Editing Machine (section)

== Mechanics ==
Usher<ref>A. P. Usher, 1929, [https://books.google.com/books?id=xuDDqqa8FlwC&q=history+of+mechanical+inventions ''A History of Mechanical Inventions''] {{webarchive|url=https://web.archive.org/web/20130602124007/http://books.google.com/books?id=xuDDqqa8FlwC&printsec=frontcover&dq=history+of+mechanical+inventions&hl=en&sa=X&ei=n5r4Tov7HaqPsQLugvWuAQ&ved=0CD8Q6AEwAA |date=2013-06-02 }}, Harvard University Press (reprinted by Dover Publications 1968).</ref> reports that [[Hero of Alexandria|Hero of Alexandria's]] treatise on ''Mechanics'' focussed on the study of lifting heavy weights. Today [[mechanics]] refers to the mathematical analysis of the forces and movement of a mechanical system, and consists of the study of the [[kinematics]] and [[analytical dynamics|dynamics]] of these systems.

===Dynamics of machines===
The [[rigid-body dynamics|dynamic analysis]] of machines begins with a rigid-body model to determine reactions at the bearings, at which point the elasticity effects are included. The [[rigid-body dynamics]] studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid, which means that they do not deform under the action of applied forces, simplifies the analysis by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body.<ref>B. Paul, Kinematics and Dynamics of Planar Machinery, Prentice-Hall, NJ, 1979</ref><ref>L. W. Tsai, Robot Analysis: The mechanics of serial and parallel manipulators, John-Wiley, NY, 1999.</ref>

The dynamics of a rigid body system is defined by its [[equations of motion]], which are derived using either [[Newtons laws of motion]] or [[Lagrangian mechanics]]. The solution of these equations of motion defines how the configuration of the system of rigid bodies changes as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of [[mechanical systems]].

=== Kinematics of machines ===
The dynamic analysis of a machine requires the determination of the movement, or [[kinematics]], of its component parts, known as kinematic analysis. The assumption that the system is an assembly of rigid components allows rotational and translational movement to be modeled mathematically as [[rigid transformation|Euclidean, or rigid, transformations]]. This allows the position, velocity and acceleration of all points in a component to be determined from these properties for a reference point, and the angular position, [[angular velocity]] and [[angular acceleration]] of the component.