Degrees of freedom (mechanics)

In physics, the degrees of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration or state. It is important in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering, robotics, and other fields. The position of a single railcar (engine) moving along a track has one degree of freedom because the position of the car is defined by the distance along the track. A train of rigid cars connected by hinges to an engine still has only one degree of freedom because the positions of the cars behind the engine are constrained by the shape of the track. An automobile with highly stiff suspension can be considered to be a rigid body traveling on a plane (a flat, two-dimensional space). This body has three independent degrees of freedom consisting of two components of translation and one angle of rotation. Skidding or drifting is a good example of an automobile's three independent degrees of freedom. The position and orientation of a rigid body in space is defined by three components of translation and three components of rotation, which means that it has six degrees of freedom. The exact constraint mechanical design method manages the degrees of freedom to neither underconstrain nor overconstrain a device. The position of an n-dimensional rigid body is defined by the rigid transformation, [T] = [A, d], where d is an n-dimensional translation and A is an n × n rotation matrix, which has n translational degrees of freedom and n(n − 1)/2 rotational degrees of freedom. The number of rotational degrees of freedom comes from the dimension of the rotation group SO(n). A non-rigid or deformable body may be thought of as a collection of many minute particles (infinite number of DOFs), this is often approximated by a finite DOF system. When motion involving large displacements is the main objective of study (e.g. for analyzing the motion of satellites), a deformable body may be approximated as a rigid body (or even a particle) in order to simplify the analysis.

Design of a Flexure-Based Flywheel for the Storage of Angular Momentum and Kinetic Energy

Simon Nessim Henein, Florent Cosandier, Hubert Pierre-Marie Benoît Schneegans, Patrick Robert Flückiger

The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wea ...

2024

Online active and dynamic object shape exploration with a multi-fingered robotic hand

Aude Billard, Kunpeng Yao, Xiao Gao, Farshad Khadivar

The sense of touch can provide a robot with a wealth of information about the contact region when interacting with an unknown environment. Nevertheless, utilizing touch information to plan exploration paths and adjust robot posture to improve task efficien ...

ELSEVIER2023

A Stable Adaptive Extended Kalman Filter for Estimating Robot Manipulators Link Velocity and Acceleration

Aude Billard, Harshit Khurana

One can estimate the velocity and acceleration of robot manipulators by utilizing nonlinear observers. This involves combining inertial measurement units (IMUs) with the motor encoders of the robot through a model-based sensor fusion technique. This approa ...

New York2023