Industrial robots: configurations and programming

Why it matters

Industrial robots weld car bodies, tend CNC machines, palletise cartons, paint, assemble electronics and load presses — work that is repetitive, heavy, hot or hazardous. Choosing the right configuration, knowing how precisely a robot can place its tool, and being able to program it are everyday tasks in automated plants. The same coordinate and kinematics ideas appear in CNC and CMM work.

Key ideas

Definition. An industrial robot is a general-purpose, programmable machine with an arm of several joints that can be reprogrammed to perform different tasks — handling parts or carrying a tool. Its anatomy: base, arm and body joints (which position the wrist), wrist joints (which orient the end effector), the end effector, drives, sensors and the controller.

Joint types (Groover's notation).

• L — linear (sliding) joint, relative motion along a common axis (telescoping).
• O — orthogonal joint, sliding perpendicular to the input link.
• R — rotational joint, rotation axis perpendicular to both links.
• T — twisting joint, rotation axis parallel to both links.
• V — revolving joint, input link parallel to the axis, output link perpendicular to it. Each joint gives one degree of freedom (DOF). Positioning a point in space needs 3 DOF; orienting the tool needs 3 more (wrist roll, pitch, yaw), so 6 DOF is typical.

Body-and-arm configurations.

• Cartesian (rectangular, gantry) — three linear joints (LOO); box-shaped work volume, simple control, very good accuracy; used for pick-and-place, gantry loading, dispensing.
• Cylindrical — vertical column rotating on the base (T), with vertical (L) and radial (O) slides (TLO); the work volume is a thick hollow cylinder.
• Polar (spherical) — base rotation, arm elevation and telescoping arm (TRL); spherical-shell work volume; used in early spot-welding and die-casting robots.
• Jointed-arm (articulated, anthropomorphic) — base twist and shoulder and elbow rotations (TRR); the most common type, with a large, irregular work volume and good access around obstacles.
• SCARA (Selective Compliance Assembly Robot Arm) — two vertical-axis revolute joints and a vertical slide (VRO); stiff vertically, compliant horizontally — ideal for fast insertion and assembly.

Drives. Electric (servo motors; precise, clean, dominant today), hydraulic (very high force for heavy payloads, but leaks and noise), pneumatic (cheap, used for small pick-and-place and grippers; limited control of intermediate positions).

End effectors. Grippers — mechanical fingers, vacuum cups, magnetic, adhesive, hooks; single or dual grippers (a dual gripper lets a machine-tending robot unload and load in one visit). Tools — spot-welding gun, arc-welding torch, spray-painting gun, drilling or deburring spindle, water-jet cutter.

Sensors. Internal (joint encoders, tachometers) and external (tactile and force/torque sensors, proximity sensors, vision for part location and inspection, safety light curtains).

Programming.

• Lead-through programming: powered lead-through with a teach pendant (move the arm step by step and record points; standard for point-to-point tasks like spot welding and machine tending) and manual lead-through (physically guide the arm through a continuous path, used for spray painting).
• Robot languages (e.g. VAL, RAPID, KRL): motion commands (MOVE, APPROACH, DEPART), interlocks with other equipment (WAIT, SIGNAL), branching and sensor input.
• Off-line programming in a simulation of the cell: the robot keeps producing while the next program is written; calibration is needed to bridge model and real cell.

Precision. Control resolution is the smallest increment the controller can command on a joint (set by the bit storage capacity and the joint range); accuracy is the ability to reach a commanded point; repeatability is the ability to return to a taught point. Robots usually have much better repeatability than absolute accuracy — which is why taught points work well and off-line programs need calibration.

Kinematics. Forward kinematics gives the tool position from joint values; inverse kinematics gives joint values for a desired position (and may have two solutions — "elbow up" and "elbow down").

Formulas

CR = R / (2ⁿ − 1)

• CR control resolution of one joint (mm or degrees); R joint range (mm or degrees); n bits of control memory for that joint.

Accuracy = CR / 2 + 3σ , Repeatability = ±3σ

• σ standard deviation of mechanical errors (mm).

x = L₁ cos θ₁ + L₂ cos(θ₁ + θ₂) , y = L₁ sin θ₁ + L₂ sin(θ₁ + θ₂)

• Forward kinematics of a planar two-link arm; L₁, L₂ link lengths (mm); θ₁ shoulder angle from the x-axis; θ₂ elbow angle relative to link 1.

cos θ₂ = (x² + y² − L₁² − L₂²) / (2 L₁ L₂) θ₁ = atan2(y, x) − atan2(L₂ sin θ₂, L₁ + L₂ cos θ₂)

• Inverse kinematics of the same arm (one of the two solutions).

V = (φ / 360°) · π (r₂² − r₁²) · h

• Work volume of a cylindrical robot (m³); r₁, r₂ minimum and maximum radial reach (m); h vertical stroke (m); φ base rotation (degrees).

Worked examples

Example 1 (standard). A sliding joint of 1 m range is controlled with 12-bit storage. Mechanical errors have σ = 0.08 mm. Find the control resolution, accuracy and repeatability.

1. CR = R / (2ⁿ − 1) = 1000 / (4096 − 1) = 1000/4095 = 0.244 mm.
2. Accuracy = 0.244/2 + 3 × 0.08 = 0.122 + 0.24 = 0.362 mm.
3. Repeatability = ±3 × 0.08 = ±0.24 mm.

Example 2 (GATE level). A planar two-link arm has L₁ = 400 mm and L₂ = 300 mm. (a) Find the tool position for θ₁ = 30°, θ₂ = 45°. (b) Find joint angles to reach (500, 300) mm.

1. (a) θ₁ + θ₂ = 75°. x = 400 cos 30° + 300 cos 75° = 346.41 + 77.65 = 424.1 mm; y = 400 sin 30° + 300 sin 75° = 200 + 289.78 = 489.8 mm.
2. (b) x² + y² = 250 000 + 90 000 = 340 000. cos θ₂ = (340 000 − 160 000 − 90 000)/(2 × 400 × 300) = 90 000/240 000 = 0.375 → θ₂ = 67.98°.
3. atan2(300, 500) = 30.96°; atan2(300 sin 67.98°, 400 + 300 cos 67.98°) = atan2(278.1, 512.5) = 28.49°.
4. θ₁ = 30.96° − 28.49° = 2.48°. Check: x = 400 cos 2.48° + 300 cos 70.46° = 399.6 + 100.4 = 500 mm ✓.

Common mistakes

• Dividing the range by 2ⁿ instead of 2ⁿ − 1 (there are 2ⁿ points but 2ⁿ − 1 intervals).
• Treating repeatability and accuracy as the same; robots repeat far better than they position absolutely.
• Measuring θ₂ from the x-axis instead of from link 1.
• Ignoring the second (elbow-up/elbow-down) inverse-kinematics solution, or a target outside the reach |L₁ − L₂| ≤ r ≤ L₁ + L₂.
• Mixing up configurations: SCARA is not a jointed-arm robot; its revolute axes are vertical.

For GATE PI

Expect MCQs on configurations and their joint notations, work-volume shapes, drives, end effectors and programming methods. Numericals cover control resolution, accuracy and repeatability, forward and inverse kinematics of a two-link planar arm, and work-volume calculations. Practise the two-link geometry with a sketch.

Quick check

1. Which configuration has a rectangular (box) work volume?
2. Which programming method suits spray painting?
3. A 0.8 m slide uses 10-bit control. Find the control resolution.
4. For L₁ = L₂ = 0.5 m, θ₁ = 60°, θ₂ = −30°, find x and y.
5. Why is SCARA suited to assembly?

Answers: 1. Cartesian. 2. Manual lead-through. 3. 800/1023 = 0.782 mm. 4. x = y = 0.683 m. 5. It is rigid vertically and compliant horizontally, which helps peg-in-hole insertion.