Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Screw theory
Summary
Screw theory is the algebraic calculation of pairs of vectors, such as forces and moments or angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies. The mathematical framework was developed by Sir Robert Stawell Ball in 1876 for application in kinematics and statics of mechanisms (rigid body mechanics).
Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamics, where lines form the screw axes of spatial movement and the lines of action of forces. The pair of vectors that form the Plücker coordinates of a line define a unit screw, and general screws are obtained by multiplication by a pair of real numbers and addition of vectors.
An important result of screw theory is that geometric calculations for points using vectors have parallel geometric calculations for lines obtained by replacing vectors with screws. This is termed the transfer principle.
Screw theory has become an important tool in robot mechanics, mechanical design, computational geometry and multibody dynamics.
This is in part because of the relationship between screws and dual quaternions which have been used to interpolate rigid-body motions. Based on screw theory, an efficient approach has also been developed for the type synthesis of parallel mechanisms (parallel manipulators or parallel robots).
Fundamental theorems include Poinsot's theorem (Louis Poinsot, 1806) and Chasles' theorem (Michel Chasles, 1832). Felix Klein saw screw theory as an application of elliptic geometry and his Erlangen Program. He also worked out elliptic geometry, and a fresh view of Euclidean geometry, with the Cayley–Klein metric. The use of a symmetric matrix for a von Staudt conic and metric, applied to screws, has been described by Harvey Lipkin. Other prominent contributors include Julius Plücker, W. K. Clifford, F. M. Dimentberg, Kenneth H. Hunt, J. R. Phillips.
A spatial displacement of a rigid body can be defined by a rotation about a line and a translation along the same line, called a screw displacement.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (1)
ME-105: Introduction to mechanical design
Le cours de ME-105 vise à l'acquisition du langage normalisé de la communication technique en conception mécanique et d'une culture technique de base, via une revue des concepts, composants, et méthod