Anthropometrics/Body Segment Parameters

Parallel Axis Theorem
• Moment of inertia values are commonly
specified relative to an axis through the
segment center of mass
• The moment of inertia about a different axis
(e.g., through the proximal joint) can be
determined using the parallel axis theorem
I A = I CM + md 2
Where I A is moment of inertia about the new axis, I CM is
moment of inertia about an axis through the CM, m is
segment mass, and d is distance between the two axes
Parallel Axis Theorem
A prosthetic lower leg has a mass of 3 kg and
a center of mass 20 cm from the knee joint.
The radius of gyration is 14.1 cm. What is the
moment of inertia about the knee joint (I KNEE )?
I CM = mk 2
I CM = (3 kg)(0.141 m) 2 = 0.06 kg⋅m 2
I KNEE = I CM + md 2
I KNEE = 0.06 kg⋅m 2 + (3 kg)(0.2 m) 2 = 0.18
kg⋅m 2
Parallel Axis Theorem
The combined moment of inertia
of several segments about a
remote axis can be calculated by
using the parallel axis theorem,
and summing across segments
I LEG(HIP) = I T(HIP) + I S(HIP) + I F(HIP)
where:
I T(HIP) = I T(CM) + m T d T
2
I S(HIP) = I S(CM) + m S d S
2
I F(HIP) = I F(CM) + m F d F
2
Hip
d F
d S
d T
m F
m T
m S
Body segment parameter
assumptions
During the period of data collection:
• The segments are perfectly rigid
• The segments are connect by frictionless
hinge or ball-and-socket joints
• The length of each segment remains constant
• The CM location of each segment remains
constant
• The mass moment of inertia of each segment
remains constant
BSP Studies/Data
Harless (1860)
– One of the earliest quantitative study of BSPs
– Dissected 2 cadavers (former prisoners who had
recently been decapitated)
– Determined segment mass & CM locations
Braun & Fischer (1889)
– Determined BSPs in 3 cadaver specimens
– Divided body into 14 segments
– Used data from individual segments to determine
center of gravity of whole body during locomotion
BSP Studies/Data
Dempster (1955)
– Did most detailed and extensive dissection to
date in 8 cadavers specimens
– Determined mass, CM location, & moment of
inertia values for all major body segments
– Expressed data as proportion of total body mass,
and relative to segment lengths
– Results have been used extensively in
biomechanics research
– However, data were from only 8 cadavers, who
were older (52-83 yrs), Caucasian males, most of
whom were reported to be emaciated
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