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Biomechanical Considerations for Striking Implements - Background

Biomechanical Considerations for Striking Implements - Background. Relationship between linear motion and rotary motion Radius of rotation Axis of rotation Relationship between torque and rotational motion Moment of Inertia: I = mk 2 Radius of gyration: k = (I/m) .5

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Biomechanical Considerations for Striking Implements - Background

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  1. Biomechanical Considerations for Striking Implements - Background • Relationship between linear motion and rotary motion • Radius of rotation • Axis of rotation • Relationship between torque and rotational motion • Moment of Inertia: I = mk2 • Radius of gyration: k = (I/m).5 • Rotational analogues of newton’s laws: T = I • Elastic properties of striking implements • Coefficient of restitution • Vibrations during the swing (bending) • Vibrations during and after impact • Sweet spot determinants • Center of percussion, vibrational nodes

  2. Relationship between linear and angular motion (kinematics)

  3. Relationship between linear and angular motion • Would you rather have a long or short baseball bat or golf club? Why?

  4. What is Moment of Inertia (MOI)? It is the resistance of a system to rotational acceleration, and is calculated at follows: Here, r (the radius of rotation) is equal to k (the radius of gyration), but that is not the case with extended bodies

  5. What is radius of gyration (k)? k 35 An indicator of distribution of mass about the axis. It is the distance from the axis to a point at which all the mass of a system of equal mass would be concentrated to have the MOI equal the original system. It is, then, the average weighted distance of the mass of a system to the axis. Equivalent systems k 35

  6. Determining MOI & K • Simple 3-segment system: • I = 3mi di2 = m1 d12 + m2 d22+ m3 d32 + . . . . . . .+ mi di2 • I = mk2 ; k = (I/m).5 • Irregularly shaped bodies But we can’t measure all of these small masses!

  7. Physical pendulum properties (rigid bodies) • Radius and axis of rotation • Radius of gyration (K) • Moment of inertia (MOI) • Center of percussion

  8. Physical pendulum method of determining MOI and K • Suspend object at axis • Measure mass (m), and distance from axis to COM, r • Measure period of oscillation (T) • Moment of inertia (I) = T2 mr * .248387 m/sec • Radius of gyration (K) = ( I/m).5

  9. Rigid Body -Bat Distance from Axis to COP: q = k2/r = I/mr = T2g/42 = .248387T2

  10. Rigid Body - Tennis Racket

  11. Rigid Body - Golf Club

  12. Semi-rigid (elastic) bodies) • Coefficient of restitution • Vibrations - nodes and modes Vibrations when bat is free (during impact with ball) Vibrations when bat is clamped (during swing )

  13. Simpler illustration of bat vibrations during swing and impact Approx 10-20 Hz Approx 150-250 HZ

  14. Bat Vibrations During Swing and Impact

  15. Coefficient of Restitution (COR) • COR is a measure of the liveliness of an object • When 2 objects collide: • When one object is stationary, this reduces to: • An alternative way to measure COR • Is to drop a ball and measure the ht • Bounced compared to ht dropped:

  16. Coefficient of Restitution (COR) • COR of balls dropped or thrown at a rigid wooden surface is shown here. • COR increases directly with temperature and inversely with impact velocity.

  17. Questions • What is the sweet spot of a striking implement? • How do we take advantage of rigid body properties to improve implement? • How do we take advantage of elastic properties to improve implement?

  18. Evaluation methods for striking implements • Apply scientific principles to evaluate mfgr claims • Use it yourself, if possible • Product reviews on the internet & in trade mags • Consult with others who use it, or supervise its use • Consult with professors, or professionals (e.g., coaches) with specialized insight and expertise • Look at research available, if any • Evaluate quality of research – • Extrinsic - who is sponsoring the research, where did it appear? • Intrinsic – methods, procedures, statistics, conclusions

  19. Next: Bats & Clubs • Tuesday, November 1 • Lecture on golf clubs – Read Ch 9 of Kreighbaum and Smith • Submit 2 questions related to readings on golf clubs • Thursday, November 3 • Guest Speaker: Chris Hay, Golf USA • Tuesday, November 8 • Lecture on softball and baseball bats – Read Ch 10 of Kreighbaum & Smith • Submit 2 questions relating to readings on bats • Thursday, November 10 • Review new bat products • 2005 catalogues from leading bat manufacturers • Bats from lab • Review for exam

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