April 5 th 2012 Aarti Mistry Definition Bharata is derived from the three syllables meaning BHAva expression Raga music TAla rhythm Natyam means dramatic art ID: 1007095
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1. Bharatanatyam BiomechanicsApril 5th 2012Aarti Mistry
2. Definition‘Bharata’ is derived from the three syllables meaning BHAva (expression), Raga (music), TAla (rhythm), ‘Natyam’ means dramatic art.Characteristics Demi-plié stance “aramandi”Balance Structured and geometric movements SymmetryIntricate foot movementsForce / ImpulseDelicate facial expression
3. Research QuestionsBalance1. Does my center of mass change when performing different steps? Symmetry2. Are my arm movements symmetrical? Position? Velocity?Momentum?Force/Impulse3. Do my jumps require the same impulse to take off from the ground?
4. VideosWalking JumpStationary StepClock Step
5. Balance & Center of MassDefinition: point in space where the entire mass of a body assumed to be concentrated.Slightly below belly button (geometric center )Female center of mass slightly lower vs. maleCOM to height ratio: 0.543 vs. 0.560To maintain balance COM must remain directly above area of contact with floorFgravity and Fground align directly through COM and there is no total forceSmaller the area (balls of the feet), harder it is to balance
6. Balance & Center of MassIn dance, must maintain demi-plié stance for FormWeight distribution Balance Standing COMCOM = COM: height ratio * heightCOM = 0.543 * 153.7 cm = 88.46 cmEstimated COM in neutral demi-plié stanceCOM = 66.47 cm (average)Height in demi-plié = 138 cm (average)COM: height ratio = 0.482
7. Position (yCOM) vs. TimeWalking JumpInitial: 63.49 cmCross over peak: 78.92 cmJump peak: 81.56 cm * Final: 66.50 cm *Stationary StepInitial: 68.52 cmJump peak (1): 79.89 cmJump peak (2): 80.20 cmFinal: 62.83 cmClock StepInitial: 67.81 cmJump peak : 82.43 cmFinal: 69.69 cm
8. Symmetry & Clock StepPosition (yRH & yLH) vs. timeArm movements trace the pattern:12 o’clock1 o’ clock/ 11 o’clock2 o’clock/ 10 o’clock3 o’clock / 9 o’clock4 o’clock / 8 o’clock5 o’clock / 7 o’clock6 o’clockCenter LH lower than RH except during jump phase and 6 o’clock∆yaverage = 4.18 cmGreatest difference is a 3 o’clock/9 o’clock position ∆ymax= 13.49 cm, i.e. LH 13.49 cm lower than RH
9. Fluidity & Clock StepVelocity (vy, RH & vy, LH) vs. timePosition differs but velocities similarMomentum ρ = m * vm = mass * body segment proportionArm: 0.05 body massSample calculation (LH peak height)vx = 0.062 m/s, vy = 4.022 m/s,v = 4.029 m/sρ = 39 kg * 0.05 * 4.029 m/sρ = 7.845 kg m/sMomentum appears to be inconsistentInitial lag in LH vs. RH then recoveryLack of fluidity?Is the clock on time?Yes taverage= 0.52 s ± 0.1 sTime (s)LH Momentum (kg m/s)RH Momentum (kg m/s)peak jump0.527.8456.72812 o’clock0.760.5270.7031 o’ clock/ 11 o’clock1.40.3521.2412 o’clock/ 10 o’clock1.840.6351.2283 o’clock / 9 o’clock2.241.0501.6364 o’clock / 8 o’clock2.881.2930.8025 o’clock / 7 o’clock3.281.2891.2106 o’clock3.881.3540.375Center4.360.5760.749
10. Footwork & ImpulseClock Step and Stationary Step contain same vertical jumpFrom personal perspective, jump in the clock step requires more momentum to jump from standstillSimilar to an athlete’s vertical jump (vs. running jump)Measured impulse on take off and landing in RF, LF and COMImpulse = ∆ρ = m * (vafter- vbefore)m = mass m = mass * body segment proportionFoot: 0.0145 body massCalculating Ilanding is less meaningful since landing is an inelastic collision IMPULSETAKE OFF (Ns)LANDING (Ns)RFLFCOMRFLFCOMCLOCK JUMP0.1370.145-2.641-0.0787-0.135-4.141STATIONARY JUMP10.2380.597-12.942-0.156-0.2332.234STATIONARY JUMP20.2300.225-12.538-0.843-0.365-1.336
11. Footwork & ImpulseDifference in momentumbetween COM and feet measurements attributed to the fact that the COM moves faster than feetBody slows down as it reaches peak height before the feet lose contact with the ground
12. Footwork & ForceFgravity= m*g = 9.81 m/s2 *39 kg = 382.59 NFtake off > Fgravity in order to jump off groundForce approximation derived from:NOTE:Clock Step values don’t seem to agreeCalculating Flanding is less meaningful since landing is an inelastic collision and we do not know Fground FORCETAKE OFF (N)LANDING (N)RFLFCOMRFLFCOMCLOCK JUMP236.537249.947-66.019-135.769-232.323-103.516STATIONARY JUMP1821.9391030.134-323.548-537.617-802.020111.713STATIONARY JUMP2792.619774.670-313.449-2907.332-1258.499-66.817
13. ConsiderationsImperfect techniqueOut of practiceFeet did not take off/ land simultaneously on some occasionsMeasurement errorCenter of mass difficult to computeOnly one trial usedStatistical significance of results?ScoliosisCurvature of spineAsymmetryComplicated movements Dynamic vs. staticTwisting/rotationOut of planeSpeed
14. Conclusions1. Does my center of mass change when performing different steps? In general, upon completion of each sequence COM is raised.When jumping, my center of mass drops initially then raises.2. Are my arm movements symmetrical? PositionQualitatively the movements appear symmetrical but video analysis shows LH generally lower than RHVelocityHands /arms may differ spatially but travel at the same speedsMomentumLH initially slower but then recovers. 3. Do my jumps require the same impulse to take off from the ground? Same jump performed in clock step requires less impulse than jumps performed in the stationary sequence. 4. For a beautiful dance, the physics are certainly ugly.
15. Future DirectionsCompare biomechanics of symmetry and balance toA more seasoned dancerSomeone with a normal spineDancing with bells (added weight)Use force plates to measure Force Address differences observed in the jumpsCompare dance jump to vertical standing athletic jumpDetermine maximal force required for take off and generated upon landing Center of MassNumerous possibilities as dance biomechanics is not well studied
16. ReferencesGambino, Stephanie et al. Center of Mass of a Human. The Physics Factbook. 2006. http://hypertextbook.com/facts/2006/centerofmass.shtml Kuznetsov, Natalia. Physics of Dance. Fermilab. 2003. http://ed.fnal.gov/trc_new/demos/present/physofballet.pdfSampradaya Dance Academy. 2011. http://www.sampradaya.ca/_bin/danceCreations/bharatanatyam.cfmSanskriti Dance Academy http://sanskritidance.com/index.php/About/Winter, D.A. Table of Body Segment Parameters. Biomechanics and Motor Control of Human Movement, 2nd edition, Toronto: John Wiley & Sons, 1990.
17. Questions