Manipulator Topologies — Family Index

A Tier-3 catalog of robot-manipulator kinematic structures, with current model designations from major vendor catalogs. Covers serial articulated, SCARA, Cartesian, parallel (delta + hexapod), hybrid, mobile, humanoid, and dual-arm topologies. Cross-references to deeper Tier-2/Tier-3 notes throughout.

1. At a glance

By kinematic chain:

• Serial (open chain) — joints in a single chain from base to tool. Most common in industry. Sub-classes by DoF count: 4-DoF (palletizers), 5-DoF (painting, simple pick-place), 6-DoF (the universal workhorse), 7-DoF (redundant — cobots + research).
• Parallel (closed chain) — end-effector connected to base by multiple independent legs. Sub-classes: delta (3-DoF translation + optional R), Stewart-Gough hexapod (6-DoF), planar 3-RRR (2 DoF + R).
• Hybrid (serial + parallel) — Tricept, Sprint Z3, Exechon. Parallel base + serial wrist.

By topology / joint sequence:

• Cartesian (PPP) — three orthogonal prismatic joints; XYZ box workspace.
• Cylindrical (RPP) — vertical column + radial arm + lift.
• Polar / spherical (RRP) — historical; Unimate.
• Articulated (RRR) — three revolute joints; near-spherical workspace. With RRR wrist becomes the canonical 6-DoF arm.
• SCARA (RRP + R wrist) — two horizontal revolute + vertical prismatic + tool rotation. Planar-compliant, Z-stiff.

By application classification:

• Industrial — high-stiffness, high-payload, fenced. Fanuc R-2000iC, ABB IRB 6700, KUKA KR Quantec.
• Collaborative (cobot) — torque-sensing, force-limited, ISO 10218 / ISO/TS 15066 compliant. UR, Franka, KUKA iiwa, Doosan.

2. Serial 6-DoF articulated arm (the workhorse)

The reference architecture: RRR base regional structure (joints 1-3) + RRR spherical wrist (joints 4-6). Workspace is approximately a sphere minus base-and-shoulder dead zones. Solves inverse kinematics in closed form via Pieper’s criterion when last 3 axes intersect at a point.

Industrial 6-DoF families (current generation):

• ABB — IRB 1100 (4 kg, small parts), IRB 1200 (5/7 kg, compact, ±0.025 mm), IRB 1300 (10/11/12 kg), IRB 1600 (6/8/10 kg), IRB 2600 (12/20 kg general), IRB 4600 (20/40/45/60 kg), IRB 6700 (150-300 kg auto BIW), IRB 8700 (550-800 kg heavy lift), IRB 1010 (1.5 kg consumer electronics).
• KUKA — KR Quantec (90-300 kg medium-heavy), KR Iontec (30-70 kg coating-resistant), KR Cybertech (8-22 kg general), KR Agilus (6-10 kg fast small), KR Iisy (3 kg cobot-ified small), KR Fortec (90-600 kg foundry/forging), KR Titan (1300 kg heavy).
• Fanuc — M-series (M-10iD/12, M-20iD/25, M-710iC/45M/50/70, M-900iB/360, M-2000iA/2300 the world’s strongest at 2300 kg), R-series (R-2000iC the auto-industry standard at 165-270 kg), CR/CRX cobot series (CRX-5iA, 10iA, 25iA).
• Yaskawa Motoman — MH-series (MH5F/12/24/50/80/180/250), GP-series (GP4/7/8/12/25/35/50/88/110/180/200/210/215/250/280/400 — the current general-purpose line), HC-series cobots (HC10DTP/20DTP/30PL).
• Stäubli — TX2-40/60/90/140/200 (general 6-axis), RX160 (legacy still in service), TX2touch HE cobot.
• Comau — NJ-series (NJ-130/165/175/220/290/370/650), NM-series Racer mid-size, Aura cobot.
• Mitsubishi Electric — RV-F/FR-series (RV-2FR, 4FR, 7FR, 13FR, 20FR, 35FR, 70FR).
• Kawasaki Robotics — BX-series (BX100N/130X/165N/200L/250L/300L), RS-series (RS003N/005L/007L/010L/013N/015X/020N/025N/030N/050N/080N), BA-series painting, duAro2 dual-arm SCARA.
• OTC Daihen (FB / FD) — FD-V8, V20, V50, V166, V210, B4, B6 (welding-focused).
• Hyundai Robotics — HH-series (HH050/120), HS-series, YL/YH (general).
• Epson — N6 SX-series (N6-A1000 6-axis compact), C-series (C4/C8/C12).
• Universal Robots (cobot 6-DoF) — UR3e (3 kg, 500 mm), UR5e (5 kg, 850 mm), UR10e (12.5 kg, 1300 mm), UR16e (16 kg, 900 mm), UR20 (20 kg, 1750 mm), UR30 (30 kg, 1300 mm). All are 6-DoF cobots — torque-sensing per joint, no inherent redundancy.

3. Serial 7-DoF redundant arm (cobot / research)

An extra revolute joint adds null-space — for a given tool pose, an internal degree of freedom remains. Used for singularity avoidance, obstacle avoidance (elbow-out clearance), joint-limit avoidance, manipulability maximization, and torque distribution.

Heritage: DLR LWR III (German Aerospace Center Lightweight Robot III, ~2002) — first widely cited 7-DoF torque-sensing arm. Technology licensed to KUKA in 2008 → LBR iiwa (intelligent industrial work assistant).

Current 7-DoF cobot families:

• KUKA LBR iiwa 7 R800 / iiwa 14 R820 — joint-torque sensors all 7 axes, the cobot reference. LBR Med 7 / 14 is the medical-grade variant (ISO 13485) used as a manipulator subsystem for surgical robotics.
• Franka Emika — original Panda (2017), then Production 3, Research 3, and FR3 (current research-grade). Torque sensors in all 7 joints, 1 kHz control with libfranka.
• Kinova — Gen2 Ultra-lightweight (Jaco, 6 or 7-DoF), Gen3 (7-DoF, 7 kg payload), Gen3 lite (6-DoF). Research-friendly ROS support.
• ABB GoFa — GoFa 5 (5 kg), GoFa 10 (10 kg), GoFa 12 (12 kg) — 6-DoF cobots actually. The 7-DoF SWIFTI is a 4 kg high-speed cobot. (ABB’s only true 7-DoF is on YuMi each arm — see dual-arm below.)
• Doosan Robotics — A-series (A0509/A0912 light), M-series (M0609/M0617/M1013/M1509), H-series (H2017/H2515 heavy 25 kg), E-series (E0509 economical). All 6-DoF; the new P-series Pro adds payload. Doosan H is the highest-payload 6-DoF cobot at 25 kg. Note: Doosan + JAKA + Aubo cobots are 6-DoF except where noted.
• Techman Robot (Quanta subsidiary) — TM5-700/900, TM12, TM14, TM16, TM25S, TM30S. 6-DoF cobots with integrated vision.
• Rethink Robotics Sawyer / Sawyer BLACK Edition — 7-DoF cobot. Original company dissolved 2018; rights now with Hahn Group (Germany), still sold.
• Kassow Robots — KR0610 (10 kg), KR0810 (10 kg), KR1018 (18 kg), KR1205 (5 kg long reach), KR1410 — all 7-DoF cobots. Kassow specifically markets the 7-DoF advantage.
• JAKA Robotics — Zu series (Zu3/5/7/12/18), Pro series, S series (food-grade), C series (cobots). 6-DoF.
• Elite Robots — EC-series (EC63/66/612), CS-series. 6-DoF.
• Neura Robotics — MAiRA (Multi-sensing Intelligent Robotic Assistant) — 7-DoF cognitive cobot. MiPA (mobile + MAiRA).
• Flexiv — Rizon 4 (4 kg), Rizon 4s (4 kg sensitive), Rizon 10 (10 kg) — 7-DoF with whole-body force/torque sensing, hierarchical-impedance control.
• Aubo Robotics — i-series (i3, i5, i7, i10, i16, i20) — 6-DoF. i7 7-DoF variant introduced 2020 for research.

4. 5-DoF and 4-DoF articulated (palletizing + economy + spray)

When the task doesn’t need full 6-DoF wrist orientation, removing axes saves cost, mass, and inertia.

4-axis palletizers (the dominant 4-DoF category): vertical Z-stack motion needs only base rotation + shoulder + elbow + wrist orientation — no roll/pitch.

• ABB IRB 460 (110 kg, 2400 mm — fast palletizing), IRB 660 (180/250 kg, 3150 mm — heavy bag/box palletizing, the warehouse standard since 2005), IRB 760 (450 kg).
• Fanuc M-410iC/185, M-410iC/315, M-410iC/500, M-410iB/700 (bag/box palletizing 185-700 kg), M-710iC/45M (45 kg, but typically 6-axis), M-410 family is the dominant palletizing platform.
• Yaskawa MPL-series — MPL80II (80 kg), MPL100II (100 kg), MPL160II (160 kg), MPL300II (300 kg), MPL500II (500 kg), MPL800II (800 kg).
• Kawasaki CP-series — CP180L (180 kg), CP300L (300 kg), CP500L (500 kg), CP700L (700 kg).
• KUKA KR Quantec PA (palletizer variant, 4-axis).

5-axis specialty: spray painting (full 360 wrist roll not needed inside a booth, removing one axis simplifies ATEX-compliant sealing).

• Fanuc P-series — P-50iB/15, P-250iB (painting 5-axis ATEX).
• Yaskawa EPX-series painting.
• Sames Kremlin / Cima retrofit packs on 5-axis arms.
• CMA Robotics GR-series painting.

Educational + desktop:

• Dobot Magician (4-axis), Dobot MG400 (4-axis SCARA), Dobot CR-series (6-axis cobot).
• uArm Swift Pro (4-axis hobby).
• Niryo Ned2 (6-axis educational cobot).

5. SCARA (Selective Compliance Articulated Robot Arm)

Invented by Hiroshi Makino at Yamanashi University, Japan, 1981. The acronym means selective compliance: stiff in Z, compliant in the XY plane — exactly what’s needed for vertical insertion (pegs, screws, pick-place).

Kinematics: R (base) + R (elbow) + P (Z lift) + R (tool yaw) = 4-DoF. Workspace is an annular region in XY at adjustable Z.

Industrial SCARA families:

• Epson — G-series (G3, G6, G10, G20 — the canonical SCARA brand), LS-series (LS3, LS6, LS10, LS20 economy), T-series all-in-one.
• Stäubli — TS2-40/60/80/100 (cleanroom-grade SCARA).
• Yamaha — YK-X-series (YK120XG, YK180X, YK220X, YK250XG, YK350XG, YK400XR, YK500XG, YK600XG, YK700XG, YK900XG, YK1200XG).
• Mitsubishi Electric — RH-F-series (RH-3FR, RH-6FR, RH-12FR, RH-20FR), RH-CR cobot SCARA.
• Denso — HS-G, HSR collaborative SCARA, XR/HM-series.
• Toshiba Machine (now Shibaura) — THE-series, THP-series, TVL-series.
• Omron (Adept legacy) — Cobra 350/450/600/800, eCobra 600/800 — SCARAs continued under Omron.
• Brooks Automation — PreciseFlex SCARA (semiconductor wafer + life-science).
• Fanuc SR-series — SR-3iA, SR-6iA, SR-12iA, SR-20iA.
• Hirata — AR-series.
• Janome — JS-series desktop SCARA.

Typical use: PCB assembly, screw driving, dispensing, life-science liquid handling, semiconductor part transfer, vertical insertion. Cycle time 0.3-0.5 s for short pick-place is the SCARA’s strong suit.

6. Parallel — Delta

Invented by Reymond Clavel at EPFL (Lausanne), Switzerland, 1985 (patent 1987). Three upper revolute joints actuated, each driving a parallelogram leg to a moving platform → 3-DoF pure translation. Optional 4th axis: central telescoping driveshaft adds tool-yaw R for 4-DoF.

Kinematic advantage: the actuators are stationary on the base — only the lightweight parallelograms and small platform move. Hence very low moving inertia → very high accelerations (up to 200 m/s²) and very high cycle rate (1500+ picks/min on small parts).

Workspace: an inverted cone or roughly cylindrical envelope under the base, ~500-1600 mm diameter, ~200-500 mm Z range typical.

Industrial delta families:

• ABB IRB 360 FlexPicker — the iconic delta (1999, evolved from 1990s development). Variants IRB 360-1/800, -1/1130, -1/1600, -3/1130, -6/1600, -8/1130 — payload 1-8 kg.
• ABB IRB 390 FlexPacker — 5-DoF delta (3 translation + 2 wrist tilt) for orientation-required pick-place.
• Fanuc M-1iA, M-2iA, M-3iA — delta family. M-1iA is the smallest (0.5 kg, 280 mm radius). M-3iA/6A is the bigger payload (6 kg).
• Fanuc DR-3iB — newer high-speed delta (3 kg, 1300 mm diameter, food-safe IP69K).
• Adept Quattro s650H / s800H — 4-arm delta (the variant with 4 parallelogram chains for kinematic over-determination → faster + smoother). Now sold by Omron.
• Codian Robotics — D2-800 / D4-800 / D5-1100 / D5-1600 / D5-1800 (4-DoF delta family, food + pharma).
• Stäubli TP80 / TP80 Fast Picker — 4-DoF delta, the cleanroom-grade delta. TS2-40 / TS2-60 stand-alone TwinCAT-class delta.
• Yaskawa MPP-series — MPP3 (3 kg / 800 mm), MPP3H, MPP3S, MPP3D (delta family).
• Yamaha YP-X-series — YP320X / YP420X / YP520X delta.
• EPSON N2 / N6 (delta-style — actually 4-axis SCARA hybrid).
• Asyril Asycube — vibratory feeder + delta combo for flexible feeding.

7. Parallel — Stewart-Gough hexapod (6-DoF parallel)

Eric Gough 1947 (tire-testing rig), D. Stewart 1965 (flight simulator). 6 prismatic actuators (legs) connecting top platform to base, each leg with spherical joints at both ends. Provides 6-DoF (XYZ + roll/pitch/yaw) with high stiffness (parallel load paths) and high precision (errors don’t accumulate as in a serial chain).

Workspace: small relative to footprint — typically ±100 mm translation, ±20-40 deg rotation. Trade-off for stiffness + accuracy.

Industrial / precision hexapod families:

• Physik Instrumente (PI) — H-810, H-811, H-820, H-824, H-840, H-841, H-845, H-850, H-860, H-900K (the precision hexapod range — sub-nm to μm positioning, 30 nm minimum step). H-811.I2V for vacuum/UHV.
• Mikrolar — P3000, P4000, R3000, R4000 (industrial hexapods, ~1-5 t payload).
• Symetrie — Joran, Atrax, Mistral, Notus, Eole, Breva, Quanta (cinema, optical alignment, ergonomic-testing motion platforms).
• ALIO Industries — Tripod + Hexapod-H series (nanometer-level).
• Moog FCS / CAE / Bosch Rexroth (industrial motion platforms) — flight + driving simulators (Stewart-platform DOF6 motion bases at 1-15 t payload).
• Aerotech HEX-RS hexapods for optical alignment.
• SmarAct SmarPod (piezo-driven micro-hexapod).

Use: flight simulators, driving simulators, telescope secondary/tertiary mirror tip-tilt-piston, semiconductor wafer alignment, optical fiber alignment, machine-tool 6-axis micromilling tables.

8. Cartesian / gantry (PPP)

Three orthogonal prismatic axes on a rigid frame. Workspace is exactly the XYZ box of the strokes. Predictable, stiff, scalable to large strokes (meters of travel). Often combined with a 1-3 axis rotational wrist to make 4-, 5-, or 6-DoF gantry robots.

Vendor systems:

• Bosch Rexroth EasyHandling modular linear+belt+ballscrew gantry.
• Festo EXCM, EXCS, EHMB Cartesian + delta combos.
• Igus drylin linear-bearing gantry (low-cost).
• THK SKR / LM-Guide-built gantries.
• Schunk PG / PSH linear axes.
• Aerotech ANT-G, ALS-25000, AGS-15000 (precision motion gantries, nm-level).
• Newport / MKS XMS / IMS / LTA linear stage gantries.
• OpenBuilds C-Beam / Workbee / Lead CNC (DIY-grade CNC gantry).
• ISEL CNC, Mecadynamics (industrial CNC gantries).
• Yamaha XY-X / TRANSERVO.
• IAI Cartesian modular linear actuator systems.

Use: semiconductor wafer handling (overhead transport), pick-place across long lines, CNC machining envelopes, lab automation (Hamilton STAR, Tecan Fluent — life-science liquid handling is essentially a Cartesian gantry with a pipette head), 3D-printer kinematic frame (Cartesian + delta + CoreXY variants).

9. Cylindrical (RPP)

Vertical base rotation + horizontal radial prismatic + vertical Z = 3-DoF working envelope (cylinder annulus). Largely historical — superseded by SCARA in the assembly market.

• Seiko + Hirata + Toshiba assembly cells (1980s-90s) used cylindrical robots extensively for small-parts assembly.
• Reis Robotics cylindrical machine-tool loaders (acquired by KUKA 2012).
• Still encountered in some legacy production lines and specialty loaders.

10. Polar / spherical (RRP)

Base rotation + shoulder rotation + radial prismatic extension = 3-DoF with a spherical sector workspace. The original industrial-robot topology.

• Unimate (Unimation Inc.) — Devol patent 1954, first installed at GM Trenton 1961, hydraulically actuated, 1800 kg arm. Designed by Joseph Engelberger + Devol. Spherical-coordinate kinematics. Sold thousands through 1980s; Unimation acquired by Westinghouse 1983, Stäubli 1988.
• AMF Versatran (1962) — competing polar arm.
• Cincinnati Milacron T3 (1970s) — popular polar/spherical arm before articulated arms took over.

Largely extinct in current catalogs.

11. Hybrid / specialty

Combine parallel-kinematic-machine (PKM) base for stiffness + serial wrist for orientation range. The aerospace-machining niche.

• Tricept (Karl-Erik Neumann, Comau / SMT Tricept, 1980s) — 3-PRPS parallel base (3 telescoping legs to triangular platform) + 2-3 DoF wrist on the moving platform. Used by Boeing + Airbus for wing-skin drilling/riveting. ~5 m/s². Now licensed under Loxin / Exechon group.
• Sprint Z3 (DS Technologie, now part of Starrag) — 3-DoF parallel machining head, integrated into 5-axis machine tools.
• Exechon XT-series — second-generation Tricept variant.
• Loxin — Tau hybrid for aerospace drilling cells.
• Fanuc M-2000iA + heavy gantry combos (serial+gantry “hybrid” in informal usage).
• KUKA KR Quantec on KL linear track — adds 1 Cartesian rail to a 6-DoF arm → 7-DoF for auto BIW.

12. Mobile manipulator (mobile base + arm)

A mobile platform (AGV/AMR/legged) carrying a manipulator. Two integration patterns: (a) commercial mobile base (MiR, OTTO, Robotnik) + commercial arm (UR, Franka) bolted on, integrated by SI; (b) purpose-built unified product.

Purpose-built unified mobile manipulators:

• Boston Dynamics Stretch — heavy boxbot, omnidirectional base + 7-DoF arm with vacuum gripper, for warehouse truck-unload (~800 boxes/hr).
• Boston Dynamics Spot + Arm (SpotArm) — quadruped + 6-DoF manipulator + gripper, for inspection + sample-grab.
• Toyota HSR (Human Support Robot) — research platform, omni base + 6-DoF arm + camera head.
• Fetch Robotics Fetch + Freight — research mobile manipulator (Fetch acquired by Zebra Technologies 2021).
• PAL Robotics TIAGo, TIAGo++, TIAGo Pro — differential/omni base + 7-DoF arm + lifting torso. TIAGo++ is dual-arm.
• Robotnik RB-VOGUI, RB-KAIROS, RB-EKEN, RB-1 BASE + arm options.
• KUKA KMR iiwa — KMP 1500 omni base + LBR iiwa 14 manipulator (the original premium mobile manipulator).
• KUKA KMR QUANTEC — heavy mobile manipulator.
• Stäubli HelMo — TX2-90 arm on AGV base.
• Neura Robotics MiPA — MAiRA 7-DoF on omni mobile base.
• Diligent Robotics Moxi — hospital service robot (telescoping arm on omni base).
• Boston Dynamics + Hyundai — joint R&D on humanoid + mobile manipulation post Hyundai acquisition 2021.

SI-assembled (cobot + AMR): UR10e + MiR250/600/1000, UR + OTTO 600/1500, Franka + Robotnik base, Doosan + Mobile Industrial Robots, KUKA LBR iiwa + KMP 200/600/1500.

13. Humanoid (bipedal)

Topology = two 6-DoF legs + dual 6/7-DoF arms + neck + grippers. See [[Robotics/humanoid-balance]] and [[Robotics/dynamic-locomotion]] for control. Current commercial+pre-commercial roster (2024-2026):

• Boston Dynamics Atlas — hydraulic legacy retired 2024; Electric Atlas (2024+) is all-electric, claimed for Hyundai factory deployment.
• Tesla Optimus Gen 2 / Gen 3 — 28+ actuators, Tesla hand with 22 DoF, targeted for vehicle manufacturing.
• Figure 02 (Figure AI) — humanoid with OpenAI language reasoning + BMW + GXO pilots.
• Apptronik Apollo — modular humanoid (Mercedes-Benz factory pilot).
• Sanctuary AI Phoenix (Generation 7) — bipedal humanoid with Carbon AI reasoning system.
• 1X Technologies NEO Beta / NEO — soft-skinned home humanoid.
• Agility Robotics Digit V4 — bird-legged humanoid for warehouse (Amazon pilot, GXO).
• Unitree H1, G1, R1 — relatively affordable humanoids (~$16k for G1).
• Fourier Intelligence GR-1, GR-2 — Chinese humanoid.
• XPENG Iron — Chinese auto-OEM humanoid.
• UBTECH Walker S1 / S2 — Chinese factory humanoid.
• Sanctuary Carbon Phoenix — newer iteration.
• Engineered Arts Ameca — face + bust expressive humanoid (no legs, for HRI/demo).
• Disney Imagineering — internal humanoid characters pre-2024.

14. Quadruped (for completeness)

Not strictly manipulators, but increasingly used as manipulator carriers (Spot + Arm pattern).

• Boston Dynamics Spot — the reference industrial quadruped.
• ANYbotics ANYmal C, ANYmal D, ANYmal X (ATEX-rated) — petrochemical inspection.
• Unitree A1, Go1, Go2, Aliengo, B1, B2 — consumer to industrial.
• MIT Mini-Cheetah, Cheetah 3 — research.
• Ghost Robotics Vision-60, Vision-100 — defense quadruped.
• DEEP Robotics (Hangzhou) — Lite3, X20, X30 (industrial).
• Xiaomi CyberDog 1 / 2 — consumer.
• Tencent Robotics X Max — research.

15. Dual-arm (two arms on one torso/base)

Two coordinated manipulators on a shared base — for bimanual assembly, parts mating, cloth/cable handling, or human-mimicking tasks.

• ABB YuMi IRB 14000 — 7+7 = 14 DoF, the original collaborative dual-arm (2015), 0.5 kg per arm. YuMi IRB 14050 (single-arm cousin).
• Yaskawa Motoman SDA10F / SDA20F — 7+7 DoF dual-arm with rotating torso (15 DoF total), 10/20 kg per arm. CSDA10F is the cleanroom variant.
• Rethink Robotics Baxter — 7+7 DoF dual-arm (the 2012 cobot pioneer); discontinued 2018, but many still in research labs.
• Kawasaki duAro2 — dual SCARA on rotating column, fast PCB-style dual pick-place.
• ABB GoFa duo — two GoFa 6-DoFs side-by-side.
• Kuka Bigfoot demos — two KR-series arms on shared base.
• Universal Robots dual-UR setup — two UR5e or UR10e on a shared frame (SI-assembled).
• PAL TIAGo++ — mobile dual-arm.
• Humanoid bust manipulators (no legs, just torso + dual arms + head): Sanctuary Phoenix, 1X NEO upper body — counted under humanoid above but functionally dual-arm.
• Stäubli + Stäubli pairs for surgical-style bench.

16. DoF / structure cheat-table

Topology	DoF	Typ reach	Typ payload	Repeat	Common use
6-DoF artic small	6	500-900 mm	3-8 kg	±0.02 mm	Small assembly, electronics
6-DoF artic mid	6	1.5-2.0 m	10-50 kg	±0.05 mm	General industry, welding
6-DoF artic heavy	6	2.5-3.5 m	150-800 kg	±0.1 mm	Auto BIW, foundry
6-DoF cobot	6	0.5-1.7 m	3-30 kg	±0.05-0.1 mm	HRC, light assembly
7-DoF cobot/research	7	0.7-1.3 m	4-14 kg	±0.1 mm	Redundancy, research
SCARA small	4	120-450 mm	2-5 kg	±0.01 mm	PCB, dispensing
SCARA mid	4	450-1000 mm	5-20 kg	±0.02 mm	Assembly, pick-place
4-axis palletizer	4	2.4-3.2 m	100-700 kg	±0.2 mm	Bag/box palletizing
Delta small	3-4	800-1200 mm dia	0.5-3 kg	±0.05 mm	High-speed pick-place
Delta mid	4	1300-1600 mm dia	6-8 kg	±0.1 mm	Food/pharma packaging
Stewart hexapod precision	6	±50-100 mm	1-100 kg	sub-μm	Optical, semiconductor
Stewart hexapod simulator	6	±0.5-1 m	1-15 t	±1 mm	Flight/driving sim
Cartesian gantry small	3-5	0.5-2 m	5-20 kg	±0.02 mm	Lab automation, CNC
Cartesian gantry large	3-5	2-30 m	20-2000 kg	±0.1 mm	Big-part machining
Cylindrical (legacy)	3+1	1 m	5-50 kg	±0.1 mm	Legacy assembly/load
Polar (legacy)	3+R	2-3 m	50-200 kg	±0.3 mm	Historical only
Hybrid Tricept	5-6	1-2 m	100-500 kg force	±0.05 mm	Aerospace drilling
Mobile + arm	6-9	base 0-∞ + arm reach	5-30 kg arm	±2-10 mm	Logistics, lab service
Humanoid arm	6-7 ea	~0.7-0.9 m ea	5-25 kg ea	±1-3 mm	R&D, manufacturing pilots
Quadruped + arm	6+	0-∞ base, 0.7 m arm	3-7 kg arm	±5-10 mm	Inspection + sampling
Dual-arm YuMi-class	7+7	559 mm each	0.5 kg ea	±0.02 mm	Bimanual small assembly
Dual-arm SDA20F	7+7+1	1.4 m	20 kg ea	±0.1 mm	Bimanual large assembly
Delta + R (4th axis)	4	1100-1600 mm dia	3-6 kg	±0.1 mm	Pick-place w/ orientation

17. Singularities

A singularity is a manipulator configuration where the Jacobian loses rank — infinite/no-solution IK + unbounded joint speeds for finite Cartesian speeds.

Three classes for 6-DoF articulated arms:

• Wrist singularity — joints 4 and 6 become coaxial (joint-5 angle = 0 in many DH conventions). The wrist loses one rotational DoF. Mid-trajectory recovery is hard. Common in painting/welding when tool axis aligns with wrist last-axis direction.
• Elbow (boundary) singularity — arm fully extended (J3 at its kinematic limit). End-effector can’t move radially outward — Cartesian motion in that direction needs infinite joint speed.
• Shoulder singularity — wrist center crosses J1 axis (above/below the column). J1 must spin instantaneously through ±π for a finite Cartesian crossing speed.

7-DoF resolution: the extra null-space lets the internal joint (typically elbow) move while keeping the tool pose constant — sidestep singularity by re-configuring through it without changing tool trajectory.

Mitigation in software: singularity avoidance via manipulability gradient ascent, damped least-squares (Levenberg-Marquardt) IK, gradient projection for redundant arms, sigma-thresholded velocity scaling. Tied to [[Robotics/manipulability-workspace]].

18. Performance metrics (ISO 9283)

Repeatability (ISO 9283 RP) — variance returning to same commanded pose. Typical:

• Universal Robots e-series: ±0.05 mm (cobot).
• ABB IRB 1200: ±0.025 mm.
• ABB IRB 6700: ±0.05 mm.
• Stäubli TX2-60: ±0.020 mm (best-in-class industrial small).
• Industrial precision arms (Fanuc M-10iD/12, Yaskawa GP8): ±0.02-0.03 mm.
• Heavy industrial (KUKA KR Quantec 270 kg): ±0.05-0.08 mm.
• SCARA Epson G3/G6: ±0.005-0.01 mm (Z, X-Y combined).
• Delta ABB IRB 360: ±0.1 mm.
• Cobot mid (Doosan H2017): ±0.1 mm.
• Hexapod PI H-850: 0.3-1 μm depending on axis.

Accuracy (ISO 9283 AP) — variance from absolute commanded pose. Without calibration: 5-20× worse than repeatability. After kinematic + dynamic calibration (DHcal, robot-tracker laser, photogrammetry): can approach repeatability.

Other:

• Max payload — at full reach, distinguishing nominal vs maximum permissible inertia loading.
• Max reach — center-of-flange envelope.
• Maximum joint speeds — degrees/s per axis.
• Mass — robot self-weight, drives base-mounting choice.
• Ingress protection — IP54 (general factory), IP65 (washdown), IP67 (food), IP69K (high-pressure washdown), IP69 (medical).
• Hazardous-area rating — ATEX zone 1/2/21/22, Class I Div 1/2 (NEC) for painting/petrochemical.
• MTBF — typical industrial 6-DoF: 50,000-100,000 hr.

19. Selection heuristics

Task	Recommended topology
Bag / box palletizing	4-axis dedicated palletizer (ABB IRB 660, Fanuc M-410iC)
PCB / electronics assembly	SCARA (Epson G-series, Yamaha YK)
High-speed food/pharma pick-place	Delta (ABB IRB 360, Fanuc M-3iA, Codian D5)
Auto BIW spot welding	6-axis industrial (Fanuc R-2000iC, KUKA KR Quantec, Yaskawa MA-series)
Auto BIW arc welding	6-axis mid (Yaskawa MA1440, Panasonic TM2000, OTC FD-V8)
Spray painting	5-axis ATEX (Fanuc P-250iB, Yaskawa EPX)
Collaborative human-robot (HRC) light assembly	6-DoF cobot (UR5e/10e, Doosan M0617)
HRC research / redundancy	7-DoF cobot (KUKA iiwa, Franka FR3, Flexiv Rizon)
Aerospace high-stiffness drilling	Hybrid PKM (Tricept, Exechon)
Flight / driving simulator	Stewart-Gough hexapod (Moog, Bosch Rexroth)
Optical / semiconductor nm-positioning	Piezo hexapod (PI H-series) or piezo Cartesian
Semiconductor wafer transfer	SCARA (Brooks PreciseFlex) or vacuum SCARA
CNC-style machining envelope	Cartesian gantry (Aerotech, ISEL)
Big-part machining (wind blades, aerospace skins)	Gantry or 6-DoF on linear track
Lab pipette / liquid handling	Cartesian gantry + pipette head (Hamilton STAR, Tecan Fluent)
Warehouse truck-unload / box-pick	Purpose-built mobile manipulator (Boston Dynamics Stretch) or cobot+AMR
Hospital service	Mobile + arm (Diligent Moxi, TIAGo)
Bimanual small-parts assembly	Dual-arm (ABB YuMi, Yaskawa SDA10F)
Humanoid manufacturing R&D	Tesla Optimus, Figure 02, Atlas Electric, Apollo
Quadruped inspection w/ sampling	Spot + Arm, ANYmal + manipulator
Educational / desktop	Niryo Ned2, Dobot Magician, UR3e

20. Cross-references

• [[Robotics/manipulator-design]] — design-rule depth (link length, motor selection, harmonic-drive sizing).
• [[Robotics/manipulability-workspace]] — workspace analysis, Jacobian conditioning, manipulability ellipsoids.
• [[Robotics/parallel-manipulators]] — deep dive on parallel kinematics (delta + Stewart-Gough + planar).
• [[Robotics/cable-driven-robots]] — cable-suspended + cable-driven (CDPR) — a related parallel class not covered here.
• [[Robotics/humanoid-balance]] — bipedal locomotion + ZMP/DCM stability.
• [[Robotics/dynamic-locomotion]] — dynamic walking, running, quadruped gaits.
• [[Robotics/Tier3/motor-families]] — actuator families (BLDC, harmonic-drive, cycloidal, quasi-direct-drive).
• [[Robotics/Tier3/end-effectors-zoo]] — grippers, suction, magnetic, multi-finger hands.
• [[Robotics/Tier3/mobile-bases]] — diff-drive, omni, mecanum, Ackermann, legged.
• [[Robotics/safety-standards]] — collaborative-robot safety standards.
• [[Robotics/kinematics-dh]] — analytical (Pieper) + numerical IK.

21. Citations

• Siciliano, B.; Sciavicco, L.; Villani, L.; Oriolo, G. Robotics: Modelling, Planning and Control. 2nd ed., Springer 2009. The standard graduate text.
• Tsai, L.-W. Robot Analysis: The Mechanics of Serial and Parallel Manipulators. Wiley, 1999. Definitive for parallel kinematics.
• Merlet, J.-P. Parallel Robots. 2nd ed., Springer 2006. Comprehensive parallel-manipulator reference.
• Craig, J. J. Introduction to Robotics: Mechanics and Control. 4th ed., Pearson 2018. Undergraduate standard.
• Lynch, K. M.; Park, F. C. Modern Robotics: Mechanics, Planning, and Control. Cambridge 2017. Screw-theory-first approach.
• ISO 9283:1998 — Manipulating industrial robots — Performance criteria and related test methods. The repeatability/accuracy specification.
• ISO 10218-1/-2:2011 — Robots and robotic devices — Safety requirements for industrial robots. Part 1 robot, Part 2 system/cell.
• ISO/TS 15066:2016 — Robots and robotic devices — Collaborative robots. Force/pressure-limit values for HRC.
• Clavel, R. “Conception d’un robot parallèle rapide à 4 degrés de liberté.” PhD thesis, EPFL, 1991. The delta-robot reference.
• Gough, V. E. “Contribution to discussion of papers on research in automobile stability and control and in tyre performance.” Proc. Auto Div. IMechE, 1956-1957. The hexapod origin.
• Stewart, D. “A platform with six degrees of freedom.” Proc. IMechE, 1965.
• Pieper, D. L. “The kinematics of manipulators under computer control.” PhD thesis, Stanford, 1968. Closed-form 6-DoF IK criterion.
• Vendor product catalogs (current): abb.com/robotics, kuka.com, fanuc.com, motoman.com (Yaskawa), staubli.com, comau.com, universal-robots.com, franka.de, kinovarobotics.com, doosanrobotics.com, omron.com (Adept legacy), epson.com (robotics), denso-wave.com, kawasakirobotics.com, otc-daihen.de, hyundai-robotics.com, bostondynamics.com, agilityrobotics.com, neura-robotics.com, flexiv.com, kassowrobots.com.
• IFR (International Federation of Robotics) World Robotics Report, annual — market and installed-base statistics by topology.