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' or `legs') 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. By contrast, [[Cartesian coordinate robot|Cartesian manipulators]] typically consist of a single [[Serial manipulator|serial]] connected kinematic linkage of mutually perpendicular linear actuators. 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.

== AttributesCharacteristics ==

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. Most commonly, [[Cartesian coordinate robot|Cartesian manipulators]] are [[Serial manipulator|serial]]-connected; i.e., they consist of a single kinematic linkage chain. On the other hand, Cartesian parallel manipulators are parallel-connected, providing inherent advantages 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 supporting heavy loads<ref> 

Cartesian parallel manipulators benefit from favorable attributes of both Cartesian and parallel manipulators. Cartesian manipulators have a simple intuitive layout that makes them easy to control. 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. Compared to serial manipulators, the synergy of the cooperating limbs of parallel manipulators, working together to support the moving-platform, give them inherent advantages in terms of stiffness, precision, dynamic performance and supporting heavy loads.

 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 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 journal|last=Gosselin|first=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=Parallel Mechanisms of the Multipteron Family: Kinematic Architectures and Benchmarking|url=http://dx.doi.org/10.1109/robot.2007.363045|journal=Proceedings 2007 IEEE International Conference on Robotics and Automation|publisher=IEEE|volume=|pages=|doi=10.1109/robot.2007.363045|isbn=1-4244-0602-1|via=}}</ref> family of manipulators have either 3, 4, 5 or 6 degrees of freedom (DoF). The Tripteron 3-DoF member has three translation ''3T'' degrees of freedom, with the subsequent members of the Multipteron family each adding a rotational ''R'' degree of freedom. Each members 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'' [[Kinematic pair|joints]].

==== Tripteron ''3T'' ====

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==== Qudrupteron ''3T1R'' ====

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

The 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|issn=0959-6518}}</ref> has ''3T1R'' DoF with (''3<u>P</u>RRU)(<u>P</u>RRR)'' joint topology.