Exercises: Robotics: Structure and movement

Explain in your own words what a robot is and what three capabilities define it (moving mechanically, being programmable, and acting on its environment). Reason why an industrial robot arm is a robot, but a fixed conveyor belt, although it moves, is not.

Explain what a degree of freedom (DOF) of a robot is: each independent movement that a joint can make. Give two examples: a hinged door (a single DOF) and your own arm, which has many, and reason why more DOFs mean more possible postures.

A robot's joints can be revolute (they rotate, like an elbow) or linear, also called prismatic (they extend, like a drawer). Explain the difference and give an everyday example of each type of movement.

Explain what a robot's end-effector is (the 'tool' attached to its wrist that performs the task) and name three different end-effectors along with the task performed by each: gripper, suction cup, and welding torch.

A robot's sensors can be proprioceptive (providing information about the robot itself) or exteroceptive (providing information about the environment). Classify these sensors: (a) the encoder measuring a joint angle, (b) a camera, (c) a touch sensor on the gripper, and (d) the gyroscope measuring chassis tilt.

Match each description with its type of robot: (1) arm fixed to the floor that welds car bodies, (2) wheeled machine that transports boxes in a warehouse, and (3) lightweight arm that works alongside humans without a safety fence, with: (a) mobile robot, (b) collaborative robot, and (c) industrial manipulator robot.

There is almost always a gearbox between the motor and the joint of a robot. Explain why: electric motors rotate very fast with low torque, and joints require the exact opposite (low speed and high torque), and the gearbox performs this conversion.

A collaborative robot can share a workbench with a person. Explain what two safety measures make this possible (limiting its force and speed, and stopping upon detecting an unexpected contact) and why a conventional industrial robot instead requires a cage or fence.

A robot arm has a base that rotates on itself, a joint at the 'shoulder', another at the 'elbow', and a rotating wrist. (a) Count its degrees of freedom. (b) Explain what movement each joint contributes to the position and orientation of the end-effector. (c) Reason why it could not orientate the gripper in any direction without the rotating wrist.

The figure shows an articulated arm with its joints labelled and one marked with a question mark, as shown in the figure.

(a) Identify the joint marked with the question mark and explain what movement it contributes to the arm. (b) Count the degrees of freedom of the complete arm, assuming that the base also rotates. (c) Describe which joints must move for the gripper to move downwards without moving closer to or further from the base.

A robot joint is driven by a $3000\ \text{rpm}$ motor through a gearbox with ratio $50:1$. (a) Calculate the rotational speed of the joint. (b) If the motor provides a torque of $0{,}2\ \text{N} \cdot \text{m}$, calculate the ideal output torque of the gearbox and the actual torque with an efficiency of $80\ \%$. (c) Explain what has been gained and what has been lost by inserting the gearbox.

Choose the most appropriate end-effector for each task and justify your choice: (a) moving flat, clean steel sheets (suction cup or electromagnet); (b) joining parts with weld beads (torch); (c) picking up boxes of various sizes (adjustable finger gripper); (d) painting car bodies (spray gun).

A joint encoder gives $360$ pulses per full revolution. (a) Calculate how many degrees correspond to each pulse. (b) Calculate the angle rotated if $180$ pulses have been counted from the reference position. (c) Explain why the robot needs a known 'reference' or zero position for the pulses to represent an absolute angle.

Mobile robots move using wheels, tracks, or legs. Choose and justify the most suitable solution for: (a) a warehouse with a smooth floor (wheels); (b) rough terrain with mud following a disaster (tracks); (c) climbing stairs or very uneven terrain (legs). Reason what is lost in each case (speed, stability, control complexity).

The figure shows, in plan view, the workspace of a robot arm fixed at the centre, with an area marked with a question mark, as shown in the figure.

(a) Explain what the annulus between the two circles, marked with the question mark, represents. (b) Explain why there is an inner dead zone that the end-effector cannot reach (with the arm folded, the end-effector cannot reach points close to the base). (c) Reason where it is best to place the parts that the robot needs to pick up: very close, in the middle region, or at the outer edge.

For each task of a mobile robot, choose the appropriate sensor and justify it: (a) following a line painted on the floor (reflective optical sensors); (b) avoiding collisions with people or shelving (ultrasonic or laser distance sensor); (c) picking up an object without crushing it (pressure sensor on the gripper). Indicate in each case whether it is proprioceptive or exteroceptive.

A robotic cell must palletize corrugated cardboard boxes (with masses between $3\ \text{kg}$ and $18\ \text{kg}$ and varying dimensions) from a conveyor belt at a height of $0{,}8\ \text{m}$ to a Euro-pallet on the floor, forming layers with interlocking patterns to ensure load stability.

(a) A novice technician proposes using a 3-degree-of-freedom Cartesian robot ($XYZ$). Prove why that configuration is insufficient to carry out this palletizing task and deduce the strict minimum kinematics (number of degrees of freedom and type of joints) required to complete the task.

(b) There is doubt between a lateral clamping mechanical gripper and a vacuum suction cup head. Evaluate the technical risks of using mechanical jaws on cardboard with a heavy load and justify which vacuum end-effector configuration (number of suction cups, level compensation, and type of ejector) would solve the problems of porosity and size variation.

(c) Design the station's sensor system: indicate which specific sensor should detect the arrival of the box without physical contact on the conveyor belt and which sensor system the robot must incorporate to deposit each box at the exact height without crushing the preceding layers or relying solely on theoretical counting.

An articulated robotic arm consists of a horizontal link of length $L = 0{,}6\ \text{m}$ and own mass $m_b = 4\ \text{kg}$ (with its center of gravity at its midpoint), which holds at its end a gripper with a part of total mass $m_p = 2{,}5\ \text{kg}$.

(a) Calculate the total static torque that the shoulder joint must overcome when the arm is fully extended in a horizontal position ($g = 9{,}8\ \text{m/s}^2$).

(b) If the arm rises by rotating to form an angle of $60^\circ$ above the horizontal, quantitatively predict the new torque experienced by the shoulder axis and physically justify the variation with respect to the horizontal position.

(c) To drive said joint, a set consisting of a servomotor with continuous rated torque $\tau_m = 0{,}35\ \text{N}\cdot\text{m}$ coupled to a gearbox with gear ratio $i = 80:1$ and a mechanical efficiency $\eta = 75\,\%$ is proposed. Determine by calculation whether the gearmotor assembly is capable of holding the horizontal load in continuous duty without overheating.

The following diagram represents the control architecture of an industrial robotic joint:

(a) Deduce what component the block "?" represents and what two specific quantities it internally compares in each sampling cycle to calculate the control signal sent to the actuators.

(b) During milling, the robot's tool hits an unforeseen zone of material of excessive hardness that momentarily brakes the joint. Describe the sequence with which the disturbance travels through the chain and how the system reacts to correct the angular position.

(c) If vibrations cause the signal cable of the position encoder (sensor block) to be severed, predict the immediate physical behavior of the motor if the system lacks open-loop diagnostic routines (runaway condition) compared to how a correctly configured safety stop should act.

For a component insertion station on printed circuit boards (PCBs) with a maximum allowable positioning tolerance of $\pm 0{,}15\ \text{mm}$, two industrial robots from different manufacturers are evaluated:

• Robot A: Absolute accuracy of $\pm 0{,}25\ \text{mm}$ and repeatability of $\pm 0{,}03\ \text{mm}$.

• Robot B: Absolute accuracy of $\pm 0{,}10\ \text{mm}$ and repeatability of $\pm 0{,}20\ \text{mm}$.

(a) Explain the physical difference between systematic error and random error in robot kinematics and relate each of them to accuracy and repeatability.

(b) Justify which of the two robots is the only viable one for the task if the controller allows applying software compensation through prior calibration with a vision camera (fixed offset), and which one would inevitably produce defective parts.

(c) A technician suggests: "To improve the repeatability of the defective robot, it is enough to reprogram the theoretical coordinates in the code." Technically refute this statement by explaining which constructive and mechanical factors repeatability depends on.

An automotive manufacturing plant needs to automate two workstations:

• Station 1: Spot welding on steel chassis, handling a $45\ \text{kg}$ welding gun at speeds of $2\ \text{m/s}$ in continuous cycles.

• Station 2: Assembly of clips and wiring inside doors, where an operator manually positions the wiring harness while the robot drives screws in the same shared space.

(a) Reasonably assign a safety solution to each station: closed cell with perimeter fencing and interlocked safety light curtains, or collaborative robot (cobot) without physical barriers.

(b) For the collaborative workstation, explain what sensory and dynamic principles safety is based on according to standards (power and force limiting versus speed and separation monitoring stop).

(c) Refute the following statement from a purchasing manager: "Replacing traditional robots with cobots is always advantageous because they take up less space and increase production throughput." Analyze the trade-off between cycle speed, load inertia, and safe stopping distance in both approaches.

A planar SCARA-type manipulator arm has two links of lengths $L_1 = 30\ \text{cm}$ and $L_2 = 30\ \text{cm}$, articulated in series at the shoulder (angle $\theta_1$) and at the elbow (angle $\theta_2$).

(a) Assuming continuous $360^\circ$ rotation at both joints, determine the maximum and minimum radial reach of the end effector, describing the exact geometry of the reachable workspace in the plane.

(b) Due to mechanical constraints and cable routing, the elbow can only move within the angular range $\theta_2 \in [30^\circ, 150^\circ]$ (where $0^\circ$ corresponds to straight-line extension). Calculate analytically the minimum and maximum radial distance at which the effector can be positioned relative to the shoulder axis.

(c) Analyze the posture in which the arm is fully outstretched (boundary kinematic singularity): demonstrate why an instantaneous degree of freedom is lost and predict what numerical problem arises in calculating joint velocities if a trajectory is programmed that forces the robot to leave that posture with non-zero velocity in a purely outward radial direction.

An automated logistics center deploys a fleet of automated guided vehicles (AGVs / AMRs) to move shelving racks to order picking stations in an environment where they coexist with workers.

(a) Compare physical guidance (inductive or magnetic using floor strips) against autonomous SLAM navigation (using LiDAR and odometry). Justify which of the two technologies is more efficient if the warehouse requires periodically reconfiguring routes and locations without stopping industrial activity.

(b) Design the safety and maneuvering sensor system for the AGV: indicate which devices and detection zones (warning field and emergency stop field) ensure that the vehicle brakes without colliding upon the sudden appearance of a pedestrian, and what specific sensor allows verifying millimeter alignment before lifting the rack.

(c) During a high-activity shift, a deadlock situation occurs where three robots face each other at a T-junction with none advancing, coinciding with a brief drop in the facility's Wi-Fi network. Propose what decentralized control and prioritization strategies the robots must incorporate to resolve this contingency without human intervention.

A traditional Cartesian 3D printer and an articulated 6-degree-of-freedom robotic arm equipped with an extruder head are programmable machines capable of manufacturing parts by material deposition.

(a) Compare Cartesian kinematics with anthropomorphic kinematics by analyzing: usable working volume relative to footprint, structural stiffness under dynamic forces, and computational complexity for calculating the inverse kinematics needed to trace a straight line at constant velocity.

(b) A typical 3D printer operates with open-loop stepper motors, while the robot arm uses closed-loop servomotors with encoders. Predict what will happen in each machine if a protrusion of solidified plastic slightly slows down the movement of the head during a layer and what effect it will have on the subsequent layers of the part.

(c) According to the ISO 8373 standard, an industrial robot is a «multipurpose, reprogrammable, automatically controlled manipulator programmable in three or more axes». Based on this definition, provide a technical argument explaining why a 3D printer is not typically classified as an industrial robot while the articulated arm with an extruder does meet this designation.

Unit Challenge. You are going to design the supervision system and kinematics of an industrial robotic station that adapts its work pace to the national power grid.

1. Real-time monitoring: Check yesterday's peninsular hourly demand on the Red Eléctrica website (REE, RedOS portal). In LibreOffice Calc, create an HMI dashboard with a time graph and conditional indicators that alert if consumption exceeds $32,5$ GW.

2. Morphology and kinematics: Design a $3$-degree-of-freedom (DOF) robotic arm to transfer heavy parts. Define the type of joints (rotary or prismatic), the required actuators, and represent its workspace in a dimensioned sketch, indicating the joint variables $\theta_1$ and $\theta_2$.

3. Supervisory logic: In Tinkercad Circuits or MakeCode, simulate a routine where the speed of the servomotors is automatically reduced during peak hours to save energy, integrating an immediate shutdown SCADA alarm if the temperature sensor exceeds a critical value.

Submit a brief report (maximum $2$ pages) containing the HMI dashboard, the kinematic diagram, and the implemented supervisory logic.

Assessment criteria:

• Rigor in data collection from REE and visual clarity of the HMI monitoring dashboard.

• Technical suitability of the robotic structure ($3$ DOF), its joints, and range of motion.

• Consistency in the integration between the supervised variables and the robot's kinematic response.