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]].<ref>{{Citation|last=Perler|first=Dominik|title=Descartes, René: Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences|date=2020|url=http://dx.doi.org/10.1007/978-3-476-05728-0_9538-1|work=Kindlers Literatur Lexikon (KLL)|pages=1–3|place=Stuttgart|publisher=J.B. Metzler|isbn=978-3-476-05728-0|access-date=2020-12-14}}</ref> 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 [[Parallel (geometry)|geometric parallelism]]; i.e., equidistant lines. [[Manipulator (device)|Manipulators]] may also be called `[[Robot|robots]]' or `[[Mechanism (engineering)|mechanisms]]'.

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== Context ==

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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 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 coordinates 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 coordinates.  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''.

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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]].<ref>{{Citation|last=Perler|first=Dominik|title=Descartes, René: Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences|date=2020|url=http://dx.doi.org/10.1007/978-3-476-05728-0_9538-1|work=Kindlers Literatur Lexikon (KLL)|pages=1–3|place=Stuttgart|publisher=J.B. Metzler|isbn=978-3-476-05728-0|access-date=2020-12-14}}</ref> 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 [[Parallel (geometry)|geometric parallelism]]; i.e., equidistant lines. [[Manipulator (device)|Manipulators]] may also be called `[[Robot|robots]]' or `[[Mechanism (engineering)|mechanisms]]'.

== Description ==

Cartesian parallel manipulators are in the intersection of two broader categories of manipulators: [[Cartesian coordinate robot|Cartesian]] and [[Parallel manipulator|parallel]]. Cartesian manipulators are driven by mutually perpendicular linear actuators. They generally have a one-to-one correspondence between the linear positions of the actuators and the ''X, Y, Z'' position coordinates of the moving platform, making them easy to control. Furthermore, Cartesian manipulators do not change the orientation of the moving platform. Most commonly, [[Cartesian coordinate robot|Cartesian manipulators]] are [[Serial manipulator|serial]]-connected; i.e., they consist of a single [[Linkage (mechanical)|kinematic linkage]] chain. On the other hand, Cartesian parallel manipulators are parallel-connected, providing innate advantages<ref>Z. Pandilov, V. Dukovski, Comparison of the characteristics between serial and parallel robots, Acta Technica Corviniensis-Bulletin of Engineering, Volume 7, Issue 1, Pages 143-160</ref> in terms of stiffness,<ref>{{Cite journal|last=Geldart|first=M|last2=Webb|first2=P|last3=Larsson|first3=H|last4=Backstrom|first4=M|last5=Gindy|first5=N|last6=Rask|first6=K|date=2003|title=A direct comparison of the machining performance of a variax 5 axis parallel kinetic machining centre with conventional 3 and 5 axis machine tools|url=http://dx.doi.org/10.1016/s0890-6955(03)00119-6|journal=International Journal of Machine Tools and Manufacture|volume=43|issue=11|pages=1107–1116|doi=10.1016/s0890-6955(03)00119-6|issn=0890-6955|via=}}</ref> precision,<ref>{{Cite journal|last=|first=|date=1997|title=Vibration control for precision manufacturing using piezoelectric actuators|url=http://dx.doi.org/10.1016/s0141-6359(97)81235-4|journal=Precision Engineering|volume=20|issue=2|pages=151|doi=10.1016/s0141-6359(97)81235-4|issn=0141-6359|via=}}</ref> dynamic performance<ref>R. Clavel, inventor, S.A. SovevaSwitzerland, assignee. Device for the movement and positioning of an element in space, USA patent number, 4,976,582 (1990)</ref> <ref>{{Cite journal|last=Prempraneerach|first=Pradya|date=2014|title=Delta parallel robot workspace and dynamic trajectory tracking of delta parallel robot|url=http://dx.doi.org/10.1109/icsec.2014.6978242|journal=2014 International Computer Science and Engineering Conference (ICSEC)|publisher=IEEE|volume=|pages=|doi=10.1109/icsec.2014.6978242|isbn=978-1-4799-4963-2|via=}}</ref> and in supporting heavy loads.<ref> 

 Stewart D. A Platform with Six Degrees of Freedom. Proceedings of the Institution of Mechanical Engineers. 1965;180(1):371-386. doi:10.1243/PIME_PROC_1965_180_029_02

 </ref>.

== Configurations ==