tightened up context section: the digression on Descartes was mostly irrelevant and the citations were to philosophical works not mathematical contributions
In robotics, '''Cartesian parallel manipulators''' are [[Manipulator (device)|manipulators]] that 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)|parallel]]; i.e., equidistant lines. [[Manipulator (device)|Manipulators]] may also be called `[[Robot|robots]]' or `[[Mechanism (engineering)|mechanisms]]'.
== Context ==
InGenerally, 1637manipulators (also called `[[René DescartesRobot|robots]]<ref>{{Cite' journal|last=Descartes|first=Rene|date=2009-01-01|title=Discourseor on`[[Mechanism the method of rightly conducting the reason, and seeking truth in the sciences(engineering)|url=http://dx.doi.org/10.5214/ans.0972.7531.2009.160108|journal=Annalsmechanisms]]') ofare Neurosciences|volume=16|issue=01|pages=17–21|doi=10.5214/ans.0972.7531.2009.160108|issn=0972-7531|hdl=2027/loc.ark:/13960/t20c64v5p|hdl-access=free}}</ref><ref>{{Citemechanical journal|last=Klubertanz|first=Georgedevices P.|date=1969|title=Discoursethat on Method, Optics, Geometry,position and Meteorology.orientate By Rene Descartesobjects. 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 fieldposition of [[mathematics]]an that studies [[geometry]]object in termsthree-dimensional of(3D) numbersspace andcan equations. Specifically, Descartesbe specified theby position of a point using twothree numbers ''X, Y, Z'' correspondingknown as to'coordinates.' the horizontal and vertical distance fromIn 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(named beafter extended[[René withDescartes]] awho thirdintroduced number[[Analytic ''Z''geometry|analytic corresponding togeometry]], the heightmathematical ofbasis thefor pointcontrolling abovemanipulators) the ''X,coordinates Y''specify plane. distances Consequently the position of a point infrom three dimensionalmutually spaceperpendicular (3D)reference can be specified by three numbers ''X, Y, Z'' known as `coordinates’planes. The orientation of an object in 3D can be specified by three additional numbers 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 coordinate 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''.
