Inverse mechanics
WCR
Summary
Observe motion. Compute the forces and torques that caused it, using the equations
F = ma
(1)
τ = Iα
(2)
(Bold type for vectors and matrices.) Observing motion means measuring segment position x(t) and
orientation θ(t). Then we compute
a = dv/dt = d2x/dt2
(3)
α = dω/dt = d2θ/dt2
(4)
We estimate segment mass m and segment inertia tensor (3x3 matrix) I. Now we use m, I, a, and α to
solve equations 1 and 2.
Articles
Manal K, McClay I, Richards J, Galinat B, Stanhope SJ (2002) "Knee moment profiles during walking:
errors due to soft tissue movement of the shank and the influence of the reference coordinate system".
Gait and Posture 15: 10-17.
Milner CE, Ferber R, Pollard CD, Hamill J, Davis IS (2006). "Biomechanical Factors Associated with Tibial
Stress Fracture in Female Runners". Med Sci Sports Exer 38: 323–328.
Purpose: Tibial stress fractures (TSF) are among the most serious running injuries, typically requiring 6–8 wk for recovery. This
cross-sectional study was conducted to determine whether differences in structure and running mechanics exist between
trained distance runners with a history of prior TSF and those who have never sustained a fracture. Methods: Female runners
with a rearfoot strike pattern, aged between 18 and 45 yr and running at least 32 kmIwkj1, were recruited for this study.
Participants in the study were 20 subjects with a history of TSF and 20 ageand mileage-matched control subjects with no
previous lower extremity bony injuries. Kinematic and kinetic data were collected during overground running at 3.7 mIsj1 using
a six-camera motion capture system, force platform, and accelerometer. Variables of interest were vertical impact peak,
instantaneous and average vertical loading rates, instantaneous and average loading rates during braking, knee flexion
excursion, ankle and knee stiffness, and peak tibial shock. Tibial varum was measured in standing. Tibial area moment of inertia
was calculated from tibial x-ray studies for a subset of runners. Results: The TSF group had significantly greater instantaneous
and average vertical loading rates and tibial shock than the control group. The magnitude of tibial shock predicted group
membership successfully in 70% of cases. Conclusion: These data indicate that a history of TSF in runners is associated with
increases in dynamic loading-related variables.
Ferber R, Noehren B, Hamill J, Davis IS (2010). "Competitive female runners with a history of iliotibial
band syndrome demonstrate atypical hip and knee kinematics." J Orthop Sports Phys Ther 40: 52-58.
STUDY DESIGN: Cross-sectional experimental laboratory study. OBJECTIVE: To examine differences in running mechanics
between runners who had previously sustained iliotibial band syndrome (ITBS) and runners with no knee-related running
injuries. BACKGROUND: ITBS is the second leading cause of knee pain in runners and the most common cause of lateral knee
pain. Despite its prevalence, few biomechanical studies have been conducted to better understand its aetiology. Because the
iliotibial band has both femoral and tibial attachments, it is possible that atypical hip and foot mechanics could result in the
development of ITBS. METHODS: The running mechanics of 35 females who had previously sustained ITBS were compared to 35
healthy age-matched and running distance-matched healthy females. Comparisons of hip, knee, and ankle 3-dimensional
kinematics and internal moments during the stance phase of running gait were measured. RESULTS: The ITBS group exhibited
significantly greater peak rearfoot invertor moment, peak knee internal rotation angle, and peak hip adduction angle compared
to controls. No significant differences in peak rearfoot eversion angle, peak knee flexion angle, peak knee external rotator
moment, or peak hip abductor moments were observed between groups. CONCLUSION: Females with a previous history of ITBS
demonstrate a kinematic profile that is suggestive of increased stress on the iliotibial band. These results were generally similar
to those reported for a prospective study conducted within the same laboratory environment.
Kirtley, C.; Whittle, M.W; and Jefferson, RJ (1985). "Influence of Walking Speed on Gait Parameters".
Journal of Biomedical Engineering 7 (4): 282–8.
Crowninshield RD, Johnston RC, Andrews JG, & Brand RA (1978). "A biomechanical investigation of the
human hip". Journal of Biomechanics 11: 75–85.
Estimating segment mass inertia tensor
Jensen RK (1989). "Changes in segment inertia proportions between four and twenty years". J Biomech
22: 529–36.
Hanavan E (1964). A Mathematical Model for the Human Body. Technical Report, Wright-Patterson Air
Force Base.