karl e. zelik, art d. kuo, mechanical engineering
TRANSCRIPT
Prince Method vs Inverse Dynamics
Karl Zelik
June 30, 2010
Equations
Power =n∑
i=1Mi · ωi
Work =∫ ba Power dt
Power =n∑
i=1Fi · vCOM
Power =n∑
i=1
12mi(vi − vCOM )2 +
12Iiω2
i + mig(hi − hCOM )
Work =n∑
i=1∆KEi/COM + ∆PEi/COM
Power = ddt(
n∑i=1
∆KEi/COM + ∆PEi/COM
Power = ddt(
n∑i=1
∆KEi/COM
1
Estimating soft tissue work…
Soft tissues may also provide a damped elastic Rebound
Soft tissues dominate negative Collision work, joints dominate positive Push-off
Do soft tissues perform significant mechanical work in walking? When?
Total Mechanical Work
Karl E. Zelik, Art D. Kuo, Mechanical Engineering, University of , Ann Arbor, MI, USA
COM Work Peripheral Work Joint Work Non-Joint Work = + net rotational joint work done by muscles and tendons as computed from standard rigid-body inverse dynamics; work estimated by integrating summed ankle, knee and hip power over time
work performed by all the other deformable soft tissues in the body; estimated as the difference between total mechanical work and joint work
work performed on the body center-of-mass (COM); estimated using Individual Limb Method (Donelan et al., 2002)
work performed relative to the body COM (e.g., due to leg swing); estimated as changes in rigid segmental energies with respect to the COM
+
Joint work performed by lower-limb muscles and tendons is considered the dominant energetic contributor to walking, but soft tissues elsewhere in the body may also do significant work. Steady level-ground walking requires zero net mechanical work per stride, yet less negative work is performed about the lower-limb joints than positive (DeVita et al., 2007). This suggests that joint work measures fail to capture some negative work performed by the body. This uncaptured work may be indicative of unmodeled soft tissue deformations, as is recognized in running and jumping impacts, but typically not in walking. We hypothesize that significant soft tissue work is performed in walking when collisions occur after heelstrike.
Not directly measureable. Estimated from Eqn above.
It is not feasible to simultaneously measure all the distributed soft tissues in the body that might perform work during walking. We propose that mechanical work performed by the body, but not captured by rigid-body joint work estimates (i.e., inverse dynamics) is an indirect indicator of soft tissue deformations. We performed standard gait analysis on subjects walking on an instrumented treadmill at various speeds (N=10, 0.7–2.0 m/s). We estimated 3D mechanical powers (outlined on the right) and integrated over individual phases of the gait cycle to compute work. We looked for indications of soft tissue work, specifically during the Collision phase immediately after heelstrike. The phases of gait – Collision, Rebound, Preload, Push-off, Swing – are defined by fluctuating regions of positive and negative COM work, beginning at heelstrike. Power and work results are plotted for a single limb over a full stride, beginning with heelstrike. Statistical analysis of covariance was used to evaluate work trends across speed.
Supported in part by a NSF Graduate Research Fellowship (K.E.Z.), the Department of Defense & NIH H0055706 (A.D.K.).
The largest difference between total mechanical work and summed ankle-knee-hip work was during Collision, with 23.5 J less joint work at 2.0 m/s. At 1.25 m/s, we observed 8.5 J of negative non-joint work, compared to only 5.5 J of negative joint work. These results suggest substantial negative soft tissue work is done during Collision, increasing with speed (P=1e-16).
No statistical difference was found between summed joint work and total mechanical work during Push-off (P>0.3). These results are consistent with muscles and tendons performing work about the joints of the trailing leg to redirect the COM during the step-to-step transition.
Another substantial difference was in the positive work of Rebound. Summed ankle-knee-hip joint work was consistently less than total mechanical work by about 5-8 J across all speeds (P=3e-5), a difference we attribute to soft tissue contributions. At 1.25 m/s, this Rebound difference constitutes about 17% of the positive work per stride performed by lower extremity joints. Soft tissue contributions to Rebound were not proportional to Collision work, but might nonetheless represent a damped elastic response that cannot be attributed to rotational contributions of the ankle-knee-hip joints.
Results/Discussion
Introduction/Methods
*No net mechanical work W is performed in steady, level ground walking.
Prince Method vs Inverse Dynamics
Karl Zelik
June 30, 2010
Equations
Power =n∑
i=1Mi · ωi
Work =∫ ba Power dt
Power =n∑
i=1Fi · vCOM
Power =n∑
i=1
12mi(vi − vCOM )2 +
12Iiω2
i + mig(hi − hCOM )
Work =n∑
i=1∆KEi/COM + ∆PEi/COM
Power = ddt(
n∑i=1
∆KEi/COM + ∆PEi/COM
Power = ddt(
n∑i=1
∆KEi/COM
1
Prince Method vs Inverse Dynamics
Karl Zelik
June 30, 2010
Equations
Power =n∑
i=1Mi · ωi
Work =∫ ba Power dt
Power =n∑
i=1Fi · vCOM
Power =n∑
i=1
12mi(vi − vCOM )2 +
12Iiω2
i + mig(hi − hCOM )
Work =n∑
i=1∆KEi/COM + ∆PEi/COM
Power = ddt(
n∑i=1
∆KEi/COM + ∆PEi/COM
Power = ddt(
n∑i=1
∆KEi/COM
1
inter-vertebraldiscs
heelpads
joints(cartilage)
visceravCOM
Fi
muscles
Mi, ωi vCOM
mi, vi, Ii, ωi
0 25 50 75 100-2
-1
0
1
2
3
4
Pow
er (W
/kg)
% Gait Cycle
Colli
sion
Rebo
und
Push
-o!
Prel
oad
Swin
g
0 25 50 75 100
0Hip
0
Knee
0Ankl
e
Summed Ankle-Knee-Hip
0 25 50 75 100% Gait Cycle
0 25 50 75 100% Gait Cycle
0 25 50 75 100% Gait Cycle
COM Work/PowerJoint Work/PowerTotal Mechanical Work/Power
Non-Joint Work/Power Peripheral Work/Power
TotalMechanical
Power
Soft tissues dominate Collision work, not joints
damped elastic Rebound?
-50
-40
-30
-20
-10
0
10
Colli
sion
Wor
k (J
)
0.6 0.8 1 1.2 1.4 1.6 1.8 2Walking Speed (m/s)
-10
0
10
20
30
Rebo
und
Wor
k (J
)
0.6 0.8 1 1.2 1.4 1.6 1.8 2Walking Speed (m/s)
0.6 0.8 1 1.2 1.4 1.6 1.8 2Walking Speed (m/s)
0.6 0.8 1 1.2 1.4 1.6 1.8 2Walking Speed (m/s)