Cartesian parallel manipulators

Generally, manipulators (also called 'robots' or '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 (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 angles.  The first  manipulators were developed after World War II for the Argonne National Laboratory to safely handle highly radioactive material remotely.  The first numerically controlled manipulators (NC machines) were developed by Parsons Corp. and the MIT Servomechanisms Laboratory, for milling applications.  These machines position a cutting tool relative to a Cartesian coordinate system using three mutually perpendicular linear actuators (prismatic P joints), with (PP)P joint topology.  The first industrial robot,George C Devol, Programmed article transfer, US patent 2988237, June 13, 1961.  Unimate, was invented in the 1950s. Its control axes correspond to a spherical coordinate system, with RRP joint topology composed of two revolute R joints in series with a prismatic P joint.  Most industrial robots today are articulated robots composed of a serial chain of revolute R joints RRRRRR.

Cartesian parallel manipulators are in the intersection of two broader categories of manipulators: Cartesian and 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 manipulators are serial-connected; i.e., they consist of a single 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, i.e. they consist of multiple kinematic linkages. Parallel-connected manipulators have innate advantagesZ. 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 in terms of stiffness,{{Cite journal|last1=Geldart|first1=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|url-access=subscription}} precision,{{Cite journal|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}} dynamic performanceR. Clavel, inventor, S.A. SovevaSwitzerland, assignee. Device for the movement and positioning of an element in space, USA patent number, 4,976,582 (1990) {{Cite book|last=Prempraneerach|first=Pradya|title=2014 International Computer Science and Engineering Conference (ICSEC) |chapter=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|pages=469–474 |publisher=IEEE|doi=10.1109/icsec.2014.6978242|isbn=978-1-4799-4963-2|s2cid=14227646 }} and in 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

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 of the moving-platform, with a single actuator per limb.

Members of the Multipteron {{Cite book|last1=Gosselin|first1=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|year=2007 |pages=555–560 |publisher=IEEE|doi=10.1109/robot.2007.363045|isbn=978-1-4244-0602-9|s2cid=5755981 }} 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.

File:Tripteron robot.jpg

The 3-DoF TripteronGosselin, C. M., and Kong, X., 2004, “Cartesian Parallel Manipulators,” U.S. Patent No. 6,729,202 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 {{Citation|last1=Kong|first1=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}} {{Citation|last1=Kim|first1=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}}{{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}} member of the Multipteron family has three parallel-connected kinematic chains consisting of a linear actuator (active prismatic P joint) in series with three revolute R joints 3(PRRR). Similar manipulators, with three parallelogram Pa limbs 3(PRPaR) are the Orthoglide{{Citation|last1=Wenger|first1=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}} {{Cite journal|last1=Chablat|first1=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|s2cid=3263909 }} and Parallel cube-manipulator.{{Cite journal|last1=Liu|first1=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}} The Pantepteron{{Cite journal|last1=Briot|first1=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}} is also similar to the Tripteron, with pantograph linkages to speed up the motion of the platform.

File:Quadrupteron robot.jpg

The 4-DoF Qudrupteron{{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}} has 3T1R DoF with (3PRRU)(PRRR) joint topology.

The 5-DoF Pentateron{{Cite book|last1=Gosselin|first1=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 |date=2007|chapter-url=http://dx.doi.org/10.1109/robot.2007.363045|pages=555–560 |publisher=IEEE|doi=10.1109/robot.2007.363045|isbn=978-1-4244-0602-9|s2cid=5755981 }} has 3T2R DoF with 5(PRRRR) joint topology.

The 6-DoF Hexapteron{{Cite book|last1=Seward|first1=Nicholas|last2=Bonev|first2=Ilian A.|title=2014 IEEE International Conference on Robotics and Automation (ICRA) |chapter=A new 6-DOF parallel robot with simple kinematic model |date=2014|chapter-url=http://dx.doi.org/10.1109/icra.2014.6907449|pages=4061–4066 |publisher=IEEE|doi=10.1109/icra.2014.6907449|isbn=978-1-4799-3685-4|s2cid=18895630 }} has 3T3R DoF with 6(PCRS) joint topology, with cylindrical C and spherical S joints.

The Isoglide family{{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|url-access=subscription}} {{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|url-access=subscription}}{{Citation|chapter=Structural synthesis|date=2008|chapter-url=http://dx.doi.org/10.1007/978-1-4020-5710-6_5|series=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 }}{{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|url-access=subscription}} includes many different Cartesian parallel manipulators from 2-6 DoF.

File:Xactuator real hardware.jpg

The 4-DoF or 5-DoF Coupled Cartesian manipulators family{{Cite journal|last=Wiktor|first=Peter|date=2020|title=Coupled Cartesian Manipulators|journal=Mechanism and Machine Theory|volume=161 |pages=103903|doi=10.1016/j.mechmachtheory.2020.103903|issn=0094-114X|doi-access=free}} are gantry type Cartesian parallel manipulators with 2T2R DoF or 3T2R DoF.

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Category:Machinery