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<title>Serial manipulator</title>

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

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><b>Serial manipulators</b> are the most common industrial robots and they are designed as a series of links connected by motor-actuated joints that extend from a base to an end-effector. Often they have an <a href="Anthropomorphism" title="Anthropomorphism">anthropomorphic</a> arm structure described as having a "shoulder", an "elbow", and a "wrist".

</p><p>Serial robots usually have six joints, because it requires at least six <a href="Degrees_of_freedom_(engineering)" class="mw-redirect" title="Degrees of freedom (engineering)">degrees of freedom</a> to place a manipulated object in an arbitrary position and orientation in the workspace of the robot.

</p><p>A popular application for serial robots in today's industry is the pick-and-place <a href="Assembly_line" title="Assembly line">assembly</a> robot, called a <a href="SCARA" title="SCARA">SCARA</a> robot, which has four degrees of freedom.

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

<p>In its most general form, a serial robot consists of a number of rigid links connected to joints. Simplicity considerations in manufacturing and control have led to robots with only <a href="Revolute_joint" title="Revolute joint">revolute</a> or <a href="Prismatic_joint" title="Prismatic joint">prismatic joints</a> and orthogonal, parallel and/or intersecting joint axes (instead of arbitrarily placed joint axes).<br>

<a href="Donald_L._Pieper" class="mw-redirect" title="Donald L. Pieper">Donald L. Pieper</a> derived the first practically relevant result in this context,<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> referred to as <a href="321_kinematic_structure" title="321 kinematic structure">321 kinematic structure</a>:

<i>The inverse kinematics of serial manipulators with six revolute joints, and with three consecutive joints intersecting, can be solved in closed-form, i.e. analytically</i>

This result had a tremendous influence on the design of industrial robots.

</p><p>The main advantage of a serial manipulator is a large <a href="Workspace" title="Workspace">workspace</a> with respect to the size of the robot and the floor space it occupies. The main disadvantages of these robots are:

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<ul><li>the low stiffness inherent to an open kinematic structure,</li>

<li>errors are accumulated and amplified from link to link,</li>

<li>the fact that they have to carry and move the large weight of most of the actuators, and</li>

<li>the relatively low effective load that they can manipulate.</li></ul>

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

<p>The position and orientation of a robot's <a href="Industrial_robot_end_effector" class="mw-redirect" title="Industrial robot end effector">end effector</a> are derived from the joint positions by means of a geometric model of the robot arm. For serial robots, the mapping from joint positions to end-effector pose is easy, the inverse mapping is more difficult. Therefore, most industrial robots have special designs that reduce the complexity of the inverse mapping.

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<div class="mw-heading mw-heading3"><h3 id="Workspace">Workspace</h3></div>

<p>The reachable workspace of a robot's end-effector is the manifold of reachable frames.<br> The dextrous workspace consists of the points of the reachable workspace where the robot can generate velocities that span the complete tangent space at that point, i.e., it can translate the manipulated object with three degrees of freedom, and rotate the object with three degrees of rotation freedom.<br>

The relationships between joint space and Cartesian space coordinates of the object held by the robot are in general multiple-valued: the same pose can be reached by the serial arm in different ways, each with a different set of joint coordinates. Hence the reachable workspace of the robot is divided in configurations (also called assembly modes), in which the kinematic relationships are locally one-to-one.

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<div class="mw-heading mw-heading3"><h3 id="Singularity">Singularity</h3></div>

<p>A singularity is a configuration of a serial manipulator in which the joint parameters no longer completely define the position and orientation of the end-effector. Singularities occur in configurations when joint axes align in a way that reduces the ability of the arm to position the end-effector. For example when a serial manipulator is fully extended it is in what is known as the boundary singularity.<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>

</p><p>At a singularity the end-effector loses one or more degrees of twist freedom (instantaneously, the end-effector cannot move in these directions).<br> Serial robots with less than six independent joints are always singular in the sense that they can never span a six-dimensional twist space. This is often called an architectural singularity.

A singularity is usually not an isolated point in the workspace of the robot, but a sub-manifold.

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<div class="mw-heading mw-heading3"><h3 id="Redundant_manipulator">Redundant manipulator</h3></div>

<p>A redundant manipulator has more than six degrees of freedom which means that it has additional joint parameters <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> that allow the configuration of the robot to change while it holds its end-effector in a fixed position and orientation.

</p><p>A typical redundant manipulator has seven joints, for example three at the shoulder, one elbow joint and three at the wrist. This manipulator can move its elbow around a circle while it maintains a specific position and orientation of its end-effector.

</p><p>A snake robot has many more than six degrees of freedom and is often called hyper-redundant.

</p>

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

<ul><li><a href="ABB_Group" class="mw-redirect" title="ABB Group">ABB Robotics</a></li>

<li><a href="Adept_Technology" class="mw-redirect" title="Adept Technology">Adept Technology</a></li>

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

<li><a href="Epson_Robots" title="Epson Robots">Epson Robots</a></li>

<li><a href="FANUC_Robotics" class="mw-redirect" title="FANUC Robotics">FANUC Robotics</a></li>

<li><a href="Kawasaki_Robotics" class="mw-redirect" title="Kawasaki Robotics">Kawasaki Robotics</a></li>

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

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

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

<li><a href="Robotics_Design" class="mw-redirect" title="Robotics Design">Robotics Design</a></li>

<li><a href="Universal_Robots" title="Universal Robots">Universal Robots</a></li></ul>

<ul><li><a href="Parallel_manipulator" title="Parallel manipulator">Parallel manipulator</a></li>

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

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

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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">D.L. Pieper. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160924184009/http://www.dtic.mil/get-tr-doc/pdf?AD=AD0680036">The kinematics of manipulators under computer control</a>. PhD Thesis, Stanford University, Department of Mechanical Engineering, 1968</span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://mecademic.com/resources/Singularities/Robot-singularities">What are singularities in a six-axis robot arm?</a></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">P. Moubarak, et al., <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180105011411/https://pdfs.semanticscholar.org/83d0/20205bb41acbcac75cfee82b8afea69bcb51.pdf">A Globally Converging Algorithm for Adaptive Manipulation and Trajectory Following for Mobile Robots with Serial Redundant Arms</a>, Robotica, 31 (8) (2013) 1299 – 1311.</span>

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

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