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IE 552 Mechanics of Musculoskeletal System Dr. Andris Freivalds Class #14

IE 552 Mechanics of Musculoskeletal System Dr. Andris Freivalds Class #14. Tension Buildup (con’t). Step: 1-e -at. Ramp: e -at /a -1/a + t. K SE =100, K PE =400, B=5 a=100, Τ =.01sec → 100 Hz. Time Constant in Muscle Response. Time Constant Corresponds to Tetanic Frequency.

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IE 552 Mechanics of Musculoskeletal System Dr. Andris Freivalds Class #14

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  1. IE 552 Mechanics of Musculoskeletal System Dr. Andris Freivalds Class #14 IE 552

  2. Tension Buildup (con’t) Step: 1-e-at Ramp: e-at/a -1/a + t KSE=100, KPE=400, B=5 a=100, Τ =.01sec → 100 Hz IE 552

  3. Time Constant in Muscle Response IE 552

  4. IE 552

  5. Time Constant Corresponds to Tetanic Frequency IE 552

  6. Summary of Muscle Model Parameter DeterminationDashpot B – Initial slope KSE – Slope from Quick Stretch IE 552

  7. Summary of Muscle Model Parameter Determination (con’t) KPE from time constant (τ): • Stress relaxation • Strain relaxation (creep) IE 552

  8. Frequency Analysis of Muscle TCE = -(Bs + KPE)ε + (Bs + KPE + KSE)/KSE T T = (Bs + KPE)ε (Bs+KPE+KSE) IE 552

  9. General Frequency Analysis For complex variable: X(ω) + jY(ω), where j =√-1 M(ω) = [X2(ω) + Y2(ω)]½ (magnitude) Φ(ω) = tan-1Y(ω)/X(ω) (argument) IE 552

  10. H(s) = 1/(s+1) (substitute s = jω) Manipulation (Frequency Domain) IE 552

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