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Three-Dimensional Force System

Three-Dimensional Force System

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...

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...

Bending of Curved Members - Strain Analysis

Bending of Curved Members - Strain Analysis

The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member is the...

Planar Rigid-Body Motion

Planar Rigid-Body Motion

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.
Planar motion is typically divided into three distinct categories. The first is rectilinear translation, demonstrated by a subway train that moves along...

Two-Dimensional Force System

Two-Dimensional Force System

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:

Transformation of Plane Strain

Transformation of Plane Strain

When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...

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Related Experiment Video

Updated: Jun 23, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Published on: April 11, 2018

Movement curvature planning through force field internal models.

Biljana Petreska¹, Aude Billard

¹Learning Algorithms and Systems Laboratory, Ecole Polytechnique Fédérale de Lausanne, EPFL-STI-I2S-LASA, Station 9, 1015, Lausanne, Switzerland. biljana.petreska@a3.epfl.ch

Biological Cybernetics

|April 22, 2009

Summary

Human movements are not always straight; curved reaching movements are essential for daily tasks. A new model suggests the body's geometry actively shapes these curved trajectories, not just the brain's direct commands.

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Published on: April 16, 2017

Area of Science:

Neuroscience
Biomechanics
Robotics

Background:

Human motion studies predominantly model straight reaching movements.
Many everyday goal-directed movements, like self-reaching, follow curved paths.
Curved movements are crucial in daily life, development, and assessing neurological deficits.

Purpose of the Study:

To propose a unified neural control model for both straight and curved reaching movements.
To investigate the role of body geometry in generating curved movement trajectories.
To present a mathematical model explaining active control strategies in human motion.

Main Methods:

Developed a nonlinear dynamical system model with a stable attractor.
Incorporated embodiment-related task constraints as a force field.
Validated the model against kinematic data of human head-reaching movements.

Main Results:

The model accurately reproduces kinematic features of human curved reaching movements.
Demonstrated that body geometry actively influences movement curvature.
Showed a single neural controller can generate diverse movement trajectories.

Conclusions:

Curved reaching movements result from an active control strategy shaped by body geometry.
Embodiment plays a significant role in determining movement trajectory curvature.
The proposed model offers insights into the neural basis of motor control.