Kinematics and Kinetics Study Guide

Kinematics and Kinetics Overview

  • Kinematics:

    • Focuses on describing motion without consideration of the forces that cause the motion.
    • Example: Examining the motion of a table lift without addressing the underlying forces involved (such as muscle activation).
    • Key terminology:
    • Elbow punch is an example of a kinematic movement, which highlights that kinematics does not involve forces or moments.

  • Kinetics:

    • Involves the study of forces and torques (moments) that cause movements.
    • Example: When lifting an object, it involves activating muscles like biceps, brachialis, and brachioradialis to produce necessary force, leading to moments around joints (elbows, wrists, and shoulders).
    • Kinetics explains how motion occurs rather than simply describing the motion; it cannot solely quantify aspects like height or length lifted, which belongs to kinematics.

Measuring Motion Outcomes

  • Outcome Measurement:
    • Simple methods exist for quantifying outcomes, which relate those outcomes back to target values.
    • Four key metrics can be calculated:
    1. Absolute Error (AE)
    2. Constant Error (CE)
    3. Variable Error (VE)
    4. Root Mean Square (RMS) Error

Example Data Set Creation

  • Selection of four random numbers between 0 and 20 for target lengths:
    • Targets chosen: 17 cm, 10 cm, 13 cm, 4 cm.

Drawing Estimation

  • Measurement process outlines guessing lengths and comparing those to desired targets:
    • Attempt to estimate without direct reference to a ruler results in:
    • Estimated lengths: 14.4 cm, 9.3 cm, 12.07 cm, 2.9 cm.

Data Recording

  • Table Construction:
    • Organizing the results into a clear format:
    • Columns defined for: target lengths, estimated outcomes, absolute error (AE), constant error (CE).

Absolute Error Calculation (AE)

  • Formula for Absolute Error:

    • ( AEn = | outcomen - target_n | )
    • Example calculations for each set:
    • For target 17 cm (outcome 14.4 cm):
      • ( AE_1 = | 14.4 - 17 | = 2.6 \, cm )
    • For target 10 cm (outcome 9.3 cm):
      • ( AE_2 = | 9.3 - 10 | = 0.7 \, cm )
    • For target 13 cm (outcome 12.07 cm):
      • ( AE_3 = | 12.07 - 13 | = 0.93 \, cm )
    • For target 4 cm (outcome 2.9 cm):
      • ( AE_4 = | 2.9 - 4 | = 1.1 \, cm )

  • Mean Absolute Error Calculation:

    • [ MAE = \frac{1}{n} \sum{i=1}^{n} AEi ]
    • Where n = 4 (number of pairs):
    • [ MAE = \frac{1}{4} (2.6 + 0.7 + 0.93 + 1.1) = 1.35 \, cm ]

Constant Error Calculation (CE)

  • Formula for Constant Error:

    • ( CEn = (outcomen - target_n) )
    • Individual constant errors:
    • For target 17 cm (outcome 14.4 cm):
      • ( CE_1 = 14.4 - 17 = -2.6 \, cm )
    • For target 10 cm (outcome 9.3 cm):
      • ( CE_2 = 9.3 - 10 = -0.7 \, cm )
    • For target 13 cm (outcome 12.07 cm):
      • ( CE_3 = 12.07 - 13 = -0.93 \, cm )
    • For target 4 cm (outcome 2.9 cm):
      • ( CE_4 = 2.9 - 4 = -1.1 \, cm )

  • Mean Constant Error Calculation:

    • [ MCE = \frac{1}{n} \sum{i=1}^{n} CEi ]
    • [ MCE = -1.35 \, cm ]

  • Interpretation:

    • Indicates bias towards outcomes being under the target value.

Variable Error Calculation (VE)

  • Formula for Variable Error:

    • ( VE = \sqrt{ \frac{1}{n} \sum{i=1}^{n} (outcomen - \text{mean})^2 } )
    • Computing the mean outcome:
    • Mean outcomes:
      • [ mean = \frac{14.4 + 9.3 + 12.07 + 2.9}{4} = 9.65 \, cm ]

  • Calculating Squared Differences:

    • For each outcome, calculate ( (outcome_n - mean)^2 ):
    • ( (14.4 - 9.65)^2 = 22.5625 \, cm^2 )
    • ( (9.3 - 9.65)^2 = 0.1225 \, cm^2 )
    • ( (12.07 - 9.65)^2 = 5.5569 \, cm^2 )
    • ( (2.9 - 9.65)^2 = 45.5625 \, cm^2 )

  • Final Calculation of Mean Variable Error (VE):

    • Add squared differences:
    • Sum = 73.76 \, cm^2
    • [ VE = \sqrt{\frac{73.76}{4}} = \sqrt{18.44} \approx 4.3 \, cm ]

Root Mean Square Error Calculation (RMS)

  • RMS Error Formula:
    • [ RMS = \sqrt{(CE)^2 + (VE)^2} ]
    • Plugging in values:
    • [ RMS = \sqrt{(-1.35)^2 + (4.3)^2} ]
    • [ = \sqrt{1.8225 + 18.49} = \sqrt{20.313} \approx 4.49 \, cm ]

Summary of Calculated Errors

  • Absolute Error (AE):
    • Measures accuracy of drawing compared to targets.
  • Constant Error (CE):
    • Indicates bias in performance (either too high or too low).
  • Variable Error (VE):
    • Reflects consistency of performance.
  • Root Mean Square Error (RMS):
    • Combines constant and variable errors; reflects overall accuracy.

Additional Notes

  • Emphasis on understanding terminology and definitions related to kinetics and kinematics that inform further analysis and application of biomechanics.
  • In practical applications, when analyzing motion, it’s crucial to compute these errors to gauge accuracy, bias, and consistency.