Cartesian parallel manipulators: Difference between revisions

Revision as of 16:56, 28 December 2020

Revision as of 08:48, 31 December 2020

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== 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|hdl=2027/loc.ark:/13960/t20c64v5p|hdl-access=free}}</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 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''.

== Description ==

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==== Tripteron ====

[[File:Tripteron robot.jpg|thumb|Tripteron]]

The 3-DoF Tripteron<ref>Gosselin, C. M., and Kong, X., 2004, “Cartesian Parallel Manipulators,” U.S. Patent No. 6,729,202</ref> <ref>Xianwen Kong, Clément M. Gosselin, Kinematics and Singularity Analysis of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator, The International Journal of Robotics Research Vol. 21, No. 9, September 2002, pp. 791-7</ref> <ref>{{Citation|last=Kong|first=Xianwen|title=Type Synthesis of Linear Translational Parallel Manipulators|date=2002|url=http://dx.doi.org/10.1007/978-94-017-0657-5_48|work=Advances in Robot Kinematics|pages=453–462|place=Dordrecht|publisher=Springer Netherlands|isbn=978-90-481-6054-9|access-date=2020-12-14|last2=Gosselin|first2=Clément M.}}</ref> <ref>{{Citation|last=Kim|first=Han Sung|title=Evaluation of a Cartesian Parallel Manipulator|date=2002|url=http://dx.doi.org/10.1007/978-94-017-0657-5_3|work=Advances in Robot Kinematics|pages=21–28|place=Dordrecht|publisher=Springer Netherlands|isbn=978-90-481-6054-9|access-date=2020-12-14|last2=Tsai|first2=Lung-Wen}}</ref><ref>{{Citation|last=Elkady|first=Ayssam|title=Cartesian Parallel Manipulator Modeling, Control and Simulation|date=2008-04-01|url=http://dx.doi.org/10.5772/5435|work=Parallel Manipulators, towards New Applications|publisher=I-Tech Education and Publishing|isbn=978-3-902613-40-0|access-date=2020-12-22|last2=Elkobrosy|first2=Galal|last3=Hanna|first3=Sarwat|last4=Sobh|first4=Tarek}}</ref> member of the Multipteron family has three parallel-connected kinematic chains consisting of a linear actuator (active prismatic ''<u>P</u>'' joint) in series with three revolute ''R'' joints ''3(<u>P</u>RRR).'' Similar manipulators, with three parallelogram ''Pa'' limbs ''3(<u>PR</u>PaR)'' are the Orthoglide<ref>{{Citation|last=Wenger|first=P.|title=Kinematic Analysis of a New Parallel Machine Tool: The Orthoglide|date=2000|url=http://dx.doi.org/10.1007/978-94-011-4120-8_32|work=Advances in Robot Kinematics|pages=305–314|place=Dordrecht|publisher=Springer Netherlands|isbn=978-94-010-5803-2|access-date=2020-12-14|last2=Chablat|first2=D.}}</ref> <ref>{{Cite journal|last=Chablat|first=D.|last2=Wenger|first2=P.|date=2003|title=Architecture optimization of a 3-DOF translational parallel mechanism for machining applications, the orthoglide|url=http://dx.doi.org/10.1109/tra.2003.810242|journal=IEEE Transactions on Robotics and Automation|volume=19|issue=3|pages=403–410|doi=10.1109/tra.2003.810242|issn=1042-296X|arxiv=0708.3381}}</ref> and Parallel cube-manipulator.<ref>{{Cite journal|last=Liu|first=Xin-Jun|last2=Jeong|first2=Jay il|last3=Kim|first3=Jongwon|date=2003-10-24|title=A three translational DoFs parallel cube-manipulator|url=http://dx.doi.org/10.1017/s0263574703005198|journal=Robotica|volume=21|issue=6|pages=645–653|doi=10.1017/s0263574703005198|issn=0263-5747}}</ref> The Pantepteron<ref>{{Cite journal|last=Briot|first=S.|last2=Bonev|first2=I. A.|date=2009-01-06|title=Pantopteron: A New Fully Decoupled 3DOF Translational Parallel Robot for Pick-and-Place Applications|url=http://dx.doi.org/10.1115/1.3046125|journal=Journal of Mechanisms and Robotics|volume=1|issue=2|doi=10.1115/1.3046125|issn=1942-4302}}</ref> is also similar to the Tripteron, with pantograph linkages to speed up the motion of the platform.

==== Qudrupteron ====

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=== Xactuator ===

[[File:Xactuator real hardware.jpg|thumb|Xactuator]]

The 4-DoF or 5-DoF Coupled Cartesian manipulators family<ref>{{Cite journal|last=Wiktor|first=Peter|date=2020|title=Coupled Cartesian Manipulators|url=http://dx.doi.org/10.1016/j.mechmachtheory.2020.103903|journal=Mechanism and Machine Theory|pages=103903|doi=10.1016/j.mechmachtheory.2020.103903|issn=0094-114X|doi-access=free}}</ref> are gantry type Cartesian parallel manipulators with ''2T2R'' DoF or ''3T2R'' DoF.

== References ==