Cartesian parallel manipulators: Difference between revisions

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'''Cartesian parallel manipulators''' move a platform using [[Parallel manipulator|parallel]] -connected kinematic [[Linkage (mechanical)|linkages]] (`limbs') lined up with a [[Cartesian coordinate system]]. Multiple limbs connect the moving platform to a base. Each limb is driven by a [[linear actuator]] and the linear actuators are mutually perpendicular. The term `parallel' here refers to the way that the kinematic linkages are put together, it does not connote geometrically [[Parallel (geometry)|geometric parallelismparallel]]; i.e., equidistant lines. [[Manipulator (device)|Manipulators]] may also be called `[[Robot|robots]]' or `[[Mechanism (engineering)|mechanisms]]'.

== Context ==

In 1637 [[René Descartes]]<ref>{{Cite journal|last=Descartes|first=Rene|date=2009-01-01|title=Discourse on the method of rightly conducting the reason, and seeking truth in the sciences|url=http://dx.doi.org/10.5214/ans.0972.7531.2009.160108|journal=Annals of Neurosciences|volume=16|issue=01|pages=17–21|doi=10.5214/ans.0972.7531.2009.160108|issn=0972-7531}}</ref><ref>{{Cite journal|last=Klubertanz|first=George P.|date=1969|title=Discourse on Method, Optics, Geometry, and Meteorology. By Rene Descartes. Trans, with Introd. Paul J. Olscamp|url=http://dx.doi.org/10.5840/schoolman196946493|journal=The Modern Schoolman|volume=46|issue=4|pages=370–371|doi=10.5840/schoolman196946493|issn=0026-8402}}</ref> introduced [[Analytic geometry|analytical geometry]], a field of [[mathematics]] that studies [[geometry]] in terms of numbers and equations. Specifically, Descartes specified the position of a point using two numbers ''X, Y'' corresponding to the horizontal and vertical distance from a reference point in a plane.  Positive or negative numbers indicate the direction of the position relative to the reference point. This `[[Cartesian coordinate system|Cartesian]] [[Coordinate system#:~:text%3DIn%20geometry%2C%20a%20coordinate%20system%2Cmanifold%20such%20as%20Euclidean%20space.|coordinate system]]’ may be extended with a third number ''Z'' corresponding to the height of the point above the ''X, Y'' plane.  Consequently the position of a point in three dimensional space (3D) can be specified by three numbers ''X, Y, Z'' known as `coordinates’.  The orientation of an object in 3D can be specified by three additional coordinatesnumbers corresponding to the orientation [[Euler angles|angles]].  Generally [[Manipulator (device)|manipulators]] or [[Robot|robots]] are mechanical devices that position and orientate objects specified by their 3D coordinatescoordinate numbers.  Analytical geometry is the mathematical basis for controlling manipulators. The first [[Remote manipulator| manipulators]] were developed after World War II for the [[Argonne National Laboratory]] to safely handle highly radioactive material [[Teleoperation|remotely]].  The first [[Numerical control|numerically controlled]] manipulators (NC machines) were developed by [[John T. Parsons|Parsons Corp]]. and the [[MIT Servomechanisms Laboratory]], for [[Milling (machining)|milling applications]].  These machines position a cutting tool relative to a Cartesian coordinate system using three mutually perpendicular linear actuators ([[Prismatic joint|prismatic ''P'' joints]]), with ''(PP)P'' [[Kinematic pair#:~:text%3DA%20kinematic%20pair%20is%20a%2Celements%20consisting%20of%20simple%20machines.|joint topology]].  The first [[industrial robot]]<ref>George C Devol, Programmed article transfer, US patent 2988237, June 13, 1961. </ref> , [[Unimation|Unimate]], was invented in the 1950’s. Its control axes correspond to a [[spherical coordinate system]], with ''RRP'' joint topology composed of two [[Revolute joint#:~:text%3DA%20revolute%20joint%20(also%20called%2Crotation%20along%20a%20common%20axis.|revolute ''R'' joints]] in series with a prismatic ''P'' joint.  Most [[Industrial robot|industrial robots]] today are [[Articulated robot#:~:text%3DAn%20articulated%20robot%20is%20a%2Cof%20means%2C%20including%20electric%20motors.|articulated robots]] composed of a serial chain of revolute ''R'' joints ''RRRRRR''.

== Description ==

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== Configurations ==

Various types of Cartesian parallel manipulators are summarized here. Only fully parallel-connected mechanisms are included; i.e., those having the same number of limbs as [[Degrees of freedom (mechanics)|degrees of freedom]] of the moving-platform, with a single actuator per limb.

=== Multipteron family ===