# Serial manipulator A **serial manipulator** is a robotic arm built as a single open kinematic chain: a sequence of rigid links, each joined to the next by one powered joint, running from a fixed base to a free tool or gripper at the tip. Every joint adds one degree of freedom, and a general-purpose arm usually stacks six of them, since three set a position in space and three more set an orientation.[^jensen24] The design is the dominant kind of [[Manipulator_(device)|manipulator]] on a factory floor: most [[Industrial_robot|industrial robots]] — welding arms, paint sprayers, pick-and-place machines — are serial manipulators, distinct from a [[Parallel_manipulator|parallel manipulator]], whose several short chains share the load on one moving platform instead of stacking into a single long one. This article's microsim poses a two- or three-joint planar arm and shades in the region its tip can reach as its joint limits tighten, and lets you swap between an articulated layout and a [[SCARA]] layout to compare their workspaces side by side. ## Kinematics Placing the tip of a serial manipulator from its joint angles is [[Robot_kinematics|forward kinematics]]: each joint contributes one rigid transform, and the chain's end pose is the product of all of them in order, most often written out with [[Denavit–Hartenberg_parameters|Denavit-Hartenberg parameters]].[^craig18][^lynchpark17] For a planar arm of two links with lengths L1 and L2 and joint angles θ1 and θ2, the tip sits at x + iy = L1 e^(iθ1) + L2 e^(i(θ1+θ2)), the same relation a third revolute joint on a 3R arm, or a sliding rail on a SCARA arm, simply extends by one more term.[^lynchpark17] The reverse problem — which joint angles reach a chosen point — is [[Inverse_kinematics|inverse kinematics]], covered on its own page along with the [[Jacobian_matrix_and_determinant|Jacobian]] that relates joint speed to tip speed and marks the poses, called singularities, where the arm loses a direction of motion.[^craig18] A serial arm's [[Degrees_of_freedom_(mechanics)|degrees of freedom]] equal its number of independently [[Actuator|actuated]] joints, and Jensen's design text works the same count through for planar and spatial [[Kinematic_chain|kinematic chains]] up to six axes.[^jensen24] ## Workspace The **reachable workspace** of a serial manipulator is the set of every point its tip can be placed at, over every combination its joints allow; the narrower **dexterous workspace** is the smaller set of points the tip can reach in *every* orientation, not just one.[^craig18][^siegwart11] For a planar two-link (2R) arm with no joint limits, the reachable set is the annulus |L1 − L2| ≤ r ≤ L1 + L2 around the base — the tip cannot get closer than the difference of the link lengths, elbow folded flat, or farther than their sum, arm fully straight.[^craig18][^lynchpark17] A third revolute joint, a 3R arm, is kinematically redundant in the plane — three angles aiming at a two-coordinate target — and fills in the hole at the annulus's centre, since the extra link lets the tip fold back on itself. Joint limits cut this shape down further. A shoulder limit removes a wedge behind the base; an elbow limit that stops the arm folding all the way removes the disc at the centre, opening a hole even in the once-solid 3R workspace, so a real limited arm's reach is usually drawn as a crescent rather than a ring.[^craig18] The microsim rasterises this directly: it samples every joint angle inside its limit, runs [[Robot_kinematics|forward kinematics]] on each sample, and shades every cell of a 64-by-64 grid the tip lands in, next to a second view of the same limits drawn as a box in joint space.[^lynchpark17] *Try: drag theta1 and theta2 to walk the arm around its joint-space box and watch the marker track the pose against the gold limit outline, then pull the limit slider down from 180 degrees toward 60 and watch the shaded reachable region in the main view shrink to a crescent as the box shrinks with it.* ## Types of serial manipulators Serial manipulators are grouped by the mix of joints in their first three axes, which sets the shape of the space the wrist can reach. A Cartesian or gantry arm slides its tool along three perpendicular [[Prismatic_joint|prismatic joints]], tracing a rectangular box; cylindrical and spherical arms swap one or two of those slides for a turning [[Revolute_joint|revolute joint]], trading a flat-sided workspace for a wedge or a dome. An [[Articulated_robot|articulated]] or anthropomorphic arm — most six-axis industrial robots — uses a revolute joint at every axis, the same shoulder-elbow-wrist layout as a human arm, which is what the microsim's two- and three-link planar model approximates.[^craig18] A [[SCARA]] arm is a fourth common layout, built for pick-and-place: two revolute joints move the tool in a horizontal plane, and a separate prismatic joint slides it up and down, so the arm is stiff against vertical loads but gives a little sideways — the "selective compliance" in its name.[^craig18] The microsim's SCARA preset uses a first link of 0.6 metres and a second of 0.5 metres swinging through about ±140°, typical figures rather than a measured machine (ILLUSTRATIVE). ## Comparison with parallel manipulators A serial manipulator's chain is open: every joint carries the weight and position error of every joint before it, so stiffness and precision fall as the chain gets longer, and the whole arm has to be strong enough to swing its own farthest joint at full extension.[^siegwart11] A [[Parallel_manipulator|parallel manipulator]] closes the chain instead, connecting several short legs from a fixed base straight to one shared platform — a [[Stewart_platform|Stewart platform]]'s six legs are the standard example — so the load splits across all of them and no single leg has to carry it alone.[^lynchpark17] The trade is workspace: a parallel machine's legs interfere with each other and limit how far or how much the platform can move, while a serial arm's open chain sweeps a much larger volume for the same footprint, which is why most factory-floor industrial robots are serial and parallel machines are chosen instead where stiffness or precision matters more than reach. ## Applications Serial manipulators are the default shape of an [[Industrial_robot|industrial robot]]: six-axis articulated arms weld, paint and handle material on assembly lines, while [[SCARA]] arms, faster and stiffer over a flat working plane, dominate electronics assembly and pick-and-place packaging.[^jensen24] Outside the factory, the same open-chain design shows up wherever one mounted base has to reach around a work volume — a laboratory pipetting arm, a robotic telescope mount, a surgical arm working inside a fixed port — trading a parallel manipulator's stiffness for a serial manipulator's reach.[^siegwart11] A single serial arm can also be re-tooled with a new end effector and reprogrammed for a new task far more cheaply than building a dedicated parallel machine, which is the main reason serial designs filled factories first and still outnumber parallel ones on the floor today.[^jensen24] The whole assembly — base, link chain and tool — is a [[Manipulator_(device)|manipulator]] in the general sense the term covers. ## See also - [[Articulated_robot]] - [[SCARA]] - [[Manipulator_(device)]] - [[Parallel_manipulator]] - [[Robot_kinematics]] - [[Inverse_kinematics]] - [[Industrial_robot]] ## References [^jensen24]: Jensen, David (2024). *Introduction to Mechanical Design and Manufacturing*. CC BY-NC. pp. 189, 194-195 (robot arms as serial mechanisms, up to six degrees of freedom). [^craig18]: Craig, John J. (2018). *Introduction to Robotics: Mechanics and Control* (4th ed.). Pearson. Ch. 3 (kinematics and workspace of serial chains). [^siegwart11]: Siegwart, Roland; Nourbakhsh, Illah R.; Scaramuzza, Davide (2011). *Introduction to Autonomous Mobile Robots* (2nd ed.). MIT Press. Ch. 3. [^lynchpark17]: Lynch, Kevin M.; Park, Frank C. (2017). *Modern Robotics: Mechanics, Planning, and Control*. Cambridge University Press. Ch. 4 (forward kinematics of open chains). <!-- ROBSIM:Serial_manipulator --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Serial_manipulator) : [Wikitube](https://en.wikitube.io/wiki/Serial_manipulator) · pinned revision [1346293941](https://en.wikipedia.org/w/index.php?oldid=1346293941) · 2026-09-23 <!-- hub_tags: Robotics, Kinematics -->