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Three-Dimensional Force System:Problem Solving

Three-Dimensional Force System:Problem Solving

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...

Planar Rigid-Body Motion

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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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Collisions in Multiple Dimensions: Problem Solving

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
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Relative Motion Analysis using Rotating Axes-Problem Solving

Relative Motion Analysis using Rotating Axes-Problem Solving

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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Coplanar Forces

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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.
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Related Experiment Video

Updated: May 29, 2026

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

Published on: October 14, 2017

Planning collision-free paths for robotic arm among obstacles.

R T Chien¹, L Zhang, B Zhang

¹Coordinated Science Laboratory, University of Illinois, Urbana, IL 61801.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|August 27, 2011

Summary

This study introduces a novel theory for planning collision-free paths for moving objects. It utilizes rotation mapping graphs (RMGs) to simplify complex pathfinding problems in robotics and obstacle navigation.

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The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

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Published on: October 14, 2017

Operation of the Collaborative Composite Manufacturing (CCM) System

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Published on: October 1, 2019

Area of Science:

Robotics
Computational Geometry
Artificial Intelligence

Background:

Path planning for moving objects in cluttered environments is a complex challenge.
Existing methods often struggle with objects that can translate and rotate simultaneously.

Purpose of the Study:

To develop a theoretical framework for planning collision-free paths for objects with translational and rotational movement.
To introduce the concept of a Rotation Mapping Graph (RMG) for representing object configurations and obstacle interactions.

Main Methods:

The study employs state space representation and rotation mapping to define the RMG.
Graph connectivity analysis using topological methods is applied to solve path planning problems.
A specific topological method is presented for rod-like objects.

Main Results:

The theory transforms the path planning problem into a graph connectivity problem.
The RMG effectively captures the relationship between object positions and collision-free orientations.
The proposed method provides a theoretical solution for planning collision-free paths for rod objects.

Conclusions:

The RMG theory offers a robust and theoretically sound approach to collision-free path planning.
This framework can be extended to complex systems like non-rigid robotic arms.
The topological solution simplifies the complexity of motion planning in dynamic environments.