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Related Concept Videos

Kinematic Equations: Problem Solving01:15

Kinematic Equations: Problem Solving

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When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...
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The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
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Kinematic Equations - II01:17

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The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:
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In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
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Determining residual reduction algorithm kinematic tracking weights for a sidestep cut via numerical optimization.

Michael A Samaan1,2, Joshua T Weinhandl3, Sebastian Y Bawab1

  • 1a Department of Mechanical and Aerospace Engineering , Old Dominion University , Norfolk , VA , USA.

Computer Methods in Biomechanics and Biomedical Engineering
|May 5, 2016
PubMed
Summary

Particle swarm optimization (PSO) and simplex simulated annealing (SIMPSA) algorithms optimized musculoskeletal models for dynamic maneuvers. PSO more accurately simulated sidestep cuts, improving kinematic data consistency.

Keywords:
Particle swarm optimizationopensimresidual reduction algorithm (RRA)sidestep cutsimulated annealing

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Area of Science:

  • Biomechanics
  • Computational modeling
  • Human movement analysis

Background:

  • Musculoskeletal modeling requires in vivo kinematic and ground reaction force (GRF) data.
  • Discrepancies between experimental and model data, and GRF inconsistencies, limit simulation accuracy.
  • Residual forces and moments are applied to reconcile these differences.

Purpose of the Study:

  • To employ numerical optimization techniques for determining optimal tracking weights in musculoskeletal models.
  • To reduce discrepancies between experimental and model marker data.
  • To minimize residual forces and moments during dynamic simulations.

Main Methods:

  • Utilized particle swarm optimization (PSO) and simplex simulated annealing (SIMPSA) algorithms.
  • Applied these algorithms to determine optimal tracking weights for a sidestep cut simulation.
  • Inputted in vivo kinematic and ground reaction force (GRF) data.

Main Results:

  • Both PSO and SIMPSA achieved model kinematics within 1.4° of experimental data.
  • Residual forces and moments were reduced to below 10 N and 18 Nm, respectively.
  • PSO demonstrated superior accuracy in replicating experimental kinematics and enhancing dynamic consistency for the sidestep cut.

Conclusions:

  • Numerical optimization, specifically PSO, effectively refines musculoskeletal model simulations.
  • PSO offers improved dynamic consistency and kinematic accuracy compared to SIMPSA for sidestep maneuvers.
  • Future research should leverage external optimization routines for dynamic consistency and report data discrepancies.