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<title>Parallel manipulator</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Parallel manipulator</span></span>

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<p>A <b>parallel manipulator</b> is a <a href="Mechanical_system" class="mw-redirect" title="Mechanical system">mechanical system</a> that uses several <a href="Serial_manipulator" title="Serial manipulator">computer-controlled serial chains</a> to support a single platform, or <a href="End-effector" class="mw-redirect" title="End-effector">end-effector</a>. Perhaps, the best known parallel manipulator is formed from six linear actuators that support a movable base for devices such as flight simulators. This device is called a <a href="Stewart_platform" title="Stewart platform">Stewart platform</a> or the Gough-Stewart platform in recognition of the engineers who first designed and used them.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>Also known as <b>parallel robots</b>, or <b>generalized Stewart platforms</b> (in the <a href="Stewart_platform" title="Stewart platform">Stewart platform</a>, the actuators are paired together on both the basis and the platform), these systems are <a href="Articulated_robot" title="Articulated robot">articulated robots</a> that use similar mechanisms for the movement of either the robot on its base, or one or more <a href="Manipulator_(device)" title="Manipulator (device)">manipulator</a> arms. Their 'parallel' distinction, as opposed to a <a href="Serial_manipulator" title="Serial manipulator">serial manipulator</a>, is that the <a href="End_effector" class="mw-redirect" title="End effector">end effector</a> (or 'hand') of this linkage (or 'arm') is directly connected to its base by a number of (usually three or six) separate and independent linkages working simultaneously. No <a href="Parallel_(geometry)" title="Parallel (geometry)">geometrical parallelism</a> is implied.

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<div class="mw-heading mw-heading2"><h2 id="Design_features">Design features</h2></div>

<p>A parallel manipulator is designed so that each chain is usually short, simple and can thus be rigid against unwanted movement, compared to a <a href="Serial_manipulator" title="Serial manipulator">serial manipulator</a>. Errors in one chain's positioning are averaged in conjunction with the others, rather than being cumulative. Each actuator must still move within its own <a href="Degrees_of_freedom_(mechanics)" title="Degrees of freedom (mechanics)">degree of freedom</a>, as for a serial robot; however in the parallel robot the off-axis flexibility of a joint is also constrained by the effect of the other chains. It is this <a href="Control_theory#Closed-loop_transfer_function" title="Control theory">closed-loop</a> stiffness that makes the overall parallel manipulator stiff relative to its components, unlike the serial chain that becomes progressively less rigid with more components.

</p><p>This mutual stiffening also permits simple construction: <a href="Stewart_platform" title="Stewart platform">Stewart platform</a> hexapods chains use <a href="Prismatic_joint" title="Prismatic joint">prismatic joint</a> <a href="Linear_actuator" title="Linear actuator">linear actuators</a> between any-axis universal <a href="Ball_joint" title="Ball joint">ball joints</a>. The ball joints are passive: simply free to move, without actuators or brakes; their position is constrained solely by the other chains. <a href="Delta_robot" title="Delta robot">Delta robots</a> have base-mounted <a href="Rotary_actuator" title="Rotary actuator">rotary actuators</a> that move a light, stiff, parallelogram arm. The effector is mounted between the tips of three of these arms and again, it may be mounted with simple ball-joints. <a href="Statics" title="Statics">Static</a> representation of a parallel robot is often akin to that of a <a href="Pin-jointed_truss" class="mw-redirect" title="Pin-jointed truss">pin-jointed truss</a>: the links and their actuators feel only tension or compression, without any bending or torque, which again reduces the effects of any flexibility to off-axis forces.

</p><p>A further advantage of the parallel manipulator is that the heavy actuators may often be centrally mounted on a single base platform, the movement of the arm taking place through struts and joints alone. This reduction in mass along the arm permits a lighter arm construction, thus lighter actuators and faster movements. This centralisation of mass also reduces the robot's overall <a href="Moment_of_inertia" title="Moment of inertia">moment of inertia</a>, which may be an advantage for a mobile or <a href="Walking_robot" class="mw-redirect" title="Walking robot">walking robot</a>.

</p><p>All these features result in manipulators with a wide range of motion capability. As their speed of action is often constrained by their rigidity rather than sheer power, they can be fast-acting, in comparison to serial manipulators.

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<div class="mw-heading mw-heading2"><h2 id="Lower_mobility">Lower mobility</h2></div>

<p>A manipulator can move an object with up to 6 <a href="Degrees_of_freedom_(mechanics)" title="Degrees of freedom (mechanics)">degrees of freedom</a> (DoF), determined by 3 translation <i>3T</i> and 3 rotation <i>3R</i> coordinates for full <i>3T3R m</i>obility. However, when a manipulation task requires less than 6 DoF, the use of lower mobility manipulators, with fewer than 6 DoF, may bring advantages in terms of simpler architecture, easier control, faster motion and lower cost.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>  For example, the 3 DoF Delta <sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> robot has lower <i>3T</i> mobility and has proven to be very successful for rapid pick-and-place translational positioning applications. The workspace of lower mobility manipulators may be decomposed into `motion’ and `constraint’ subspaces. For example, 3 position coordinates constitute the motion subspace of the 3 DoF Delta robot and the 3 orientation coordinates are in the constraint subspace.  The motion subspace of lower mobility manipulators may be further decomposed into independent (desired) and dependent subspaces: consisting of `concomitant’ or `parasitic’ motion which is undesired motion of the manipulator.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>  The debilitating effects of parasitic motion should be mitigated or eliminated in the successful design of lower mobility manipulators.  For example, the Delta robot does not have parasitic motion since its end effector does not rotate.

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<div class="mw-heading mw-heading2"><h2 id="Comparison_to_serial_manipulators">Comparison to serial manipulators</h2></div>

<p>Most robot applications require rigidity. Serial robots may achieve this by using high-quality rotary joints that permit movement in one axis but are rigid against movement outside this. Any joint permitting movement <i>must</i> also have this movement under deliberate control by an actuator. A movement requiring several axes thus requires a number of such joints. Unwanted flexibility or sloppiness in one joint causes a similar sloppiness in the arm, which may be amplified by the distance between the joint and the end-effectuor: there is no opportunity to brace one joint's movement against another. Their inevitable <a href="Hysteresis" title="Hysteresis">hysteresis</a> and off-axis flexibility accumulates along the arm's <a href="Kinematic_chain" title="Kinematic chain">kinematic chain</a>; a precision serial manipulator is a compromise between precision, complexity, mass (of the manipulator and of the manipulated objects) and cost. On the other hand, with parallel manipulators, a high rigidity may be obtained with a small mass of the manipulator (relatively to the charge being manipulated). This allows high precision and high speed of movements, and motivates the use of parallel manipulators in <a href="Flight_simulator" title="Flight simulator">flight simulators</a> (high speed with rather large masses) and <a href="Electrostatic_lens" title="Electrostatic lens">electrostatic</a> or <a href="Magnetic_lens" title="Magnetic lens">magnetic lenses</a> in <a href="Particle_accelerator" title="Particle accelerator">particle accelerators</a> (very high precision in positioning large masses).

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<p>A drawback of parallel manipulators, in comparison to serial manipulators, is their limited workspace. As for serial manipulators, the workspace is limited by the geometrical and mechanical limits of the design (collisions between legs maximal and minimal lengths of the legs). The workspace is also limited by the existence of <i>singularities</i>, which are positions where, for some trajectories of the movement, the variation of the lengths of the legs is infinitely smaller than the variation of the position. Conversely, at a singular position, a force (like gravity) applied on the end-effector induce infinitely large constraints on the legs, which may result in a kind of "explosion" of the manipulator. The determination of the singular positions is difficult (for a general parallel manipulator, this is an open problem). This implies that the workspaces of the parallel manipulators are, usually, artificially limited to a small region where one knows that there is no singularity.

</p><p>Another drawback of parallel manipulators is their <a href="Nonlinear" class="mw-redirect" title="Nonlinear">nonlinear</a> behavior: the command which is needed for getting a linear or a circular movement of the end-effector depends dramatically on the location in the workspace and does not vary linearly during the movement.

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<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

<p>Major industrial applications of these devices are:

</p>

<ul><li><a href="Flight_simulator" title="Flight simulator">flight simulators</a></li>

<li>automobile simulators</li>

<li>in work processes</li>

<li><a href="Photonics" title="Photonics">photonics</a> / <a href="Optical_fiber" title="Optical fiber">optical fiber</a> alignment<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li></ul>

<p>They have also become more popular:

</p>

<ul><li>in high speed, high-accuracy positioning with limited workspace, such as in assembly of <a href="Printed_circuit_board" title="Printed circuit board">PCBs</a></li>

<li>as micro manipulators mounted on the end effector of larger but slower <a href="Serial_manipulator" title="Serial manipulator">serial manipulators</a></li>

<li>as high speed/high-precision <a href="Milling_machine" class="mw-redirect" title="Milling machine">milling machines</a></li></ul>

<p>Parallel robots are usually more limited in the workspace; for instance, they generally cannot reach around obstacles. The calculations involved in performing a desired manipulation (forward kinematics) are also usually more difficult and can lead to multiple solutions.

</p>

<p>Two examples of popular parallel robots are the <a href="Stewart_platform" title="Stewart platform">Stewart platform</a> and the <a href="Delta_robot" title="Delta robot">Delta robot</a>.

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<ul><li><a href="Robot_kinematics" title="Robot kinematics">Robot kinematics</a></li>

<li><a href="Cartesian_parallel_manipulators" title="Cartesian parallel manipulators">Cartesian parallel manipulators</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFMerlet2008" class="citation book cs1">Merlet, J.P. (2008). <i>Parallel Robots, 2nd Edition</i>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4020-4132-7</bdi>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFDi2006" class="citation cs2">Di, Raffaele (2006-12-01), Cubero, Sam (ed.), <a rel="nofollow" class="external text" href="http://www.intechopen.com/books/industrial_robotics_theory_modelling_and_control/parallel_manipulators_with_lower_mobility">"Parallel Manipulators with Lower Mobility"</a>, <i>Industrial Robotics: Theory, Modelling and Control</i>, Pro Literatur Verlag, Germany / ARS, Austria, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.5772%2F5030">10.5772/5030</a></span>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-86611-285-8</bdi><span class="reference-accessdate">, retrieved <span class="nowrap">2020-12-03</span></span></cite></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Device for the movement and positioning of an element in space, R. Clavel - US Patent 4,976,582, 1990</span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">R. Clavel, <b>Delta: a fast robot with parallel geometry,</b> Proc 18th Int Symp Ind Robots; Sydney, Australia (1988), pp. 91-100</span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFNigatuYihun2020" class="citation cs2">Nigatu, Hassen; Yihun, Yimesker (2020), Larochelle, Pierre; McCarthy, J. Michael (eds.), <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="http://link.springer.com/10.1007/978-3-030-43929-3_22">"Algebraic Insight on the Concomitant Motion of 3RPS and 3PRS PKMS"</a></span>, <i>Proceedings of the 2020 USCToMM Symposium on Mechanical Systems and Robotics</i>, Mechanisms and Machine Science, vol. 83, Cham: Springer International Publishing, pp. <span class="nowrap">242–</span>252, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-030-43929-3_22">10.1007/978-3-030-43929-3_22</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-030-43928-6</bdi>, <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:218789290">218789290</a><span class="reference-accessdate">, retrieved <span class="nowrap">2020-12-13</span></span></cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFNigatuChoiKim2021" class="citation journal cs1">Nigatu, Hassen; Choi, Yun Ho; Kim, Doik (2021-10-01). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.mechmachtheory.2021.104409">"Analysis of parasitic motion with the constraint embedded Jacobian for a 3-PRS parallel manipulator"</a>. <i>Mechanism and Machine Theory</i>. <b>164</b>: 104409. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.mechmachtheory.2021.104409">10.1016/j.mechmachtheory.2021.104409</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0094-114X">0094-114X</a>.</cite></span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFNigatuKim2021" class="citation journal cs1">Nigatu, Hassen; Kim, Doik (2021-01-01). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fapp11104690">"Optimization of 3-DoF Manipulators' Parasitic Motion with the Instantaneous Restriction Space-Based Analytic Coupling Relation"</a>. <i>Applied Sciences</i>. <b>11</b> (10): 4690. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fapp11104690">10.3390/app11104690</a></span>.</cite></span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140529143050/http://www.mecademic.com/DexTAR.html">"DexTAR - an educational parallel robot"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.mecademic.com/DexTAR.html">the original</a> on 2014-05-29.</cite></span>

</li>

<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.jarkman.co.uk/catalog/robots/sketchy.htm">"Sketchy, a home-constructed drawing robot"</a>. Jarkman.</cite></span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20061211040917/http://www.pb.izm.fhg.de/p2sa/020_Technologies/Optik/FundE_Faserjustage.html">"Active and Passive Fiber Alignment"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.pb.izm.fhg.de/p2sa/020_Technologies/Optik/FundE_Faserjustage.html">the original</a> on 2006-12-11<span class="reference-accessdate">. Retrieved <span class="nowrap">2007-03-29</span></span>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFGogu2008" class="citation book cs1">Gogu, Grigore (2008). <i>Structural Synthesis of Parallel Robots, Part 1: Methodology</i>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4020-5102-9</bdi>.</cite></li>

<li><cite id="CITEREFGogu2009" class="citation book cs1">Gogu, Grigore (2009). <i>Structural Synthesis of Parallel Robots, Part 2: Translational topologies with Two and Three Degrees of Freedom</i>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4020-9793-5</bdi>.</cite></li>

<li><cite id="CITEREFMerlet2008" class="citation book cs1">Merlet, J.P. (2008). <i>Parallel Robots, 2nd Edition</i>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4020-4132-7</bdi>.</cite></li>

<li><cite id="CITEREFKongGosselin2007" class="citation book cs1">Kong, X.; Gosselin, C. (2007). <i>Type Synthesis of Parallel Mechanisms</i>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-71989-2</bdi>.</cite></li></ul>

<ul><li><cite id="CITEREFGallardo-Alvarado2016" class="citation book cs1">Gallardo-Alvarado, J. (2016). <i>Kinematic Analysis of Parallel Manipulators by Algebraic Screw Theory</i>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-319-31124-1</bdi>.</cite></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

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<div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Parallel_robots" class="extiw external" title="commons:Category:Parallel robots">Parallel robots</a></span>.</div></div>

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<ul><li><a rel="nofollow" class="external text" href="http://www.parallemic.org">Parallel Mechanisms Information Center</a></li>

<li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140629140810/http://www.mecademic.com/What-is-a-parallel-robot.html">What is a parallel robot?</a></li>

<li><a rel="nofollow" class="external text" href="http://www-sop.inria.fr/members/Jean-Pierre.Merlet//merlet_eng.html">References on parallel robot</a></li></ul>

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</style><div id="Robotics434" style="font-size:114%;margin:0 4em"><a href="Robotics" title="Robotics">Robotics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Main articles</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Outline_of_robotics" title="Outline of robotics">Outline</a></li>

<li><a href="Glossary_of_robotics" title="Glossary of robotics">Glossary</a></li>

<li><a href="Index_of_robotics_articles" title="Index of robotics articles">Index</a></li>

<li><a href="History_of_robots" title="History of robots">History</a></li>

<li><a href="Geography_of_robotics" title="Geography of robotics">Geography</a></li>

<li><a href="Robot_ethics" title="Robot ethics">Ethics</a></li>

<li><a href="Robot_competition" title="Robot competition">Competitions</a></li>

<li><a href="Competitions_and_prizes_in_artificial_intelligence" title="Competitions and prizes in artificial intelligence">AI competitions</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="8" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Robot" title="Robot">Types</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Aerobot" title="Aerobot">Aerobot</a></li>

<li><a href="Anthropomorphic" class="mw-redirect" title="Anthropomorphic">Anthropomorphic</a>

<ul><li><a href="Humanoid_robot" title="Humanoid robot">Humanoid</a></li>

<li><a href="Android_(robot)" title="Android (robot)">Android</a></li>

<li><a href="Cyborg" title="Cyborg">Cyborg</a></li>

<li><a href="Gynoid" title="Gynoid">Gynoid</a></li></ul></li>

<li><a href="Claytronics" class="mw-redirect" title="Claytronics">Claytronics</a></li>

<li><a href="Companion_robot" title="Companion robot">Companion</a></li>

<li><a href="Automaton" title="Automaton">Automaton</a>

<ul><li><a href="Animatronics" title="Animatronics">Animatronic</a>

<ul><li><a href="Audio-Animatronics" title="Audio-Animatronics">Audio-Animatronics</a></li></ul></li></ul></li>

<li><a href="Industrial_robot" title="Industrial robot">Industrial</a></li>

<li><a href="Articulated_robot" title="Articulated robot">Articulated</a>

<li><a href="Domestic_robot" title="Domestic robot">Domestic</a></li>

<li><a href="Educational_robotics" title="Educational robotics">Educational</a></li>

<li><a href="Entertainment_robot" title="Entertainment robot">Entertainment</a></li>

<li><a href="Juggling_robot" title="Juggling robot">Juggling</a></li>

<li><a href="Military_robot" title="Military robot">Military</a></li>

<li><a href="Medical_robot" title="Medical robot">Medical</a></li>

<li><a href="Service_robot" title="Service robot">Service</a></li>

<li><a href="Disability_robot" class="mw-redirect" title="Disability robot">Disability</a></li>

<li><a href="Agricultural_robot" title="Agricultural robot">Agricultural</a></li>

<li><a href="Automated_restaurant" title="Automated restaurant">Food service</a></li>

<li><a href="Automated_retail" title="Automated retail">Retail</a></li>

<li><a href="BEAM_robotics" title="BEAM robotics">BEAM robotics</a></li>

<li><a href="Soft_robotics" title="Soft robotics">Soft robotics</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Classifications</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Biorobotics" title="Biorobotics">Biorobotics</a></li>

<li><a href="Cloud_robotics" title="Cloud robotics">Cloud robotics</a></li>

<li><a href="Continuum_robot" title="Continuum robot">Continuum robot</a></li>

<li><a href="Unmanned_vehicle" class="mw-redirect" title="Unmanned vehicle">Unmanned vehicle</a>

<ul><li><a href="Unmanned_aerial_vehicle" title="Unmanned aerial vehicle">aerial</a></li>

<li><a href="Unmanned_ground_vehicle" title="Unmanned ground vehicle">ground</a></li></ul></li>

<li><a href="Mobile_robot" title="Mobile robot">Mobile robot</a></li>

<li><a href="Microbotics" title="Microbotics">Microbotics</a></li>

<li><a href="Nanorobotics" title="Nanorobotics">Nanorobotics</a></li>

<li><a href="Necrobotics" title="Necrobotics">Necrobotics</a></li>

<li><a href="Robotic_spacecraft" class="mw-redirect" title="Robotic spacecraft">Robotic spacecraft</a>

<ul><li><a href="Space_probe" class="mw-redirect" title="Space probe">Space probe</a></li></ul></li>

<li><a href="Swarm_robotics" title="Swarm robotics">Swarm</a></li>

<li><a href="Telerobotics" title="Telerobotics">Telerobotics</a></li>

<li><a href="Autonomous_underwater_vehicle" title="Autonomous underwater vehicle">Underwater</a>

<ul><li><a href="Remotely_operated_underwater_vehicle" title="Remotely operated underwater vehicle">remotely-operated</a></li>

<li><a href="Robotic_fish" class="mw-redirect" title="Robotic fish">Robotic fish</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Robot_locomotion" title="Robot locomotion">Locomotion</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Continuous_track" title="Continuous track">Tracks</a></li>

<li><a href="Legged_robot" title="Legged robot">Walking</a>

<ul><li><a href="Hexapod_(robotics)" title="Hexapod (robotics)">Hexapod</a></li></ul></li>

<li><a href="Climber_(BEAM)" class="mw-redirect" title="Climber (BEAM)">Climbing</a></li>

<li><a href="Electric_unicycle" title="Electric unicycle">Electric unicycle</a></li>

<li><a href="Robotic_fin" class="mw-redirect" title="Robotic fin">Robotic fins</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Robotic_navigation" class="mw-redirect" title="Robotic navigation">Navigation</a> and <a href="Robotic_mapping" title="Robotic mapping">mapping</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Motion_planning" title="Motion planning">Motion planning</a></li>

<li><a href="Simultaneous_localization_and_mapping" title="Simultaneous localization and mapping">Simultaneous localization and mapping</a></li>

<li><a href="Visual_odometry" title="Visual odometry">Visual odometry</a></li>

<li><a href="Vision-guided_robot_systems" title="Vision-guided robot systems">Vision-guided robot systems</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Research</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Evolutionary_robotics" title="Evolutionary robotics">Evolutionary</a></li>

<li><a href="Robotics_simulator" title="Robotics simulator">Simulator</a></li>

<li><a href="Robotics_suite" title="Robotics suite">Suite</a></li>

<li><a href="Open-source_robotics" title="Open-source robotics">Open-source</a></li>

<li><a href="Robot_software" title="Robot software">Software</a></li>

<li><a href="Adaptable_robotics" title="Adaptable robotics">Adaptable</a></li>

<li><a href="Developmental_robotics" title="Developmental robotics">Developmental</a></li>

<li><a href="Human%E2%80%93robot_interaction" title="Human–robot interaction">Human–robot interaction</a></li>

<li><a href="Robotic_paradigm" title="Robotic paradigm">Paradigms</a></li>

<li><a href="Perceptual_robotics" title="Perceptual robotics">Perceptual</a></li>

<li><a href="Situated_robotics" title="Situated robotics">Situated</a></li>

<li><a href="Ubiquitous_robot" title="Ubiquitous robot">Ubiquitous</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="List_of_robotics_companies" title="List of robotics companies">Companies</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Amazon_Robotics" title="Amazon Robotics">Amazon Robotics</a></li>

<li><a href="Anybots" title="Anybots">Anybots</a></li>

<li><a href="Barrett_Technology" title="Barrett Technology">Barrett Technology</a></li>

<li><a href="Boston_Dynamics" title="Boston Dynamics">Boston Dynamics</a></li>

<li><a href="Doosan_Robotics" title="Doosan Robotics">Doosan Robotics</a></li>

<li><a href="Energid_Technologies" title="Energid Technologies">Energid Technologies</a></li>

<li><a href="FarmWise" title="FarmWise">FarmWise</a></li>

<li><a href="FANUC" title="FANUC">FANUC</a></li>

<li><a href="Figure_AI" title="Figure AI">Figure AI</a></li>

<li><a href="Foster-Miller" title="Foster-Miller">Foster-Miller</a></li>

<li><a href="Harvest_Automation" title="Harvest Automation">Harvest Automation</a></li>

<li><a href="HD_Hyundai_Robotics" title="HD Hyundai Robotics">HD Hyundai Robotics</a></li>

<li><a href="Honeybee_Robotics" title="Honeybee Robotics">Honeybee Robotics</a></li>

<li><a href="Intuitive_Surgical" title="Intuitive Surgical">Intuitive Surgical</a></li>

<li><a href="IRobot" title="IRobot">IRobot</a></li>

<li><a href="Rainbow_Robotics" title="Rainbow Robotics">Rainbow Robotics</a></li>

<li><a href="Starship_Technologies" title="Starship Technologies">Starship Technologies</a></li>

<li><a href="Symbotic" title="Symbotic">Symbotic</a></li>

<li><a href="Universal_Robotics" title="Universal Robotics">Universal Robotics</a></li>

<li><a href="Wolf_Robotics" title="Wolf Robotics">Wolf Robotics</a></li>

<li><a href="Yaskawa_Electric_Corporation" title="Yaskawa Electric Corporation">Yaskawa</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Critique_of_work" title="Critique of work">Critique of work</a></li>

<li><a href="Powered_exoskeleton" class="mw-redirect" title="Powered exoskeleton">Powered exoskeleton</a></li>

<li><a href="Workplace_robotics_safety" title="Workplace robotics safety">Workplace robotics safety</a>

<ul><li><a href="Robotic_tech_vest" title="Robotic tech vest">Robotic tech vest</a></li></ul></li>

<li><a href="Technological_unemployment" title="Technological unemployment">Technological unemployment</a></li>

<li><a href="Terrainability" title="Terrainability">Terrainability</a></li>

<li><a href="List_of_fictional_robots_and_androids" title="List of fictional robots and androids">Fictional robots</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> <b>Category</b></li>

<li><span class="noviewer" typeof="mw:File"><span title="Outline"></span></span> <b><a href="Outline_of_robotics" title="Outline of robotics">Outline</a></b></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q12065277#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata646" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q12065277#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata646" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh00000121">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007290697605171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/concept/6940e5bc-8b5d-4ee9-b3b5-5acb392d9c5c">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div>

<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite id="CITEREFNigatuChoiKim2021" class="citation journal cs1">Nigatu, Hassen; Choi, Yun Ho; Kim, Doik (2021-10-01). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.mechmachtheory.2021.104409">"Analysis of parasitic motion with the constraint embedded Jacobian for a 3-PRS parallel manipulator"</a>. <i>Mechanism and Machine Theory</i>. <b>164</b>: 104409. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.mechmachtheory.2021.104409">10.1016/j.mechmachtheory.2021.104409</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0094-114X">0094-114X</a>.</cite></span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite id="CITEREFNigatuKim2021" class="citation journal cs1">Nigatu, Hassen; Kim, Doik (2021-01-01). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fapp11104690">"Optimization of 3-DoF Manipulators' Parasitic Motion with the Instantaneous Restriction Space-Based Analytic Coupling Relation"</a>. <i>Applied Sciences</i>. <b>11</b> (10): 4690. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fapp11104690">10.3390/app11104690</a></span>.</cite></span>

</li>

</ol></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-05-23" href="https://en.wikipedia.org/wiki/?title=Parallel_manipulator&oldid=1291799745">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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