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Unformatted text preview: Lecture 8 Inverse Dynamic Analyses EML 5595 Mechanics of the Human Locomotor System Outline Basic Inverse Dynamics Methods Advanced Inverse Dynamics Method y Remy and Thelen (2009) Outline Basic Inverse Dynamics Methods Basic Methods Matrix Equations Bottom Up Top Down Matrix Equations Matrix Equations M(q)q = N(q)T + G(q) + V(q, q) N(q)T = M(q)q  G(q)  V(q, q) Matrix Equations M(q)q = N(q)T + G(q) + V(q, q) N(q) T = M(q)q  G(q)  V(q, q)
A x b T = N 1 (q) [ M(q)q  G(q)  V(q, q) ] Bottom Up Top Down Summary Bottom Up Requires kinematic and ground reaction data Each segment is only susceptible to kinematic g y p
errors in segments at or below it Residual forces and torques at top of chain are not zero Summary Bottom Up Requires kinematic and ground reaction data Each segment is only susceptible to kinematic g y p
errors in segments at or below it Residual forces and torques at top of chain are not zero Top Down (and Matrix Equations) Only requires kinematic data Each segment is only susceptible to kinematic errors in segments at or above it Residual forces and torques at bottom of chain do not match ground reactions Question If the inverse dynamics problem can be solved without ground reaction force and torque data, how can we make use of these additional (i.e., redundant) data to improve the accuracy of our calculations AND have zero residual forces and torques at the ends of the chain (i.e., dynamic consistency)? (i e Outline Basic Inverse Dynamics Methods Advanced Inverse Dynamics Method y Remy and Thelen (2009) Residual Elimination Algorithm Observation 3 other dynamics equations Only ground reactions appear 3 dynamics equations Only joint torques appear Matrix Equations
M(q)q = N(q)T + G(q) + V(q, q) + F M(q)q  F = G(q) + V(q, q) q [ M(q)  I ] = [G(q) + V(q, q)] F q A(q) = B(q, q) F Variation Formulation
Let L t q = q* + q F = F* + F Then
If q and F are zero, then zero
the equations do not balance. q* + q A(q) * = B(q, q) If we change q, then q will no F + F g longer be consistent with q and q. or q* q A(q) = B(q, q)  A(q) * (q (q (q F F Variation Solution q* q A(q) = B(q, q)  A(q) * F F A(q) = C(q, q, q* , F* )
Undetermined system = A(q) C(q, q, q* , F* )
A(q) is the p (q pesudoinverse Kinematic Updating
q = q* + q
Guess for qo plus integration q
Guess f qo plus integration G for l i t ti
q Optimization Formulation Gait Example Initial Residual Loads Final Residual Loads Generalized Coordinate Changes Pelvis Coordinate Changes Inverse Dynamics Improvements Error Assessment
For the experimental gait data: Prior to residual elimination, average marker errors from inverse kinematics were 10 9 1 2 mm 10.9 1.2 mm. After residual elimination, average marker errors were 12.9 1.7 mm. What could the authors have done to achieve lower marker errors? How much d d t e residual e o uc did the es dua elimination a go t at o algorithm change the ground reaction forces and moments? How did the authors significantly improve computational speed without losing much accuracy? For Next Time Download and read Gilchrist and Winter (1997). Bring any questions you have thus far on inverse or forward dynamics concepts. ...
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 Spring '08
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