Calculation of the Hip Joint Centers
James Richards
Minor edits by WCR
Three markers are placed on the pelvic girdle at the locations of the left and right anterior
superior iliac spines (ASIS) and the sacrum. A unit vector (n) then is created to define
the direction from the left ASIS marker to the right ASIS marker. A vector originating
from the sacrum to the left ASIS is then crossed onto a vector originating from the
sacrum to the right ASIS to create the (l) unit vector. Finally, the (m) unit vector is
created by crossing (n) onto (l). Vector (n) points to the right; (l) points down; (m) points
forward. They are guaranteed to be orthogonal and of unit length. Therefore the vectors
form a rotation matrix for the pelvis.
𝑛=
𝑙=
𝑅𝐴𝑆𝐼𝑆 − 𝐿𝐴𝑆𝐼𝑆
‖𝑅𝐴𝑆𝐼𝑆 − 𝐿𝐴𝑆𝐼𝑆‖
(𝐿𝐴𝑆𝐼𝑆 − 𝑆𝑎𝑐𝑟) × (𝑅𝐴𝑆𝐼𝑆 − 𝑆𝑎𝑐𝑟)
‖(𝐿𝐴𝑆𝐼𝑆 − 𝑆𝑎𝑐𝑟) × (𝑅𝐴𝑆𝐼𝑆 − 𝑆𝑎𝑐𝑟)‖
𝑚 =𝑛×𝑙
We define the origin as the midpoint of the ASIS markers:
𝑜𝑟𝑖𝑔𝑖𝑛 = (𝑅𝐴𝑆𝐼𝑆 + 𝐿𝐴𝑆𝐼𝑆)⁄2
The location of the hip centers in global coordinate space are then determined with the
equation:
 Xhip  Xorigin  l1
  
 
 Yhip    Yorigin   m1
 Zhip   Zorigin  n
  
  1
l2
m2
n2
l3   0.24  ASISBreadth


m3    0.21  ASISBreadth

n3  
 0.32  ASISBreadth
where hip and origin are the global coordinates of the hip center and the origin marker
respectively, and lpelvis, mpelvis,and npelvis are the vector components of the pelvic
rotation matrix. Origin=(RASIS+LASIS)/2. ASIS breadth is the absolute distance
between the markers on the left and right anterior superior iliac spines. The ±
differentiates between the right (+) and the left (-) hip joints. Arrows 1, 2, 3 in the
diagram correspond to l, m, n, and the light green marker indicates the origin.
Several investigators have provided solutions to locating the hip joint centers from the
same three pelvic markers. Most of the solutions utilize the midpoint between the two
ASIS markers as the origin, while Vaughn is the only investigator to utilize the sacrum as
the point of origin. All of the methods express the hip center locations as a percentage of
the ASIS breadth relative to the point of origin. The constants reported by other
investigators are presented below:
Hip Center Location (% of ASIS Breadth)
Vector:
1
2
3
Origin
Dostre & Andrews (1981)
Bell (1990)
Davis (1991)
Leardini et al. (1999)
Campbell et al. (N/A)
Vaughn et al. (1992)
31.9
30.0
42.0
39.0
24.0
29.0
-22.7
-19.0
-17.0
-24.0
-21.0
59.8
+/-30.4
+/-36.0
+/-31.0
+/-39.0
+/-32.0
+/-34.4
Mid ASIS
Mid ASIS
Mid ASIS
Mid ASIS
Mid ASIS
Sacrum