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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]]<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 [[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 ==

Generally, manipulators (also called '[[Robot|robots]]' or '[[Mechanism (engineering)|mechanisms]]') are mechanical devices that position and orientate objects. The position of an object in three-dimensional (3D) space can be specified by three numbers ''X, Y, Z'' known as 'coordinates.' In a [[Cartesian coordinate system|Cartesian]] [[Coordinate system#:~:text%3DIn geometry%2C a coordinate system%2Cmanifold such as Euclidean space.|coordinate system]] (named after [[René Descartes]] who introduced [[analytic geometry]], the mathematical basis for controlling manipulators) the coordinates specify distances from three mutually perpendicular reference planes.  The orientation of an object in 3D can be specified by three additional numbers corresponding to the orientation [[Euler angles|angles]].  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 kinematic pair is a%2Celements consisting of simple machines.|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 1950s. Its control axes correspond to a [[spherical coordinate system]], with ''RRP'' joint topology composed of two [[Revolute joint#:~:text%3DA revolute joint (also called%2Crotation along a common axis.|revolute ''R'' joints]] in series with a prismatic ''P'' joint.  Most [[Industrial robot|industrial robots]] today are [[Articulated robot#:~:text%3DAn articulated robot is a%2Cof means%2C including electric motors.|articulated robots]] composed of a serial chain of revolute ''R'' joints ''RRRRRR''.

== 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, i.e. the first linear actuator moves the second one and so on. On the other hand, Cartesian parallel manipulators are parallel-connected, providingi.e. they consist of multiple kinematic linkages. Parallel-connected manipulators have 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|lastlast1=Geldart|firstfirst1=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|viaurl-access=subscription}}</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|viaurl-access=subscription}}</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 journalbook|last=Prempraneerach|first=Pradya|datetitle=2014 International Computer Science and Engineering Conference (ICSEC) |titlechapter=Delta parallel robot workspace and dynamic trajectory tracking of delta parallel robot |date=2014|chapter-url=http://dx.doi.org/10.1109/icsec.2014.6978242|journalpages=2014469–474 International Computer Science and Engineering Conference (ICSEC)|publisher=IEEE|volume=|pages=|doi=10.1109/icsec.2014.6978242|isbn=978-1-4799-4963-2|vias2cid=14227646 }}</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 ==

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 ===

Members of the Multipteron <ref>{{Cite journalbook|lastlast1=Gosselin|firstfirst1=Clement M.|last2=Masouleh|first2=Mehdi Tale|last3=Duchaine|first3=Vincent|last4=Richard|first4=Pierre-Luc|last5=Foucault|first5=Simon|last6=Kong|first6=Xianwen|title=Proceedings 2007 IEEE International Conference on Robotics and Automation |chapter=Parallel Mechanisms of the Multipteron Family: Kinematic Architectures and Benchmarking |chapter-url=http://dx.doi.org/10.1109/robot.2007.363045|journalyear=Proceedings 2007 IEEE|pages=555–560 International Conference on Robotics and Automation|publisher=IEEE|volume=|pages=|doi=10.1109/robot.2007.363045|isbn=978-1-4244-0602-19|vias2cid=5755981 }}</ref> family of manipulators have either 3, 4, 5 or 6 degrees of freedom (DoF). The Tripteron 3-DoF member has three translation degrees of freedom ''3T'' DoF, with the subsequent members of the Multipteron family each adding a rotational ''R'' degree of freedom. Each member of the family has mutually perpendicular linear actuators connected to a fixed base. The moving platform is typically attached to the linear actuators through three geometrically parallel revolute ''R'' joints. See [[Kinematic pair]] for a description of shorthand joint notation used to describe manipulator configurations, like revolute ''R'' joint for example.

==== 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|lastlast1=Kong|firstfirst1=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.|doi=10.1007/978-94-017-0657-5_48 |url-access=subscription}}</ref> <ref>{{Citation|lastlast1=Kim|firstfirst1=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|doi=10.1007/978-94-017-0657-5_3 |url-access=subscription}}</ref><ref>{{Citation|last1=Elkady|first1=Ayssam|title=Cartesian Parallel Manipulator Modeling, Control and Simulation|date=2008-04-01|work=Parallel Manipulators, towards New Applications|publisher=I-Tech Education and Publishing|isbn=978-3-902613-40-0|last2=Elkobrosy|first2=Galal|last3=Hanna|first3=Sarwat|last4=Sobh|first4=Tarek|doi=10.5772/5435 |doi-access=free}}</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|lastlast1=Wenger|firstfirst1=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.|doi=10.1007/978-94-011-4120-8_32 |s2cid=5485837 |arxiv=0707.3666}}</ref> <ref>{{Cite journal|lastlast1=Chablat|firstfirst1=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|viaarxiv=0708.3381|s2cid=3263909 }}</ref> and Parallel cube-manipulator.<ref>{{Cite journal|lastlast1=Liu|firstfirst1=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|s2cid=35529910 |issn=0263-5747|url-access=subscription}}</ref>. The Pantepteron<ref>{{Cite journal|lastlast1=Briot|firstfirst1=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 ====

[[File:Quadrupteron robot.jpg|link=link=Special:FilePath/Quadrupteron.png|thumb|Quadrupteron]]

The 4-DoF Qudrupteron<ref>{{Cite journal|last=Gosselin|first=C|date=2009-01-06|title=Compact dynamic models for the tripteron and quadrupteron parallel manipulators|url=http://dx.doi.org/10.1243/09596518jsce605|journal=Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering|volume=223|issue=1|pages=1–12|doi=10.1243/09596518jsce605|s2cid=61817314|issn=0959-6518|url-access=subscription}}</ref> has ''3T1R'' DoF with (''3<u>P</u>RRU)(<u>P</u>RRR)'' joint topology.

==== Pentapteron ====

The 5-DoF Pentateron<ref>{{Cite journalbook|lastlast1=Gosselin|firstfirst1=Clement M.|last2=Masouleh|first2=Mehdi Tale|last3=Duchaine|first3=Vincent|last4=Richard|first4=Pierre-Luc|last5=Foucault|first5=Simon|last6=Kong|first6=Xianwen|datetitle=Proceedings 2007 IEEE International Conference on Robotics and Automation |titlechapter=Parallel Mechanisms of the Multipteron Family: Kinematic Architectures and Benchmarking |date=2007|chapter-url=http://dx.doi.org/10.1109/robot.2007.363045|journalpages=Proceedings555–560 2007 IEEE International Conference on Robotics and Automation|publisher=IEEE|volume=|pages=|doi=10.1109/robot.2007.363045|isbn=978-1-4244-0602-19|vias2cid=5755981 }}</ref> has ''3T2R'' DoF with ''5(<u>P</u>RRRR)'' joint topology.

==== Hexapteron ====

The 6-DoF Hexapteron<ref>{{Cite journalbook|lastlast1=Seward|firstfirst1=Nicholas|last2=Bonev|first2=Ilian A.|datetitle=2014 IEEE International Conference on Robotics and Automation (ICRA) |titlechapter=A new 6-DOF parallel robot with simple kinematic model |date=2014|chapter-url=http://dx.doi.org/10.1109/icra.2014.6907449|journalpages=20144061–4066 IEEE International Conference on Robotics and Automation (ICRA)|publisher=IEEE|volume=|pages=|doi=10.1109/icra.2014.6907449|isbn=978-1-4799-3685-4|vias2cid=18895630 }}</ref> has ''3T3R'' DoF with ''6(<u>P</u>CRS)'' joint topology, with cylindrical ''C'' and spherical ''S'' joints.

=== Isoglide ===

The Isoglide family<ref>{{Cite journal|last=Gogu|first=Grigore|date=2004|title=Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations|url=http://dx.doi.org/10.1016/j.euromechsol.2004.08.006|journal=European Journal of Mechanics - A/Solids|volume=23|issue=6|pages=1021–1039|doi=10.1016/j.euromechsol.2004.08.006|bibcode=2004EJMS...23.1021G |issn=0997-7538|viaurl-access=subscription}}</ref> <ref>{{Cite journal|last=Gogu|first=Grigore|date=2007|title=Structural synthesis of fully-isotropic parallel robots with Schönflies motions via theory of linear transformations and evolutionary morphology|url=http://dx.doi.org/10.1016/j.euromechsol.2006.06.001|journal=European Journal of Mechanics - A/Solids|volume=26|issue=2|pages=242–269|doi=10.1016/j.euromechsol.2006.06.001|bibcode=2007EJMS...26..242G |issn=0997-7538|viaurl-access=subscription}}</ref><ref>{{Citation|titlechapter=Structural synthesis|date=2008|chapter-url=http://dx.doi.org/10.1007/978-1-4020-5710-6_5|workseries=Solid Mechanics and its Applications |volume=149 |pages=299–328|place=Dordrecht|publisher=Springer Netherlands|doi=10.1007/978-1-4020-5710-6_5 |isbn=978-1-4020-5102-9|access-date=2020-12-14|title=Structural Synthesis of Parallel Robots }}</ref><ref>{{Cite journal|last=Gogu|first=G.|date=2009|title=Structural synthesis of maximally regular T3R2-type parallel robots via theory of linear transformations and evolutionary morphology|url=http://dx.doi.org/10.1017/s0263574708004542|journal=Robotica|volume=27|issue=1|pages=79–101|doi=10.1017/s0263574708004542|s2cid=32809408 |issn=0263-5747|viaurl-access=subscription}}</ref> includes many different Cartesian parallel manipulators from 2-6 DoF.

=== 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|volume=161 |pages=103903|doi=10.1016/j.mechmachtheory.2020.103903|issn=0094-114X|viadoi-access=free}}</ref> are gantry type Cartesian parallel manipulators with ''3T1R2T2R'' DoF or ''3T2R'' DoF.

== References ==