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Kinetics (continued) Dr. Moran EXS 587 April 12, 2006

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Course Outline From Static to Dynamic What changes? Measurement of Force What devices to use? Operating Principles of the Force Plate Combined Force Plate and Kinematic Data Lab Experience Collecting Force Plate Data

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Inverse Dynamics Newton-Euler Equations External Forces Distal Forces + Moments Motion Proximal Forces + Moments

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Standing Still What forces are active? When standing still your weight vector is seeking to accelerate you downward at 9.81 m/s 2. The person does NOT accelerate downward because the ground exerts an equal and opposite force upward W F g W + F g = 0 F g ground reaction force

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What if it is not a static situation? ∑F x = ma x ∑F y = ma y ∑M = I o α Example #3 (con’t from last lecture) From the data collected during the swing of the foot, calculate the muscle moment and reaction forces at the ankle. The subject’s mass was 80 kg and the ankle- metatarsal length was 20.0 cm. Use Table 3.1 to calculate the inertial characteristics of the foot. Table 3.1 Calculations m = 0.0145 * 80 = 1.16 kg p o = 0.475 * 0.20 = 0.095 m I o = 1.16(0.095) = 0.0105 kg ∙ m 2

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Example #3 (continued) FW Rx Ry M Measured Kinematics –Accelerations of Center of Mass A x = 9.07 m/s A y = -6.62 m/s 2 α = 21.69 rad/s –Distances From Ankle Joint to Center of Mass –What are we solving for? Ankle Joint Reaction Force Muscle Moment about Ankle Joint Solution: see handout

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Example #4 For the same instant in time, calculate the muscle moments and reaction forces at the knee joint. The leg segment is 43.5 cm long.

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Ways to Measure Force Transducers Force Platforms Pressure Distribution Sensors Internally applied force sensors »Buckle transducers »Fiber Optics Isokinetic Devices

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Force Transducers Operating Principles Resistive (piezoresistive) Elements Deformation (very small, micro) causes an electrical change in resistance that is measured as a voltage change Based upon semiconductive material (i.e. silicon) Piezoelectric Elements Naturally occurring mineral that produces electric charge in response to deformation

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Force Platforms Most common transducer used in biomechanics Two types (1)strain-gauge: less expensive, good for static measurement, less of a range (2)Piezoelectric: more expensive, high- frequency response

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Force Platforms Any single 3-D force vector applied to the force plate can be described by 9 quantities: (1) 3 Forces: Fx, Fy, Fz (2) Force Vector Location: x, y, z (3) 3 Orthogonal Moments: Mx, My, Mz

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Force Platform Outputs: Vertical Fy1 Fy2 Fy3 Fy4 X y z Fy = Fy1 + Fy2 + Fy3 + Fy4

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Force Platform Outputs: Shear Forces Fx1 Fx2Fx3 Fx4 X y z Fx = (Fx1 + Fx4) + (Fx2 + Fx3)

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Force Platform Outputs: Shear Forces Fz1 Fz2 Fz3 Fz4 X y z Fz = (Fz1 + Fz2) + (Fz3 + Fz4)

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Force Platform Calculations: The Center of Pressure (no shear forces) Fy1 Fy2 Fy3 Fy4 X y z Measured Reaction Moments: Mx = (Fy2 + Fy3)*b - (Fy1 + Fy4)*b Mz = (Fy3 + Fy4)*a – (Fy1 + Fy2)*a Calculated Reaction Moments: Mx = -(Fy*Cpz) Mz = -(-Fy*Cpx) Fy CPx CPz 2a 2b Thus: Cpx = Mz/Fy Cpz = -Mx/Fy

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Force Platform Calculations: Effect of Origin Location with Shear Forces x y d Fx Additional Shear Force Contribution to Reaction Moment Mz = -Fx*d Fz Z Y d Additional Shear Force Contribution to Reaction Moment Mx = Fz*d

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Final Center of Pressure Calculation: CPx = (Mz-Fx*d)/Fy CPz = -(Mz+Fz*d)/Fy

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Center of Pressure Misconceptions: –COP gives no insight into the pressure at any of the contact points under the foot »During stance both your heel and the ball of feet in contact with ground »Use a pressure measurement system to get insight on the pressure underneath all contact areas »TekscanTekscan –COP relative to the foot can not be determined from force plate output alone. You need to know where the foot is placed relative to the force plate CS

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Internal vs External Joint Moments Internal produced from soft tissues (muscles, ligaments, etc) External produced about a joint by some force external to the body (ex. GRF, weight of segment) GRF d W

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Data Synchonization Kinetic & Kinematic Data Kinetic and kinematic come from different sources Same event MUST be captured at the same time Examples »Vertical channel of Force Plate triggers a LED Sampling frequencies must be at an even multiple

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Research Article (handout) Influence of a custom foot orthotic intervention on lower extremity dynamics in healthy runners »MacLean et al. (2006)

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