Serial Manipulator Design — 6-DOF Arms, SCARA, Delta — Robotics Reference

Serial Manipulator Design — 6-DOF Arms, SCARA, Delta

See also (Tier 3 family index): Manipulator Topologies

1. At a glance

Manipulator design is the act of choosing a joint topology, sizing actuators + transmissions, picking a structural form, instrumenting it with sensors, and wrapping it in a safety layer such that the resulting machine meets a payload / reach / repeatability / cycle-time / cost specification. It is the first-principles output of a robotics program — the physical artefact that every downstream layer (kinematics, dynamics, control, perception, planning) is built on top of. Get it wrong here and no amount of clever software recovers.

As of 2026 the production landscape is dominated by three serial-arm classes plus two parallel / specialty classes:

• Articulated 6-DOF serial arm with spherical wrist — ~90 % of installed industrial base. Reach 0.5 m to 4 m, payload 0.5 kg to 2300 kg, repeatability ±0.02 mm to ±0.5 mm. Closed-form inverse kinematics. The reference architecture: Fanuc M-series, KUKA KR, ABB IRB, Yaskawa MotoMan, Stäubli TX, Universal Robots e-Series (non-spherical but Pieper-decomposable per Olsen 2018).
• 7-DOF redundant cobot — power-and-force-limited, torque-sensing in every joint, redundancy resolution for elbow placement. Franka FR3, KUKA LBR iiwa, Kinova Gen3, Kassow K-series, Doosan H-series.
• SCARA (4-DOF: 2R + 1P + 1R) — selective-compliance assembly-robot arm. Planar pick-and-place at 0.3–0.8 s cycle time. Epson G-series, Stäubli TS2, Yamaha YK, Mitsubishi RH.
• Delta parallel (3T + 1R, sometimes 4T+1R) — three (or four) parallel kinematic legs driving a light end platform. Highest acceleration density in robotics; 200+ picks/min at ≤ 3 kg payload. ABB IRB 360 FlexPicker, Fanuc M-1iA / M-3iA, Stäubli TP80, Kawasaki YF003N.
• Cartesian gantry (3P + optional wrist) — pure prismatic, trivial kinematics, very large workspace. Bosch Rexroth, Festo EXCM, Igus drylin.

Plus the specialised topologies that all share the same design vocabulary: surgical 7-DOF teleoperated arms (Intuitive da Vinci Xi, CMR Versius), humanoid arms (Tesla Optimus, Figure 02, 1X Neo, Apptronik Apollo, Unitree H1/G1), and cable-driven research arms (Barrett WAM, Whole-Arm Manipulator).

Where it sits in the design stack: above CAD + material selection, below kinematics and dynamics. The DH table that a kinematic analyst writes down describes a physical machine that someone has already designed; the inertia tensors that a dynamicist needs are computed from a CAD solid that someone has already drawn. Manipulator design owns those upstream artefacts.

First ask before turning a knob in CAD:

1. What is the payload-reach-repeatability triplet the application demands? A 5 kg / 1 m / ±0.05 mm cobot is a different machine from a 50 kg / 2 m / ±0.5 mm industrial arm.
2. What is the cycle time target? Cycle time selects topology before payload does — a 0.3 s pick-and-place rules out 6-DOF serial, a 30 s assembly task rules out delta.
3. Human interaction? Cobot (ISO/TS 15066) vs caged industrial (ISO 10218-1/-2). Drives torque-sensing requirement, max joint speed, structural padding, and 5× the per-axis cost.
4. Backdrivability? Required for compliant manipulation, prosthetics, surgical force feedback. Rules out high-ratio harmonic drives unless paired with joint torque sensing.
5. Cleanroom / pharma / food / explosive atmosphere? Drives sealing rating (IP65 / IP67 / IP69K), wash-down compatibility, lubricant grade, materials list, and entire-arm cost.

2. First principles

Kinematic topology choice

A serial chain’s joint sequence determines its workspace shape, IK class, and singularity structure. Six common shapes:

• Serial 6R with spherical wrist — three “base” axes (${\theta }_1$ shoulder-yaw, ${\theta }_2$ shoulder-pitch, ${\theta }_3$ elbow) position the wrist; three intersecting “wrist” axes (${\theta }_4,{\theta }_5,{\theta }_6$) orient the tool. Pieper’s criterion satisfied (1968) ⇒ closed-form IK exists. Workspace is quasi-spherical. Eight IK solutions per pose generically.
• Serial 7R redundant — one extra joint creates a self-motion null-space. The elbow lies on a circle (“swivel circle”) around the shoulder-to-wrist line; parameterising the swivel angle reduces redundant IK to a one-parameter family of 6-DOF Pieper solves. Lets the controller avoid joint limits, obstacles, and singularities while preserving end-effector path.
• SCARA — RRPR — two parallel revolute joints (${\theta }_1,{\theta }_2$) for X-Y reach, one prismatic ($d_3$) for Z, one revolute (${\theta }_4$) for tool yaw. Rigid in Z (peg-in-hole assembly), fast in X-Y, no tool tilt. Closed-form IK is a two-link planar problem.
• Delta 3-RUU parallel — three identical revolute-universal-universal legs constrain the platform to pure translation by a parallelogram structure. Forward kinematics requires solving an 8th-order polynomial (Merlet 2006); inverse kinematics is three independent sphere-intersections. Very low moving mass (the heavy actuators live at the base).
• Cartesian 3P — three orthogonal prismatic axes. FK and IK are coordinate identities. Largest accessible workspace per dollar; orientation requires a wrist add-on.
• Cable-driven (Barrett WAM-style) — cables route from base-mounted motors through the arm to drive distal joints. Minimal moving mass, intrinsically backdrivable, low inertia, but compliant (cables stretch) and routing-limited.

Workspace + payload

The reachable workspace is the swept volume of all end-effector positions over the joint range. For a generic serial 6R arm with link lengths $L_2,L_3$ (upper arm, forearm) and wrist offsets, the workspace is bounded by a torus-like volume of outer radius $L_2+L_3$ and inner radius $|L_2-L_3|$. The dexterous workspace (subset reachable in any orientation) is much smaller — typically 30–50 % of the reachable volume.

Payload–reach trade. Industrial arms cluster around a 1:10 payload-to-reach ratio: 5 kg @ 850 mm cobot, 50 kg @ 2.05 m KR50, 1500 kg @ 3 m KUKA Titan. The ratio is set by joint-2/3 torque: gravity scales as $\tau =m_{\text{payload}}\cdot g\cdot L_{\text{reach}}$, so doubling reach doubles required torque at fixed payload.

Cycle time and acceleration density. A pick-and-place benchmark (Adept 25-305-25 mm or 25-100-25 mm) measures end-effector throughput. Cycle time is dominated by joint acceleration, not maximum joint velocity — the trajectory rarely reaches top speed on short moves. Acceleration in turn is set by ${\tau }_{\text{peak}}/J_{\text{reflected}}$; harmonic-drive arms (high ratio, high reflected inertia at the joint output) accelerate slower than direct-drive deltas at the same payload.

Repeatability vs accuracy

ISO 9283:1998 defines:

• Pose repeatability $RP$ — the radius of the smallest sphere that contains all measured TCP positions when commanded to the same target N times. Industrial-arm spec is typically ±0.02 mm (Stäubli TX2) to ±0.1 mm (KR1000). Sources: encoder resolution, gearbox lost motion, thermal drift, control loop noise.
• Pose accuracy $AP$ — the distance between commanded target and the centroid of measured positions. Uncalibrated factory arms run ±0.5 mm to ±5 mm. Sources: manufacturing tolerances on link lengths, gear ratios, encoder zero offsets. Closes to ±0.1 mm after kinematic calibration (Hayati 1985).

Repeatability is given for free by the encoder + gearbox; accuracy is bought by calibration. Most controllers ship with a 24-to-28-parameter kinematic identification routine — laser tracker (Leica AT960, FARO Vantage) or stereo-vision rig measures the TCP across 30–100 poses, an optimiser identifies the corrections to the nominal DH parameters.

Stiffness

Joint compliance:

$K_{\text{joint}}=\frac{\tau }{\Delta \varphi }$

is set by gearbox stiffness (harmonic drive ~10⁴ N·m/rad, cycloidal ~10⁵ N·m/rad), encoder coupling, and motor-shaft windup. Link stiffness is structural — a hollow aluminium tube of length $L$, OD $D$, wall $t$ has cantilever stiffness $K_{\text{link}}=3EI/L^3$. Series compliance combines: $1/K_{\text{total}}=1/K_{\text{joint}}+1/K_{\text{link}}$.

Deflection under payload $\delta =F/K$ shows up as a pose-dependent accuracy error — looks like a calibration bug but is actually structural. The standard fix is either stiffer structure (CFRP forearm, ribbed castings) or measurement-based compensation (laser interferometer feedback à la KUKA KR-Reference).

Safety

Two regulatory worlds in 2026:

• Caged industrial — ISO 10218-1:2025 (robot) and ISO 10218-2:2025 (robot system). Hard guards, light curtains, area scanners, dual-channel safety PLC, brake-on-power-loss, redundant encoders for safety-rated speed monitoring.
• Cobot, collaborative operation — ISO/TS 15066:2025. Four modes: safety-rated monitored stop, hand-guiding, speed and separation monitoring, power and force limiting (PFL). PFL is the dominant mode for Franka, iiwa, UR — limits transient + quasi-static forces to biomechanical thresholds (Annex A of the spec: ~150 N transient on the forearm, ~140 N on the back of the hand, etc.).

The PFL biomechanical thresholds (Haddadin 2009, the experimental basis for Annex A of ISO/TS 15066) come from cadaver impact studies plus human volunteer pressure-pain tests; they distinguish quasi-static (clamping, pinching) from transient (free-space collision) contacts because the pain threshold for the former is roughly half the latter. Concrete numbers for the back of the hand: 280 N transient / 140 N quasi-static; for the upper arm: 300 N transient / 150 N quasi-static; for the face: cobot operation is prohibited at face level — only safety-rated monitored stop applies.

A cobot meeting PFL through the kinematic-energy route uses $E_K=\frac{1}{2}{m}_{\text{eff}}{v}^2\le 65$ J max, with $m_{\text{eff}}$ the effective body-part mass at the contact direction and $v$ limited by controller-enforced TCP speed (commonly 250 mm/s when sharing workspace with a human, raised to design speed when scanners report no human presence). A 10 kg cobot moving at 250 mm/s carries 0.3 J — three orders of magnitude under the threshold.

3. Practical math + worked examples

Example A — 6-DOF arm joint-1 sizing from spec

Spec: payload $m_p=5$ kg, reach $R=1.0$ m, repeatability ±0.05 mm, target pick-place cycle 1 s.

Step 1 — gravity torque on joint 2 (shoulder pitch). Worst case: arm horizontal, payload at full reach. Approximate link masses: upper arm 4 kg at 0.3 m COG; forearm 3 kg at 0.7 m COG; wrist + flange 2 kg at 0.95 m COG.

${\tau }_{\text{grav}}=m_{p}gR+\sum m_{i}g{L}_i$ $=5\cdot 9.81\cdot 1.0+4\cdot 9.81\cdot 0.3+3\cdot 9.81\cdot 0.7+2\cdot 9.81\cdot 0.95$ $=49.05+11.77+20.60+18.64\approx 100\text{ Ncdotpm}$

Step 2 — inertial torque for the cycle. Assume joint 2 must accelerate the arm + payload through 60° in 0.5 s with trapezoidal profile (peak $\dot{\theta }=4.2$ rad/s, $\ddot{\theta }=17$ rad/s²). Reflected joint inertia:

$J=m_p{R}^2+\sum m_i{L}_i^2=5\cdot 1.0+4\cdot 0.09+3\cdot 0.49+2\cdot 0.9025\approx 8.6{\text{ kgcdotpm}}^2$

${\tau }_{\text{accel}}=J\ddot{\theta }=8.6\cdot 17\approx 146\text{ Ncdotpm}$

Step 3 — peak joint torque. Sum (worst case overlaps): ${\tau }_{\text{peak}}=100+146=246$ N·m. Continuous (gravity only): 100 N·m.

Step 4 — select transmission. Harmonic Drive CSF-32-100 (size 32, ratio 100:1): rated output 178 N·m continuous, momentary peak 433 N·m, lost motion ≤ 1.5 arc-min. Pass on peak; mildly over on continuous → step up to CSF-40-100 (rated 281 N·m continuous, peak 686 N·m).

Step 5 — select motor. Reflected continuous torque at motor with $\eta =0.75$: ${\tau }_{\text{motor}}=100/(100\cdot 0.75)=1.33$ N·m. Peak: 246 / 75 = 3.28 N·m. Maxon EC-i 70 frameless (90 mm OD, K_T = 0.13 N·m/A, continuous 1.5 N·m, peak ~6 N·m at 30 A) — pass.

Step 6 — output speed check. Cycle requires $\dot{\theta }=4.2$ rad/s = 40 rpm at joint output. Motor side: 40 × 100 = 4000 rpm. EC-i 70 no-load at 48 V is 5800 rpm — pass.

Step 7 — encoder. Renishaw Aksim2 19-bit absolute on the joint output (524 288 counts/rev → 0.69 arcsec resolution → ±2 µm at 1 m reach). Second 17-bit encoder on motor shaft for FOC commutation and safety-rated speed monitoring.

Example B — SCARA cycle-time analysis

The Adept 25-305-25 mm benchmark cycle: 25 mm up, 305 mm horizontal, 25 mm down, hold gripper 50 ms, reverse. With trapezoidal profile, peak acceleration $a$ and peak velocity $v_{\text{max}}$:

For a single 305 mm move with $a=80$ m/s² (8 g — modern SCARA target) and $v_{\text{max}}=6$ m/s:

• Time to reach $v_{\text{max}}$: $t_a=v_{\text{max}}/a=6/80=0.075$ s; distance covered in accel: $d_a=v_{\text{max}}^2/(2a)=36/160=0.225$ m. Move is 0.305 m, so a brief constant-velocity phase exists: $d_v=0.305-2\cdot 0.225=-0.145$ — negative means the move is too short to hit top speed. Use triangular profile instead.
• Triangular: $t=2\sqrt{d/a}=2\sqrt{0.305/80}=0.123$ s for the horizontal move.
• Two 25 mm vertical moves: $t=2\sqrt{0.025/80}=0.0354$ s each → 0.071 s combined.
• Two horizontal moves (out + back) plus two vertical (down + up) plus gripper hold 0.05 s × 2: total $2\cdot 0.123+2\cdot 0.0354\cdot 2+0.1=0.246+0.141+0.1=0.487$ s, round up to ~0.5 s/cycle.

A modern Stäubli TS2-40 or Yamaha YK250XGL is published at 0.29–0.35 s on this benchmark, hitting it by stretching peak acceleration toward 10–12 g and tuning the jerk profile.

Example C — Delta robot pick rate and IK

ABB IRB 360 FlexPicker: payload 1 kg, hemispherical workspace 1130 mm diameter, 200 picks/min sustained.

Per-pick cycle 0.3 s; the FlexPicker uses S-curve jerk-limited trajectories with peak end-effector acceleration ~100 m/s² (10 g). The three parallel RUU legs each see a relatively small actuated angle change (~30° per pick); the inverse kinematics for each leg, with upper-arm length $L_a=350$ mm and lower-arm parallelogram length $L_b=800$ mm, reduces to sphere-intersection. For platform position $(x,y,z)$ and leg $i$ at base angle ${\varphi }_i=120°(i-1)$:

${\theta }_i=atan2(z_i^{\prime },x_i^{\prime })-\arccos \left(\frac{L_a^2+r_i^2+z_i^{\prime 2}-L_b^2}{2L_a\sqrt{r_i^2+z_i^{\prime 2}}}\right)$

where $(x_i^{\prime },z_i^{\prime })$ are the platform coordinates rotated into leg $i$‘s working plane and $r_i$ accounts for the platform end-joint offset. Closed-form per leg, ~5 µs each on a 1 GHz controller; the limiting factor is servo update (4 kHz), not IK.

Calibration: each leg’s $L_a,L_b$ and base-joint position is identified separately by touching the end platform against a reference probe at 20–30 poses; a Levenberg-Marquardt solver fits the geometric parameters to ±0.05 mm RMS.

Throughput math: 200 picks/min = one pick every 0.3 s. Two short straight-line moves at peak 10 g end-effector acceleration cover the typical 100–300 mm pick-place stroke in under 200 ms; the residual 100 ms goes to gripper open/close (vacuum on/off in 30–50 ms) and trajectory blending. ABB’s spec sheet for IRB 360-1/1130 cites 76 cycles/min on the “Adept 25-700-25 mm” cycle (longer stroke), which is the practically relevant number for case-packing applications.

4. Design heuristics

Topology selection

• 3D motion in a fixed workspace, sub-second cycle not critical → 6-DOF arm. Default to spherical wrist for closed-form IK.
• Planar pick-and-place of small parts → SCARA. 4-DOF is enough for 80 % of these tasks; cycle time and Z-axis stiffness are unmatched.
• Very high speed, light payload (≤ 3 kg), small footprint → delta parallel. Accept the smaller workspace.
• Large workspace, simple kinematics → Cartesian gantry. Cheapest dollars-per-m³ of any topology.
• Human collaboration in the same workspace → 7-DOF cobot with per-joint torque sensing. PFL mode via ISO/TS 15066.
• Dexterous / surgical / dual-arm coordination → 7-DOF redundant. Pay for the seventh joint.

Actuator + transmission

• High-payload industrial: brushless servo + RV cycloidal reducer (Nabtesco RV-N or RV-C) for joints 1–3, harmonic drive for joints 4–6. Cycloidal handles shock and overhung load better; harmonic is more compact for wrist joints.
• Cobot: brushless servo + harmonic drive (CSF or CPL) on every joint + joint torque sensor (ATI TIA / Sensitec / OEM strain-gauge ring). The torque sensor closes the PFL safety loop.
• High-speed delta: direct-drive permanent-magnet servo on each leg, no gearbox. Backlash is zero; cycle-time benefits from minimum reflected inertia.
• Backdrivable joints (cobot wrist, prosthetic, legged QDD): low-ratio (6:1 to 10:1) planetary, or transparent harmonic drive (Harmonic Drive HD or HD-LW with low friction), or cable-and-capstan.
• Surgical (patient-side): no gears in the sterile field. Cable-and-capstan transmission to base-mounted actuators (da Vinci pattern); enables sterilisable, low-mass, intrinsically backdrivable distal joints.

Structural design

• Aluminium 6061-T6 or 7075-T6 castings/billet — workhorse for industrial-arm links. High specific stiffness, machinable, ~100 MPa fatigue limit, cost ~$5–15/kg machined.
• Carbon-fibre-reinforced polymer (CFRP) tubes — long-reach arms (2 m+). Specific stiffness 5× aluminium; reduces moving mass and raises first natural frequency. Common in 6-DOF arms targeting reach > 1.5 m at moderate payload (Stäubli RX160L, ABB IRB 6700).
• Invar / graphite — inspection-grade arms (Renishaw REVO, FARO Edge, Hexagon ROMER). Thermal expansion ~10⁻⁶ /K vs aluminium’s 23·10⁻⁶ /K → negligible thermal drift in a temperature-uncontrolled shop floor.
• Hollow shaft routing — cables, pneumatics, data lines route through the centre of each joint. UR, KUKA Iontec, Franka, Stäubli all do this; eliminates the swinging external harness that abrades and snags. Adds gearbox cost (hollow-shaft variants are 20–30 % pricier) but is now industry-standard.
• Modular joint design (HEBI, Dynamixel, Maxon IDX) — each joint is a self-contained drive + encoder + comms module. Rapid prototyping and field-replacement. Cost premium ~3× vs custom for high-volume builds.

Repeatability budget

A reasonable budget for ±0.05 mm cobot repeatability at 1 m reach:

Source	Contribution at TCP	Note
Encoder resolution (19-bit on output)	±2 µm	At 1 m, $5\cdot 10^{-6}$ rad × 1 m
Harmonic-drive lost motion	±15 µm	30 arcsec at output ≈ 0.15 mrad × 1 m
Structural deflection at 5 kg	±20 µm	$K_{\text{link}}\approx 5\cdot 10^6$ N/m typical
Thermal drift, 5 °C swing	±10 µm	Aluminium $\alpha =23\cdot 10^{-6}/\text{K}$, $\Delta L=\alpha L\Delta T$ for $L=1$ m, $\Delta T=0.5$ K
Controller noise + delays	±5 µm	1 kHz loop, well-tuned
RSS total	±28 µm	Within ±50 µm budget

Calibration

The Hayati–Mirmirani 1985 model identifies 4 base + 4 × (n−1) per-link + 6 tool = 26 parameters for a 6-DOF arm with one parallel-axes pair. Procedure:

1. Mount a high-accuracy probe on the TCP (or a vision target).
2. Drive to N ≥ 30 well-distributed poses spanning the dexterous workspace.
3. Measure TCP position (laser tracker, indoor GPS, calibrated stereo).
4. Identified parameter vector $\mathbf{\xi }$ minimises ${\sum }_k\Vert {\mathbf{p}}_{\text{meas}}(k)-{\mathbf{p}}_{\text{model}}({\mathbf{q}}_k,\mathbf{\xi }){\Vert }^2$ by Levenberg-Marquardt.
5. Push the identified $\mathbf{\xi }$ into the controller’s kinematic model.

Result: typical drop from ±2.5 mm to ±0.15 mm accuracy. Repeatability is unchanged (it’s a different error class).

Cable + power routing

External cable harnesses (looped from base to wrist along the outside of the arm) abrade against link surfaces, snag on the workpiece, and have a finite flex life — typically 5–10 million cycles before the inner conductors fatigue. Internal routing through hollow joints (UR e-series, KUKA Iontec, Franka, ABB Lean ID) extends life to 50+ million cycles and removes the snag risk entirely. Always specify the cable bend radius in the joint design; data + power lines have published minimum bend radii (igus chainflex CF77 = 7.5×OD for continuous flex).

Brake sizing

Every gravity-loaded joint needs a brake that holds the maximum static torque with a safety factor. The Mayr ROBA-stop-M 891.110 holds 13 N·m at the motor shaft — through a 100:1 harmonic drive this becomes 1300 N·m at the joint output (ignoring back-driving efficiency), more than enough for any joint that’s downstream of a 100 N·m gravity load. ISO 10218-1 requires the brake to engage on any loss of power or safety signal within the controller’s specified single-fault response time (typically ≤ 250 ms); test interval is annual at minimum, monthly for surgical / aerospace.

Workspace orientation

A wall-mounted arm doubles the effective vertical reach but adds a constant lateral gravity load on joint 1 — sizing joint 1 for wall mount is closer to industrial sizing for joint 2 of a floor-mounted arm. A ceiling-mounted (inverted) arm has the workspace below the base; gravity reverses sign on every joint. Always declare the mount orientation to the controller (UR safety_setup_set_mount, KUKA \$ROBROOT, Fanuc \$MNUTOOLNUM + gravity vector) — wrong mount means wrong gravity compensation, which manifests as a constant offset force on every contact and ruins force control.

Modularity vs custom

Approach	Time-to-prototype	Per-unit cost (5 kg cobot joint)	Maintainability	When to pick
Modular smart joint (HEBI X-8-9, Maxon IDX, Dynamixel-Pro)	Days	$1500–$4000	Field-swap module	Research, < 100 units, fast iteration
OEM joint module (Kollmorgen TBM + harmonic + drive)	Weeks	$800–$2500	Reasonable	Mid-volume, 100–1000 units
Fully custom integrated joint (Franka pattern)	Months	$300–$900 at volume	Difficult	Mass production, > 5000 units

5. Components & sourcing

Industrial 6-DOF arms by payload class

Payload class	Representative models	Reach	Repeatability
Mini (< 1 kg)	Yaskawa MotoMini, ABB IRB 120, KUKA Agilus KR3 R540	0.35–0.58 m	±0.02 mm
Small (1–5 kg)	Fanuc LR Mate 200iD/4S, ABB IRB 1200-5/0.9, KUKA KR6 R900, Stäubli TX2-40	0.7–0.9 m	±0.02 mm
Medium (5–20 kg)	UR5e/UR10e/UR16e, KUKA KR10/16 R900, Fanuc M-10iD, ABB IRB 1300, Doosan M0509	0.85–1.4 m	±0.03–0.05 mm
Large (20–50 kg)	Fanuc M-20iD/35, KUKA KR 50 R3100, ABB IRB 4600, Yaskawa GP25	1.6–2.1 m	±0.05–0.07 mm
Heavy (50–500 kg)	Fanuc M-2000iA, KUKA KR 500-2, ABB IRB 6700	2.4–3.5 m	±0.05–0.15 mm
Super-heavy (500–2300 kg)	KUKA KR 1000 Titan, Fanuc M-2000iA/2300, ABB IRB 8700	3.0–4.2 m	±0.1–0.3 mm

7-DOF cobots (redundant)

• Franka Emika FR3 (Panda successor, 2024) — 7 axes, 3 kg payload, torque sensing on every joint, libfranka 0.13 + franka_ros2 API.
• KUKA LBR iiwa 7 R800 / 14 R820 — torque sensors on all 7 axes, KRC5 controller, KUKA Sunrise.OS, 7 / 14 kg payload.
• Kassow Robotics K850, K1101, K1410, K1805 — 7-DOF, payload 5–18 kg, reach 850–1800 mm.
• Kinova Gen3 (7-DOF) / Gen3 lite (6-DOF) / Link 6 — lightweight, popular in research and rehabilitation robotics.
• Doosan H-series — H2017 (7-DOF, 20 kg, 1700 mm).

6-DOF cobots (non-redundant, PFL-rated)

• Universal Robots e-series: UR3e, UR5e, UR10e, UR16e, UR20, UR30. 50+ k units installed, the reference architecture.
• Doosan A-series: A0509, A0912, A0509s.
• Techman Robot TM5/TM12/TM14 — integrated vision.
• AUBO i5/i10/i20 — Chinese-market cobot.
• Elite EC66 / CS66 — value-tier.

SCARA

Make / model	Payload	Reach	Adept cycle
Epson G6 / T6	6 kg	600 mm	0.35 s
Stäubli TS2-40 / TS2-60 / TS2-80	4 / 6 / 8 kg	400–800 mm	0.29 s (TS2-40)
Yamaha YK250XGL / YK400XR	1–5 kg	250–800 mm	0.32 s
Mitsubishi RH-3FHR / RH-12FH	3–12 kg	350–700 mm	0.30–0.38 s
Omron i4H	25 kg	1200 mm	0.50 s

Delta parallel

• ABB IRB 360 FlexPicker — 1 / 3 / 6 / 8 kg variants, 1130 mm Ø workspace, 200 picks/min.
• Fanuc M-1iA / M-2iA / M-3iA — 0.5 / 6 / 12 kg payload deltas; M-1iA is 6-DOF (3T+3R).
• Stäubli TP80 — 1 kg, 800 mm Ø workspace, 200 picks/min.
• Kawasaki YF003N / Hitachi BR-1 — 1–3 kg, food-grade IP65.
• Codian D2 / D4 — Eurotech / Codian, lightweight delta.

Cartesian gantry

• Festo EXCM — small XY gantry, integrated drives.
• IAI Robo-Cylinder Tabletop — three-axis tabletop SCARA-replacement.
• Bosch Rexroth EasyHandling — modular Cartesian system.
• Igus drylin E — low-cost polymer-bearing gantries.

Surgical and medical

• Intuitive Surgical da Vinci Xi / SP — 7-DOF EndoWrist patient-side arms, teleoperated.
• Medtronic Hugo — modular four-arm surgical platform, 2024 EU release.
• CMR Versius — bedside-cart-mounted 6+ DOF arms with wristed instruments.

Humanoid arms (2025–2026 wave)

• Tesla Optimus Gen 2 — 28-DOF total robot, per-arm published torques at AI Day 2024.
• Figure 02 — proprietary 7-DOF arm, partnership with BMW.
• 1X Technologies Neo — soft-tissue cobot-style arm for home use.
• Apptronik Apollo — 7-DOF arms, Mercedes-Benz partnership.
• Unitree H1 / G1 — open-architecture humanoid, ~7 kg payload per arm.
• Sanctuary AI Phoenix — 21-DOF hand + 7-DOF arm.
• Boston Dynamics Atlas (electric, 2024) — research humanoid, ~9-DOF per arm.
• NASA Valkyrie, IIT WALK-MAN, AIST HRP-5P — government / academic.

Component vendors

Part class	Vendors	Notable products
Frameless servo motors	Allied Motion, Kollmorgen TBM, Moog FASTACT, Maxon EC-i, RoboDrive ILM	Allied Motion Megaflux MF0095; Kollmorgen TBM-7615
Geared servo	Maxon DCX/EC-i + GP gearhead, Faulhaber DC, Mitsubishi HG, Yaskawa Sigma-7	Sigma-7 SGM7J
Harmonic drives	Harmonic Drive LLC (US) / Sumitomo (JP)	CSF series, CSG series, SHF/CPL
Cycloidal reducers	Nabtesco, Sumitomo, Shimpo, Spinea	RV-N, RV-C; TwinSpin
Planetary gearboxes	Wittenstein alpha, Apex Dynamics, Neugart, Bonfiglioli	TP+, AB-series
Joint encoders	Renishaw RESOLUTE / Aksim2, Heidenhain ECN / ECI, RLS, Netzer	Aksim2 19-bit, ECN 1325
Torque sensors	ATI Industrial Automation (TIA), Sensitec, OnRobot HEX, Bota Systems	ATI Axia-80, Bota Rokubi
Brakes	Mayr ROBA-stop, Kendrion, Mönninghoff	ROBA-stop-M 8911
End-effectors	Schunk, OnRobot, Robotiq, SMC, Festo, Soft Robotics	Robotiq 2F-85, OnRobot RG6
Controllers	B&R, Beckhoff TwinCAT, Elmo Motion (Gold Twitter), Synapticon SOMANET, Granite Devices IONI	Elmo G-TWI-15/100; Synapticon SOMANET Node 1000

6. Reference data

Repeatability vs payload vs reach (catalogue published)

Robot	Reach (mm)	Payload (kg)	Repeatability (mm)	Cycle benchmark
Stäubli TX2-40	515	1.7	±0.020	—
Fanuc LR Mate 200iD/4S	550	4	±0.020	0.32 s (Adept 25-305-25)
UR5e	850	5	±0.030	—
KUKA KR 10 R900-2	901	10	±0.030	—
ABB IRB 1300-10/1.15	1150	10	±0.020	—
Franka FR3	855	3	±0.050	—
KUKA LBR iiwa 7 R800	800	7	±0.100	—
Fanuc M-20iD/25	1831	25	±0.030	—
ABB IRB 6700-200/2.60	2600	200	±0.050	—
KUKA KR 1000 Titan	3202	1300	±0.110	—

Cobot torque-sensing capability

Cobot	Torque sensor per joint	Sensor type	PFL-rated
Franka FR3	All 7	Strain-gauge ring at output	Yes
KUKA LBR iiwa 7/14	All 7	Strain-gauge ring	Yes
Kassow K-series	All 7	Strain-gauge	Yes
UR e-series	None per-joint (current-based estimation)	Motor current + Cartesian F/T option	Yes (via current model)
Doosan A/M/H	All 6 (M, H), none (A)	Strain-gauge	Yes
Kinova Gen3	All 7	Strain-gauge	Limited PFL
Techman TM	None per-joint	End-of-arm F/T	Limited

Cycle-time benchmarks (Adept 25-305-25 mm, 1 kg)

Robot	Class	Published cycle (s)
Stäubli TS2-40	SCARA	0.29
Yamaha YK250XGL	SCARA	0.32
Epson G6-453S	SCARA	0.31
ABB IRB 360-1/1130	Delta	0.30
Fanuc M-1iA/0.5	Delta	0.28
Stäubli TP80	Delta	0.30
Fanuc LR Mate 200iD	6-DOF	0.38
UR3e	6-DOF cobot	0.55

Joint stiffness ranges by gearbox class

Transmission	Output stiffness (N·m/rad)	Lost motion	Backdrivable?
Direct-drive (frameless servo)	~∞ (motor stiffness only)	0	Yes
Low-ratio planetary (6:1–10:1)	10⁴–10⁵	1–3 arcmin	Yes (QDD)
Harmonic drive CSF/CSG	1–5 × 10⁴	20–60 arcsec	Marginal (~15–25 % efficiency reverse)
Cycloidal RV	5 × 10⁴–2 × 10⁵	1 arcmin	No
High-ratio planetary (50:1+)	5 × 10³–10⁴	3–10 arcmin	No
Worm	10³–10⁴	5–30 arcmin	No (self-locking)
Cable-capstan	10³–10⁴	0 (cable stretch only)	Yes

Joint topology decision table

Constraint	Topology
Sub-second pick of < 3 kg	Delta or SCARA
Sub-second pick of 5–20 kg	SCARA (planar) or fast 6-DOF
General 3D motion, payload 1–50 kg	Spherical-wrist 6-DOF
Human collaboration, mid payload	7-DOF cobot (Franka, iiwa, Kassow)
Singularity avoidance critical	7-DOF redundant
Multi-tonne payload	Heavy 6-DOF (KR 1000, M-2000)
Very large workspace, simple motion	Cartesian gantry
Wall- or ceiling-mounted	6-DOF (inverted) or delta
Surgical / inside human body	Cable-driven 7-DOF

Typical link-mass distribution (5 kg cobot, 850 mm reach)

Link	Mass (kg)	COG from prev joint (mm)	Material
Base + joint 1 housing	7.0	—	Cast aluminium A356-T6
Shoulder (link 1, joint 2)	4.5	120	A356-T6
Upper arm (link 2)	3.8	200	6061-T6 tube + cast ends
Forearm (link 3)	2.6	180	6061-T6 tube
Wrist (joints 4, 5, 6)	2.2	100	7075-T6 billet
Total moving mass	13.1	—	—
Payload + EOAT	5 + 1	—	—
Total moving + payload	19.1	—	—

Total robot mass with base, controller cable, brakes, encoders: ~24 kg — matches the published mass of UR5e (20.6 kg without controller).

Servo loop bandwidths (typical)

Loop	Sample rate	Crossover	Notes
FOC current (inner)	10–40 kHz	1–5 kHz	Set by PWM frequency and inductance
Joint velocity	4–16 kHz	200–800 Hz	Limited by current loop
Joint position	1–8 kHz	30–150 Hz	Limited by structural mode
Cartesian (kinematic)	1–4 kHz	20–80 Hz	Limited by IK + dynamics solve
Compliance / impedance	1 kHz	5–30 Hz	Limited by torque-sensor noise

7. Failure modes & debugging

• Drift in joint zero after power cycle — single-turn encoder + lost battery on multi-turn module. Fix: replace battery (Maxon, Heidenhain modules) or upgrade to true absolute multi-turn encoder (Aksim2, RESOLUTE).
• Gearbox backlash growing over months — wear-induced. Harmonic-drive flexsplines fatigue at ~10⁹ cycles; cycloidal RV needles wear sooner under shock. Symptom: pose error in the direction of last gravity-loaded motion. Fix: schedule preventive replacement at 80 % of L₁₀ life; if cobot, the joint-torque sensor detects rising lost motion before it’s visible.
• Cable harness fatigue at joint flex zones — power and data conductor breaks after millions of flex cycles. Symptom: intermittent encoder drop-out, brake fault. Fix: use chainflex / high-flex cable; route through hollow shafts; replace cables on schedule.
• Motor brake failure — single-point failure that lets the arm fall under gravity when E-stopped. Industrial spec (ISO 10218-1) requires brake on every gravity-loaded joint. Fix: dual brakes on safety-critical joints; periodic brake-torque test.
• Belt slippage in older SCARA Z-axis — was common in 1990s designs; modern SCARAs use ground ball-screw or direct-drive linear motor. Fix: re-tension or convert to direct-drive.
• Resonance vibration at low-damped structural modes (typically 5–30 Hz for a 1-m-reach arm) — controller bandwidth crosses a structural mode. Symptom: TCP oscillates at one specific frequency on transitions. Fix: notch filter in the velocity loop tuned to the offending mode; or stiffen the link; or add gravity-tuned mass damper at the wrist.
• Singularity navigation faults — IK solver returns infeasible joint velocity near ${\theta }_5=0$. Fix: damped least squares with $\lambda \sim 0.05$, or re-plan the trajectory to avoid the wrist-aligned region (UR controllers have a built-in workspace zone for this).
• Self-collision with own base + cabling — most controllers run an SBC collision check against a URDF-described model. If the URDF is wrong (forgot a payload, wrong tool transform), the arm punches the base. Fix: maintain the URDF in version control; run a simulator (Drake, Isaac Sim, Gazebo, MoveIt) sweep through worst-case trajectories before deploy.
• Payload mass change without notification — operator swaps gripper but forgets to update the controller’s tool-mass entry. Symptom: cobot fault on “torque limit” or industrial arm shows poor accuracy. Fix: automatic payload identification — drive a calibration trajectory, fit gravity model to joint torques (UR set_payload, Franka setLoad, KUKA LoadDataDetermination).
• Temperature-induced drift after long continuous runs — joint and link heat soak. Aluminium expansion at 23 µm/m/K means a 1-m arm heated 10 °C grows 0.23 mm. Fix: thermal sensor in each motor; controller compensation table (KUKA KR-Reference, Stäubli uniVAL); or cycle a “cooling pose” between heavy moves.
• Encoder noise on long cable — > 5 m cable from encoder to drive picks up EMI on shop floor. Fix: differential signaling (RS-485 / BiSS / EnDat); shielded twisted-pair; ferrite chokes on power lines.
• End-of-life signs — increasing motor current for same trajectory (gearbox losses); oil leakage from harmonic-drive seal; warmer joints in IR camera; vibration spectrum showing tooth-mesh sidebands; backlash sweep showing > 2× rated lost motion. Plan replacement before unplanned downtime.
• Wrist singularity stall on welding torch — torch axis aligns with joint-6 axis at ${\theta }_5\approx 0$. Common in arc-welding. Fix: rotate the workpiece by 5° about the seam line so the torch never lines up with the wrist axis.
• Joint torque sensor drift — strain-gauge ring sensors drift with temperature (~0.5 % FS per 10 K typical). Symptom: cobot reports phantom contact force at “rest”. Fix: re-tare on every cycle start; thermal compensation curve identified at commissioning.
• Encoder coupling slippage on a press-fit hub — sub-arcminute slip puts a constant offset into joint zero. Symptom: TCP drifts in one direction over weeks, jumps back after rehoming. Fix: keyed or pinned hub, not press-fit.
• Hollow-shaft cable harness twist — internal cabling cannot rotate freely at joint 1 (continuous rotation), causing winding fatigue. Symptom: cable failure at joint-1 entry after ~10⁶ rotations. Fix: a rotary union or slip ring at joint 1 (UR uses a slip ring on the e-series; KUKA Iontec has factory-fitted rotary union).
• Misaligned tool transform causes Cartesian-mode runaway — operator updates the gripper but forgets to update TCP offset. The controller’s Jacobian then reports the wrong end-effector pose; under Cartesian velocity control, joint 6 spins to “correct” a phantom error. Fix: enforce a checksum on the active tool table; controllers like Stäubli uniVAL and Franka libfranka flag mismatches at runtime.

8. Case studies

Universal Robots UR5e — the cobot reference architecture

Six harmonic-drive joints sized CSF-25-100 (joints 1–3) down to CSF-14-100 (joints 5–6), driven by custom brushless servos with Renishaw Aksim absolute encoders on the joint output. The arm runs at 24 V on a single CAT5e + power umbilical to a fanless control box; on-board PC (industrial Atom-class as of e-series) runs URControl + URScript over the local socket interface. Per-joint torque is estimated from motor current, not measured directly — cheaper than Franka’s strain-gauge approach and good enough for PFL-rated collaboration (ISO/TS 15066) at the published 250 mm/s collaborative speed.

The single most influential design decision is the non-spherical wrist — UR’s joints 4, 5, 6 have small offsets that prevent classical Pieper IK. Olsen & Tegnander (2018) published a closed-form solution that exploits the parallel shoulder/elbow joints, yielding all 8 IK solutions in ~120 µs on a 1.4 GHz ARM CPU. Every UR clone (Doosan, Techman, AUBO, Elite, Han’s, Jaka) has adopted the same non-spherical wrist + Olsen-style closed-form IK pattern.

UR’s published repeatability is ±0.03 mm; uncalibrated accuracy is around ±1 mm and falls to ~0.1 mm after the factory 24-parameter DH calibration. Over 75 000 units installed worldwide as of late 2025 (UR reports), making it the single most-deployed cobot platform.

Boston Dynamics Stretch — purpose-built for case-handling

Stretch (commercial release 2022) is a single-arm mobile manipulator built for warehouse truck-unloading and palletising. The arm is a 7-DOF compact serial chain with a custom vacuum end-effector capable of lifting 23 kg boxes; the manipulator sits on a square-base mobile platform with a counterweight that extends to keep the centre of gravity inside the wheelbase as the arm reaches into a trailer. The 7th degree of freedom enables “wrist-flick” placement of boxes onto a conveyor without rotating the whole base.

Engineering trade-offs: pure-force control wasn’t viable (boxes vary 1–23 kg with no advance knowledge), so the controller fuses joint-torque sensing with the suction-pad force feedback. The arm runs in admittance control during the suck-and-lift, transitioning to position control during the place. Deployed by FedEx, DHL, Maersk, and Gap.

Tesla Optimus Gen 2 — humanoid manipulator

Tesla revealed the Gen 2 humanoid in December 2023 with notable arm-design details published at AI Day 2024:

• 11-DOF hand per side (vs Gen 1’s 11), with custom magnetic-encoder finger joints and tendon-driven distal joints.
• Custom brushless actuators with planetary gearheads; published per-joint torque density target 0.5 N·m/g, comparable to Apptronik Apollo and Figure 02.
• Whole-arm DOF: 7 (shoulder × 3 + elbow × 1 + wrist × 3) + 11 in hand = 18 per arm; 36 total in upper body.
• Aluminium + titanium structure; carbon-fibre forearm shell on Gen 2.

The relevance to manipulator design is the integration density: every joint contains its own custom servo + planetary + encoder + brake + thermal sensor + harness pass-through, packaged at scale-of-thousands-units cost targets. The trade-off Tesla has signalled: lower stiffness than industrial harmonic-drive arms (target ~10⁴ N·m/rad per joint) accepted in exchange for backdrivability and human-safe collision behaviour.

ABB IRB 360 FlexPicker — 25 years of delta refinement

ABB’s IRB 360 (and predecessors IRB 340 / 940) is the dominant industrial delta parallel robot. Generations have iterated on the same Reymond Clavel 1988 architecture: three RUU legs driven by base-mounted brushless servos with cycloidal reducers (Spinea TwinSpin), an aluminium-CFRP composite end platform, and a hollow axial shaft providing the optional fourth-axis end-effector rotation.

What design decisions matter at the architectural level:

• Actuators at the base, not at the joints. Reflected inertia at the end-effector is tiny because the heavy motors don’t move. End-effector mass is sub-1 kg even for a 6 kg payload variant.
• Cycloidal over harmonic drive. Shock loading from the cycle-end deceleration would fatigue a harmonic drive’s flexspline; Spinea cycloidal handles the impulsive torque profile.
• Parallelogram lower legs. Three pairs of parallel rods constrain rotation, forcing pure translation of the end platform. Any twist between the rods of a pair indicates wear and is detected by ABB’s diagnostic system.
• Calibration is per-leg + per-base-joint, 9 parameters total plus the platform geometry — much shorter calibration than a 6-DOF serial arm (26 parameters).
• Workspace limited by parallelogram geometry, not motor range. Doubling motor torque doesn’t help; the leg geometry caps reach at ~565 mm radius for the 1130 mm-diameter variant.

ABB has shipped > 15 000 IRB 360 units to food packaging, pharmaceuticals, electronics assembly, and small-parts handling lines worldwide. Stäubli TP80 and Fanuc M-1iA / M-3iA share the same architecture with different proportions; Codian and Codian-style smaller deltas dominate the sub-1-kg pick-and-place segment.

9. Cross-references

• kinematics-dh — forward and inverse kinematics on the DH table that describes the arm designed here.
• dynamics-rigid-body — inverse and forward dynamics on the inertias / masses that come out of the CAD model.
• motors-electric — actuator sizing and family selection (BLDC, servo, QDD, Dynamixel).
• sensors-pose-motion — joint encoders (Aksim, RESOLUTE, ECN), IMUs, end-of-arm pose sensors.
• sensors-force-tactile — joint torque sensors, wrist F/T (ATI, Bota, OnRobot HEX), tactile pads.
• pid-control — joint-space position and velocity PID; the inner control loop on every arm.
• state-space-lqr — modal-space and joint-space LQR for multi-axis coordinated control.
• impedance-control — Cartesian and joint-space impedance / admittance control; the cobot interaction layer.
• trajectory-generation — point-to-point, S-curve, joint-space vs Cartesian-space interpolation that feeds the inner loop.
• path-planning — RRT / PRM / lattice planners that generate the waypoints which trajectory generation interpolates.
• gears-power-transmission — harmonic-drive, RV cycloidal, planetary gear design (ratios, stiffness, lost motion, lubrication).
• materials-aluminum — 6061 / 7075 aluminium for arm castings.
• materials-composites — CFRP forearm tubes and structural panels.
• bearings — joint bearings (cross-roller, deep-groove, four-point) and runout budget.
• fasteners-bolts — preload, ISO metric grades, locking; every joint flange uses these.
• electric-motors — motor first-principles (back-EMF, FOC, thermal limits).
• robotics-control — controller languages (URScript, KRL, RAPID, KAREL, INFORM, V+) that drive the designed arm.

10. Citations

1. Craig, J.J. Introduction to Robotics: Mechanics and Control, 4th ed., Pearson, 2018. ISBN 978-0-13-348960-8.
2. Spong, M.W., Hutchinson, S. & Vidyasagar, M. Robot Modeling and Control, 2nd ed., Wiley, 2020. ISBN 978-1-119-52399-3.
3. Lynch, K.M. & Park, F.C. Modern Robotics: Mechanics, Planning, and Control, Cambridge University Press, 2017. ISBN 978-1-107-15630-2.
4. Siciliano, B., Sciavicco, L., Villani, L. & Oriolo, G. Robotics: Modelling, Planning and Control, 2nd ed., Springer, 2010. ISBN 978-1-84628-642-1.
5. Asada, H. & Slotine, J.-J. Robot Analysis and Control, Wiley-Interscience, 1986. ISBN 978-0-471-83029-4.
6. Tsai, L.-W. Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley, 1999. ISBN 978-0-471-32593-2.
7. Merlet, J.-P. Parallel Robots, 2nd ed., Springer, 2006. ISBN 978-1-4020-4132-7. Delta + Stewart + 6-DOF parallel kinematics reference.
8. Khalil, W. & Dombre, E. Modeling, Identification and Control of Robots, Butterworth-Heinemann, 2002. ISBN 978-1-903996-66-9.
9. Featherstone, R. Rigid Body Dynamics Algorithms, Springer, 2008. ISBN 978-0-387-74314-1.
10. Pieper, D.L. The Kinematics of Manipulators Under Computer Control. PhD thesis, Stanford University, 1968. Establishes the closed-form 6-DOF IK criterion.
11. Albu-Schäffer, A., Haddadin, S., Ott, Ch., Stemmer, A., Wimböck, T. & Hirzinger, G. “The DLR Lightweight Robot — design and control concepts for robots in human environments.” Industrial Robot, 34(5):376–385, 2007. iiwa precursor.
12. Pratt, G.A. & Williamson, M.M. “Series Elastic Actuators.” Proc. IEEE/RSJ IROS, vol. 1, pp. 399–406, 1995. DOI:10.1109/IROS.1995.525827.
13. Hayati, S. & Mirmirani, M. “Improving the absolute positioning accuracy of robot manipulators.” Journal of Robotic Systems, 2(4):397–413, 1985. Kinematic calibration foundation.
14. Hollerbach, J.M. “A Recursive Lagrangian Formulation of Manipulator Dynamics and a Comparative Study of Dynamics Formulation Complexity.” IEEE Transactions on Systems, Man, and Cybernetics, 10(11):730–736, 1980.
15. Whitney, D.E., Lozinski, C.A. & Rourke, J.M. “Industrial robot forward calibration method and results.” ASME J. Dynamic Systems, Measurement, and Control, 108(1):1–8, 1986.
16. Olsen, A.L. & Tegnander, A.O. “An analytical closed-form inverse kinematics method for the Universal Robots.” Preprint / ur_kinematics ROS package, 2018.
17. Haddadin, S., Albu-Schäffer, A. & Hirzinger, G. “Requirements for safe robots: Measurements, analysis and new insights.” International Journal of Robotics Research, 28(11-12):1507–1527, 2009. The biomechanical-threshold basis of ISO/TS 15066.
18. ISO 10218-1:2025 — Robotics — Safety requirements — Part 1: Industrial robots. International Organization for Standardization.
19. ISO 10218-2:2025 — Robotics — Safety requirements — Part 2: Robot applications and robot cells. International Organization for Standardization.
20. ISO/TS 15066:2025 — Robots and robotic devices — Collaborative robots. Power-and-force-limit thresholds.
21. ISO 9283:1998 — Manipulating industrial robots — Performance criteria and related test methods. Repeatability / accuracy definitions used by every catalogue spec sheet.
22. Universal Robots e-Series — Service Manual. Universal Robots A/S, rev 5.13, 2023-10.
23. Franka Emika Robot — System Documentation. Franka Emika GmbH, rev 4.2.1, 2022. https://frankaemika.github.io/docs/
24. KUKA LBR iiwa 7 R800 / 14 R820 Datasheet. KUKA Roboter GmbH, 2018.
25. Fanuc M-20iD/35 Datasheet, ABB IRB 6700 Product Specification, Stäubli TX2 series Product Specification, Yaskawa MotoMan GP25 Datasheet, Kawasaki BX series spec sheet. Manufacturer datasheets, all current revisions (2023–2025).
26. Harmonic Drive LLC Engineering Data — Component Sets, Speed Reducers, Gearheads. Harmonic Drive LLC, 2024 catalogue.
27. Nabtesco Precision Reducer Catalogue — RV-N, RV-C, RV-E series. Nabtesco Corporation, 2024.
28. Renishaw RESOLUTE™ encoders — Datasheet L-9517-9520. Renishaw plc, 2024.
29. ATI Industrial Automation — Multi-Axis Force/Torque Sensor System Installation and Operation Manual. ATI document 9610-05-1015, current rev.
30. Mayr ROBA-stop®-M brakes — Type 891 / 893 documentation. Mayr Antriebstechnik, 2023.

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