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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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Equation of Motion: General Plane motion - Problem Solving01:16

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Consider a lawn roller with a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied to this roller, angled at 60 degrees from the horizontal plane. What will be the angular acceleration of the lawn roller?
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Planar Rigid-Body Motion01:22

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Understanding the movement of a rigid body in planar motion involves recognizing that every particle within this body is traversing a path that maintains a consistent distance from a specific plane. This concept is fundamental in the study of physics and mechanical engineering, and it allows us to comprehend better how objects move in space.
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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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Kinematic Equations - III01:18

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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 - I01:26

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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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Related Experiment Video

Updated: Sep 7, 2025

In Vivo Quantification of Hip Arthrokinematics during Dynamic Weight-bearing Activities using Dual Fluoroscopy
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A generalised smoothing approach for continuous, planar, inverse kinematics problems.

Andrew J Pohl1, Matthew R Schofield2, Reed Ferber3

  • 1Human Performance Laboratory, Faculty of Kinesiology, University of Calgary, 2500 University Dr. NW, Calgary, AB, Canada T2N 1N4.

Journal of Biomechanics
|June 16, 2022
PubMed
Summary

This study introduces a generalized smoothing approach for Bayesian inverse kinematics, improving time-continuous motion capture data analysis. The method enhances accuracy and handles missing data, offering a more robust solution for kinematic problems.

Keywords:
Bayesian inferenceFunctional data analysisGeneralised additive modelsMeasurement errorOptical motion captureOrdinary differential equations

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Area of Science:

  • Biomechanics
  • Computational Kinematics
  • Bayesian Inference

Background:

  • Marker-based motion capture often uses Bayesian methods for inverse kinematics.
  • Current frame-by-frame Bayesian solutions can result in temporally discontinuous estimates.
  • Addressing temporal continuity is crucial for accurate motion analysis.

Purpose of the Study:

  • To develop a continuous, time-dependent Bayesian approach for planar inverse kinematics.
  • To overcome the limitations of frame-by-frame solutions in motion capture.
  • To improve the accuracy and robustness of kinematic parameter estimation.

Main Methods:

  • Utilized finite basis representations to model kinematic quantities as smooth, continuous functions.
  • Developed a generalized smoothing approach for planar inverse kinematics problems.
  • Applied the method to systems of ordinary differential equations and human gait analysis.

Main Results:

  • Achieved accurate approximation of solutions for both simple and complex planar inverse kinematics problems.
  • Demonstrated a significant decrease in Root Mean Square Error (RMSE) for joint angle estimation (e.g., 0.025 rad for ankle angle).
  • Successfully estimated kinematic parameters and their derivatives even with missing data, without pre-filtering.

Conclusions:

  • The generalized smoothing approach provides continuous and accurate solutions for Bayesian inverse kinematics.
  • This method offers substantial improvements over previous time-independent techniques.
  • The approach is robust to missing data and capable of estimating kinematic derivatives, enhancing motion analysis capabilities.