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Three-Dimensional Force System:Problem Solving01:30

Three-Dimensional Force System:Problem Solving

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A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...
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Three-Dimensional Force System01:30

Three-Dimensional Force System

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In mechanical engineering, a three-dimensional force system is a system of forces acting in three dimensions, with forces applied along the x, y, and z coordinate axes. The three-dimensional force system is an important concept in mechanical engineering, as it allows engineers to understand and analyze the behavior of objects and structures in three dimensions. By understanding the forces acting on a system, engineers can design more efficient and effective mechanical systems that can withstand...
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Two-Dimensional Force System: Problem Solving01:29

Two-Dimensional Force System: Problem Solving

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Solving problems related to two-dimensional force systems is an essential aspect of mechanics and engineering. By applying the principles of vector analysis and force equilibrium, one can determine the effect of multiple forces acting on an object in a two-dimensional space.
The first step to solving a two-dimensional force system problem is to draw a free-body diagram of the object under consideration. This diagram helps identify all the external forces acting on the object, including their...
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

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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.
Here, in order to determine the magnitude of velocity and acceleration for point...
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Two-Dimensional Force System01:20

Two-Dimensional Force System

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A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as:
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Relative Velocity in Two Dimensions01:11

Relative Velocity in Two Dimensions

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Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by...
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Related Experiment Video

Updated: Jun 22, 2025

A Networked Desktop Virtual Reality Setup for Decision Science and Navigation Experiments with Multiple Participants
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Real-Time Trajectory Smoothing and Obstacle Avoidance: A Method Based on Virtual Force Guidance.

Yongbin Su1, Chenying Lin1, Tundong Liu1

  • 1Pen-Tung Sah Institute of Micro-Nano Science and Technology, Xiamen University, Xiamen 361104, China.

Sensors (Basel, Switzerland)
|June 27, 2024
PubMed
Summary

This study introduces a new real-time trajectory smoothing method that uses virtual forces to avoid obstacles. The approach generates smooth, collision-free paths efficiently for dynamic environments.

Keywords:
real-time obstacle avoidancereal-time trajectory smoothingtrajectory planningvirtual force guidance

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Area of Science:

  • Robotics
  • Artificial Intelligence
  • Control Systems

Background:

  • Real-time trajectory planning in dynamic environments demands smooth paths.
  • Sampling-based planners often yield jerky trajectories needing post-processing.
  • Current local smoothing techniques risk obstacle collisions due to disconnected optimization.

Purpose of the Study:

  • To develop a novel real-time trajectory smoothing method incorporating obstacle constraints.
  • To enable parallel execution with trajectory planning for efficiency.
  • To reduce computational overhead in trajectory smoothing.

Main Methods:

  • Introduced virtual attractive forces from original trajectory points.
  • Incorporated virtual repulsive forces from obstacles.
  • Utilized the resultant force to guide smooth trajectory generation.

Main Results:

  • Achieved real-time trajectory smoothing in experiments.
  • Effectively avoided obstacles during trajectory generation.
  • Demonstrated low computational overhead and parallel execution capability.

Conclusions:

  • The proposed method successfully generates smooth, obstacle-free trajectories in real-time.
  • It offers an efficient and computationally inexpensive solution for dynamic environments.
  • Addresses limitations of existing local smoothing methods by integrating obstacle avoidance.