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Related Concept Videos

Physical Pendulum01:06

Physical Pendulum

When a rigid body is hanging freely from a fixed pivot point and is displaced, it oscillates similar to a simple pendulum and is known as a physical pendulum. The period and angular frequency of a physical pendulum are obtained by using the small-angle approximation and drawing parallels with a spring-mass system. The small-angle approximation (sinθ=θ) is valid up to about 14°.
When dealing with complicated systems, the mass moment of inertia is an important parameter, as it describes the mass...
Simple Pendulum01:10

Simple Pendulum

A simple pendulum consists of a small diameter ball suspended from a string, which has negligible mass but is strong enough to not stretch. In our daily life, pendulums have many uses, such as in clocks, on a swing set, and on a sinker on a fishing line.
The period of a simple pendulum depends on two factors: its length and the acceleration due to gravity. The period is completely independent of any other factors, such as mass or maximum displacement. For small displacements, a pendulum is...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Measuring Acceleration Due to Gravity01:12

Measuring Acceleration Due to Gravity

Consider a coffee mug hanging on a hook in a pantry. If the mug gets knocked, it oscillates back and forth like a pendulum until the oscillations die out.
A simple pendulum can be described as a point mass and a string. Meanwhile, a physical pendulum is any object whose oscillations are similar to a simple pendulum, but cannot be modeled as a point mass on a string because its mass is distributed over a larger area. The behavior of a physical pendulum can be modeled using the principles of...
Torsional Pendulum01:09

Torsional Pendulum

A torsional pendulum involves the oscillation of a rigid body in which the restoring force is provided by the torsion in the string from which the rigid body is suspended. Ideally, the string should be massless; practically, its mass is much smaller than the rigid body's mass and is neglected.
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...
Trapezoidal Rule01:26

Trapezoidal Rule

Estimating the distance traveled by a vehicle using its recorded velocity over time is a common problem in physics and engineering. When velocity data is available at discrete time intervals, rather than as a continuous function, numerical integration methods such as the trapezoidal rule are often employed to approximate the total displacement.The trapezoidal rule works by dividing the total time interval into several equal segments. Within each segment, the recorded velocities at the endpoints...

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Related Experiment Video

Updated: May 7, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
10:52

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

Foot trajectory approximation using the pendulum model of walking.

Juan Fang1, Aleksandra Vuckovic, Sujay Galen

  • 1Division of Mechanical Engineering, Department of Engineering and Information Technology, Institute for Rehabilitation and Performance Technology, Bern University of Applied Sciences, 3400, Burgdorf, Switzerland.

Medical & Biological Engineering & Computing
|September 24, 2013
PubMed
Summary
This summary is machine-generated.

Human walking trajectories can be modeled as a rigid pendulum, centered at the hip. This finding supports using pendulum models for designing robotic gait orthoses for walking rehabilitation.

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Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb
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Published on: August 30, 2016

Area of Science:

  • Robotics
  • Biomechanics
  • Gait Analysis

Background:

  • Natural foot trajectory generation is crucial for robotic walking rehabilitation.
  • Human walking exhibits pendular properties, inspiring pendulum models in bipedal robots.
  • The applicability of pendulum models to natural foot trajectories requires investigation for gait orthosis design.

Purpose of the Study:

  • To investigate the circle approximation of foot trajectories using the pendulum model of walking.
  • To analyze the geometry of the pendulum model in relation to human walking.
  • To determine if pendulum models can accurately represent natural foot trajectories for gait orthosis development.

Main Methods:

  • Collected overground walking data from three able-bodied subjects at various speeds.
  • Analyzed foot trajectories relative to the hip.
  • Developed four circle approximation approaches and best-fit circle algorithms for ankle, heel, and toe trajectories.

Main Results:

  • Ankle and heel trajectories during stance, and toe trajectories during stance and swing phases, were well-modeled by a rigid pendulum.
  • Pendulum models were consistently centered around the hip.
  • Pendular lengths approximated the segment distances from the hip.

Conclusions:

  • The rigid pendulum model effectively approximates human foot trajectories during walking.
  • Findings validate the use of pendulum models in gait analysis and robotic rehabilitation.
  • This study offers a novel approach for integrating pendulum dynamics into gait orthosis design.