA
MVF (geome ic mean)
Quad uped HPDI 0.95 0.8 0.5
Biped HPDI 0.95 0.8 0.5
Figu e 60: P edic ed MVF by FSA and gai o chimpanzees.
6 FSA IN CHIMPANZEES
51
Table 37: Geome ic mean MVF by gai (a e aged
o e FSA).
gai lowe _95_HPDI uppe _95_HPDI
Biped 301 328
Quad uped 206 251
Table 38: Geome ic mean MVF by gai and FSA g oups.
sa_g oups gai lowe _95_HPDI uppe _95_HPDI
-10° o 0° Biped 269 282
-10° o 0° Quad uped 230 243
0° o 10° Biped 317 328
0° o 10° Quad uped 228 241
10° o 20° Biped 363 379
10° o 20° Quad uped 213 228
>20° Biped 398 417
>20° Quad uped 223 239
Table 39: Pe cen change in MVF (geome ic mean)
om quad uped o biped, o each FSA
g oup.
sa_g oups lowe _95_HPDI uppe _95_HPDI
-10° o 0° 12.4% 20.7%
0° o 10° 33.2% 42.3%
10° o 20° 62.2% 74.7%
>20° 69.9% 83.4%
6 FSA IN CHIMPANZEES
52
Quad uped
Biped
−0.8% −0.6% −0.4% −0.2% 0% 0.2%
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
Ins an aneous % change in MVF
(geome ic mean) pe ° FSA
Pos e io Densi y
Figu e 61: Pos e io densi ies o he ins an aneous a e o change in geome ic-mean MVF wi h espec
o FSA (MVF uni s pe deg ee).
Table 40: Ins an aneous % change in MVF (geome -
ic mean) pe ° FSA.
gai lowe _95_HPDI uppe _95_HPDI
Biped -0.4% 0.1%
Quad uped -0.7% -0.2%
Table 41:
Pos e io p obabili ies ha he ins an aneous a e o change in
geome ic-mean MVF wi h espec o FSA (MVF uni s pe
deg ee) is g ea e han 0
Gai ℙ(<0)
Biped 0.914
Quad uped 1.000
6 FSA IN CHIMPANZEES
53
0.00
0.25
0.50
0.75
1.00
±0.0% ±0.2% ±0.4% ±0.6% ±0.8%
ROPE h eshold (% change in MVF
geome ic mean pe ° FSA)
Pos e io p obabili y
ou side ROPE
Biped Quad uped
Figu e 62: Pos e io p obabili ies o he ins an aneous a e o change in geome ic-mean MVF wi h espec
o FSA (MVF uni s pe deg ee).
Biped
Quad uped
−2 −1 0 1 −2 −1 0 1
0.00
0.25
0.50
0.75
1.00
Ins an aneous change in MVF (geome ic mean) pe ° FSA
Pos e io Densi y
FSA
−10° o 0°
0° o 10°
10° o 20°
>20°
Figu e 63: Pos e io densi ies o he ins an aneous a e o change in geome ic-mean MVF wi h espec
o g ouped FSA (MVF uni s pe deg ee).
7 DIFFERENCES BETWEEN SPECIES AND POSTURES
54
7 Di e ences be ween species and pos u es
7.1 MLR
Di e ence in MLR be ween species and pos u es o bipedal gai .
MLR𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(species𝑖𝑗)+𝛽2(pos u e𝑖𝑗)+𝛽3(species𝑖𝑗 ×pos u e𝑖𝑗)
+𝛽4( oude𝑖𝑗)+𝛽5(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−5 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
(1)
Heel
Mid oo
5k 25k 45k 65k 85k
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
MLR
Pos e io densi y
Chimp Human
Figu e 64: P edic ed MLR by species and pos u e o bipedal gai .
7 DIFFERENCES BETWEEN SPECIES AND POSTURES
55
Heel
Mid oo
10k 20k 30k 40k 50k
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
MLR Geome ic Mean
Pos e io densi y
Chimp Human
Figu e 65: P edic ed MLR by species and pos u e o bipedal gai .
Table 42: Geome ic mean MLR by species and pos u e o
bipedal gai .
species pos u e lowe _95_HPDI uppe _95_HPDI
Chimp Mid oo 12,704 23,799
Chimp Heel 24,631 46,564
Human Heel 23,958 46,422
7 DIFFERENCES BETWEEN SPECIES AND POSTURES
56
0.00
0.25
0.50
0.75
1.00
−50% 0% 50% 100% 150%
∆% MLR (geome ic mean)
Pos e io Densi y
Mid oo o Heel Chimp o Human
Figu e 66: Pe cen change in species e ec o heel s ikes and pe cen change in pos u e e ec s o
chimps.
Table 43: Pe cen change (%) in geome ic mean MLR be-
ween species (chimp o human) o heel s ikes
con as lowe _95_HPDI uppe _95_HPDI
Chimp o Human -53.8% 70.1%
Table 44:
Pos e io p obabili y ha he % change in he geome ic mean o
MLR be ween chimp and human heel s iking is wi hin a ±25%
ROPE
ℙ(<±25%)
0.595
Table 45: Pe cen change (%) in geome ic mean MLR
be ween pos u es (mid oo o heel) o chim-
panzees
con as lowe _95_HPDI uppe _95_HPDI
Mid oo o Heel 57.9% 138.1%
7 DIFFERENCES BETWEEN SPECIES AND POSTURES
57
Table 46:
Pos e io p obabili y ha he % change in he geome ic mean o
MLR be ween mid oo and heel s iking in chimps is g ea e
han 0 o bipedal s eps
ℙ(>0)
1.000
0.00
0.25
0.50
0.75
1.00
±0% ±50% ±100%
Chimp −> Human
Pos e io p obabili y
ou side ROPE
A
±0% ±50% ±100% ±150%
Mid oo −> Heel
B
ROPE h eshold (% change in MLR geome ic mean)
Figu e 67: Pos e io p obabili ies o species e ec o heel s ikes and pos u e e ec s o chimps, o
bipedal gai .
7 DIFFERENCES BETWEEN SPECIES AND POSTURES
64
0.00
0.25
0.50
0.75
1.00
−20% −10% 0% 10% 20%
∆% MVF (geome ic mean)
Pos e io Densi y
Mid oo o Heel Chimp o Human
Figu e 74: Pe cen change in species e ec o heel s ikes and pe cen change in pos u e e ec s o
chimps.
Table 53: Pe cen change (%) in geome ic mean MVF be-
ween species (chimp o human) o heel s ikes
con as lowe _95_HPDI uppe _95_HPDI
Chimp o Human -20.8% 23.8%
Table 54:
Pos e io p obabili y ha he % change in he geome ic mean o
MVF be ween chimp and human heel s iking is wi hin a ±25%
ROPE
ℙ(<±25%)
0.965
Table 55: Pe cen change (%) in geome ic mean MVF
be ween pos u es (mid oo o heel) o chim-
panzees
con as lowe _95_HPDI uppe _95_HPDI
Mid oo o Heel -5.9% -0.9%
7 DIFFERENCES BETWEEN SPECIES AND POSTURES
65
Table 56:
Pos e io p obabili y ha he % change in he geome ic mean o
MVF be ween mid oo and heel s iking in chimps is less han 0
o bipedal s eps
ℙ(<0)
0.997
0.00
0.25
0.50
0.75
1.00
±0% ±25% ±50%
Chimp −> Human
Pos e io p obabili y
ou side ROPE
A
±0% ±4% ±8%
Mid oo −> Heel
B
ROPE h eshold (% change in MVF geome ic mean)
Figu e 75: Pos e io p obabili ies o species e ec o heel s ikes and pos u e e ec s o chimps, o
bipedal gai .
8 DIFFERENCE IN COT BETWEEN POSTURES IN HUMANS
66
8 Di e ence in CoT be ween pos u es in humans
Di e ence in cos o anspo (CoT) in be ween pos u es in humans.
CoT𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(pos u e𝑖𝑗)+𝛽2(age𝑗)+𝛽3(weigh 𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−3 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
0.00
0.25
0.50
0.75
1.00
2.5 3 3.5 4
CoT
Pos e io densi y
Heel Mid oo
Figu e 76: P edic ed CoT by pos u e o humans.
8 DIFFERENCE IN COT BETWEEN POSTURES IN HUMANS
67
0.00
0.25
0.50
0.75
1.00
2.4 2.8 3.2 3.6
CoT Geome ic Mean
Pos e io densi y
Heel Mid oo
Figu e 77: P edic ed CoT by pos u e o humans.
Table 57: Geome ic mean CoT by pos u e o hu-
mans.
pos u e lowe _95_HPDI uppe _95_HPDI
Heel 2.48 2.68
Mid oo 3.31 3.58
0.00
0.25
0.50
0.75
1.00
25% 35% 45%
∆% CoT (geome ic mean)
Heel −> Mid oo
Pos e io Densi y
Figu e 78: Pe cen change in pos u e e ec o humans.
8 DIFFERENCE IN COT BETWEEN POSTURES IN HUMANS
68
Table 58: Pe cen change (%) in geo-
me ic mean CoT be ween
pos u es (heel o mid oo )
lowe _95_HPDI uppe _95_HPDI
26.1% 40.8%
0.00
0.25
0.50
0.75
1.00
±0% ±10% ±20% ±30% ±40%
ROPE h eshold (% change in CoT
geome ic mean: Heel −> Mid oo )
Pos e io p obabili y
ou side ROPE
Figu e 79: Pos e io p obabili ies o pos u e e ec o humans.
9 CORRELATION OF FSA AND ANKLE ANGLE
69
9 Co ela ion o FSA and Ankle Angle
−3
−2
−1
0
1
2
−2 −1 0 1 2 3
Ankle angle (s anda dized)
FSA (s anda dized)
Mid oo Heel
Figu e 80: Co ela ion be ween FSA and Ankle Angle. Dashed line indica es an iden i y ela ionship. Poly-
gon ellipses encompass 50% and 95% o he da a, espec i ely.
9.1 Be ween-subjec s
(FSA𝑖𝑗 |𝑏FSA
0𝑗 )∼No mal(𝜇FSA
𝑖𝑗 ,𝜎FSA)
𝜇FSA
𝑖𝑗 =𝑏FSA
0𝑗
𝑏FSA
0𝑗 ∼No mal(0,𝜏FSA)
(AA𝑖𝑗 |𝑏AA
0𝑗 )∼No mal(𝜇AA
𝑖𝑗 ,𝜎AA)
𝜇AA
𝑖𝑗 =𝑏AA
0𝑗
𝑏AA
0𝑗 ∼No mal(0,𝜏AA)
log 𝜎FSA,log 𝜎AA ∼S uden (3,0,2.5)
log 𝜏FSA,log 𝜏AA ∼S uden (3,0,2.5)
Be ween-subjec co ela ion:
𝜌𝑏=co (𝑏FSA
0𝑗 ,𝑏AA
0𝑗 )
9 CORRELATION OF FSA AND ANKLE ANGLE
70
0.00
0.25
0.50
0.75
1.00
−1.0 −0.5 0.0 0.5 1.0
Be ween subjec co ela ion
o FSA and Ankle Angle
Pos e io Densi y
Figu e 81: Be ween-subjec s co ela ion be ween FSA and Ankle Angle.
Table 59: Be ween-subjec s co e-
la ion coe icien o FSA
e sus Ankle Angle
lowe _95_HPDI uppe _95_HPDI
-0.999 0.902
9.2 Wi hin-subjec s
(FSA𝑖𝑗,AA𝑖𝑗 |𝑏0𝑗)∼Mul i a ia e No mal ((𝜇FSA
𝑖𝑗
𝜇AA
𝑖𝑗 ),(𝜎2
FSA 𝜌𝜖𝜎FSA𝜎AA
𝜌𝜖𝜎FSA𝜎AA 𝜎2
AA ))
𝜇FSA
𝑖𝑗 =𝑏FSA
0𝑗
𝜇AA
𝑖𝑗 =𝑏AA
0𝑗
𝑏FSA
0𝑗 ,𝑏AA
0𝑗 ∼Mul i a ia e No mal ((0
0),(𝜏2
FSA 𝜌𝑏𝜏FSA𝜏AA
𝜌𝑏𝜏FSA𝜏AA 𝜏2
AA ))
log 𝜎FSA,log 𝜎AA ∼S uden (3,0,2.5)
log 𝜏FSA,log 𝜏AA ∼S uden (3,0,2.5)
Wi hin-subjec co ela ion:
𝜌𝜖=co (𝜖FSA
𝑖𝑗 ,𝜖AA
𝑖𝑗 )
9 CORRELATION OF FSA AND ANKLE ANGLE
71
0.00
0.25
0.50
0.75
1.00
−0.8 −0.7 −0.6 −0.5
Wi hin−subjec s co ela ion
o FSA and Ankle Angle
Pos e io Densi y
Figu e 82: Wi hin-subjec s co ela ion be ween FSA and Ankle Angle.
Table 60: Wi hin-subjec s co ela ion
coe icien o FSA e sus
Ankle Angle
lowe _95_HPDI uppe _95_HPDI
-0.750 -0.507
10 DIFFERENCE IN FSA BETWEEN SPECIES AND GAITS
72
10 Di e ence in FSA be ween species and gai s
10.1 FSA
Di e ence in FSA be ween species and gai s.
FSA𝑖𝑗 ∼No mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(species𝑖𝑗)+𝛽2(gai 𝑖𝑗)+𝛽3(species𝑖𝑗 ×gai 𝑖𝑗)+𝛽4( oude𝑖𝑗)+𝛽5(bm𝑗)
𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−5 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
Biped
Quad uped
−5° 0° 5° 10° 15° 20° 25° 30°
−5° 0° 5° 10° 15° 20° 25° 30°
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
FSA
Pos e io densi y
Chimp Human
Figu e 83: P edic ed FSA by species and gai .
10 DIFFERENCE IN FSA BETWEEN SPECIES AND GAITS
73
Biped
Quad uped
0° 5° 10° 15° 20°
0° 5° 10° 15° 20°
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
FSA
Pos e io densi y
Chimp Human
Figu e 84: P edic ed FSA by species and gai .
Table 61: A i hme ic mean FSA by species and gai .
species gai lowe _95_HPDI uppe _95_HPDI
Chimp Quad uped 5.25 11.83
Chimp Biped 2.95 9.45
Human Biped 10.66 19.28
Human Biped − Chimp Biped
Human Biped − Chimp Quad uped
Chimp Quad uped − Chimp Biped
0° 5° 10° 15°
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
∆ FSA (a i hme ic mean)
Pos e io Densi y
Figu e 85: Change in FSA by species and gai .
11 DIFFERENCE BETWEEN POSTURES IN HUMANS
80
Table 67: Geome ic mean IPF by pos u e o hu-
mans.
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 111.3 122.9
Heel 319.8 351.9
0.00
0.25
0.50
0.75
1.00
160% 180% 200% 220%
∆% IPF (geome ic mean)
Mid oo −> Heel
Pos e io Densi y
Figu e 93: Pe cen change in pos u e e ec o humans.
Table 68: Pe cen change (%) in ge-
ome ic mean IPF be ween
pos u es (mid oo o heel)
lowe _95_HPDI uppe _95_HPDI
167.5% 205.5%
11 DIFFERENCE BETWEEN POSTURES IN HUMANS
81
0.00
0.25
0.50
0.75
1.00
±0% ±100% ±200%
ROPE h eshold (% change in IPF
geome ic mean: Mid oo −> Heel)
Pos e io p obabili y
ou side ROPE
Figu e 94: Pos e io p obabili ies o pos u e e ec o humans.
11 DIFFERENCE BETWEEN POSTURES IN HUMANS
82
11.3 MVF
Di e ence in MVF be ween pos u es in humans.
MVF𝑖𝑗 ∼Logno mal(𝜇𝑖𝑗,𝜎𝑗)
𝜇𝑖𝑗 =𝛽0+𝑏0𝑗 +𝛽1(pos u e𝑖𝑗)+𝛽2( oude𝑖𝑗)+𝛽3(bm𝑗)
log 𝜎𝑗=𝛾0+𝑔0𝑗
𝑏0𝑗 ∼No mal(0,𝜏0)
𝑔0𝑗 ∼No mal(0,𝜙0)
𝛽1−3 ∼S uden (3,0,2.5)
𝛾0∼S uden (3,0,2.5)
log 𝜏0∼S uden (3,0,2.5)
log 𝜙0∼S uden (3,0,2.5)
0.00
0.25
0.50
0.75
1.00
700 900 1.1k
MVF
Pos e io densi y
Mid oo Heel
Figu e 95: P edic ed MVF by pos u e o humans.
0.00
0.25
0.50
0.75
1.00
825 830 835 840 845
MVF Geome ic Mean
Pos e io densi y
Mid oo Heel
Figu e 96: P edic ed MVF by pos u e o humans.
11 DIFFERENCE BETWEEN POSTURES IN HUMANS
83
Table 69: Geome ic mean MVF by pos u e o
humans.
pos u e lowe _95_HPDI uppe _95_HPDI
Mid oo 827 839
Heel 831 843
0.00
0.25
0.50
0.75
1.00
−1% 0% 1% 2%
∆% MVF (geome ic mean)
Mid oo −> Heel
Pos e io Densi y
Figu e 97: Pe cen change in pos u e e ec o humans.
Table 70: Pe cen change (%) in geo-
me ic mean MVF be ween
pos u es (mid oo o heel)
lowe _95_HPDI uppe _95_HPDI
-0.6% 1.5%
11 DIFFERENCE BETWEEN POSTURES IN HUMANS
84
0.00
0.25
0.50
0.75
1.00
±0% ±1% ±2%
ROPE h eshold (% change in MVF
geome ic mean: Mid oo −> Heel)
Pos e io p obabili y
ou side ROPE
Figu e 98: Pos e io p obabili ies o pos u e e ec o humans.
