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Robotics and Mechatronics

Combine mechanisms, sensors, actuators, circuits, control, embedded code, and robotic kinematics.

Course outline only for now. Full chapter-level lessons are still in progress. Use this page for readiness, concepts, worked-example format, practice, review, and portfolio direction. Complete course contents are live today for Math, Physics, and Statics.

Readiness check

Before starting, confirm the prerequisite habits.

Use trigonometry deliberately.
Read sensor and actuator roles.
Understand feedback loops.
Write simple control logic.

0 or 1 weak itemContinue, but slow down at the worked example.

2 weak itemsReview the foundation page linked in the roadmap before solving practice problems.

3 or more weak itemsStep back to prerequisites; this module depends on them.

The core idea

Model a robotic system from geometry, actuation, sensing, and control logic.

Robotics couples geometry, dynamics, sensing, and control: forward kinematics maps joint angles to a tool position, and the whole field is keeping that map consistent as the robot moves and senses.

x = L1 c1 + L2 c12

Works when: you keep a consistent frame convention and verify forward kinematics against a reachable hand-computed pose.

Breaks down when: you mix degrees and radians, or lose track of which frame an angle is measured in.

Figure 1. Concept model for Robotics and Mechatronics. The figure names inputs, computed variables, geometry, and result.

input/load result/constraint computed variable dimension/model geometry

The method

1Model

Make the physical situation visible.

2Relate

Translate the model into symbols.

3Solve

Calculate only after the model is clear.

4Check

Use units, scale, and limiting cases.

Worked example

Figure 2. Worked problem setup: A planar robot has L1 = 0.30 m, L2 = 0.20 m, theta1 = 40 deg, and theta2 = 50 deg measured relative to link 1. Find endpoint coord

Figure 3. Calculation model. The result follows from the model, units, and reasonableness check.

A planar robot has L1 = 0.30 m, L2 = 0.20 m, theta1 = 40 deg, and theta2 = 50 deg measured relative to link 1. Find endpoint coordinates.

Problem A planar robot has L1 = 0.30 m, L2 = 0.20 m, theta1 = 40 deg, and theta2 = 50 deg measured relative to link 1. Find endpoint coordinates.
Given and find L1 = 0.30 m, L2 = 0.20 m, theta1 = 40 deg, theta2 = 50 deg. Find: x and y of the tool point.
Assumptions Idealized model, consistent units, and no hidden effects outside the stated scope.
Step Use theta12 = theta1 + theta2 = 90 deg.
Step x = 0.30 cos40 + 0.20 cos90 = 0.230 m.
Step y = 0.30 sin40 + 0.20 sin90 = 0.393 m.
Step Check: total reach is less than 0.50 m.
Conclusion x = 0.230 m, y = 0.393 m. Carry this result into the design decision, not just into the answer box.

Misconceptions and diagnostics

Mistake	Symptom	Diagnostic question	Correction
Frame confusion	Angle measured from the wrong link	Which frame is this angle relative to?	Define and label every coordinate frame.
Degrees vs. radians	Trig gives a nonsense position	Is your calculator or code in the right mode?	Keep one unit; convert explicitly.
Ignoring dynamics	Plans a path the motors can't drive	Can the actuators supply the required torque?	Check joint torque limits against the dynamics.

Practice ladder

Level 1: direct skill

Redo the worked example with one changed input. Predict the trend before calculating.

Check yourself

The trend must match the governing relation: x = L1 c1 + L2 c12.

Level 2: mixed concept

Draw the model from memory, label knowns and unknowns, then write the first equation without looking.

Check yourself

Your first equation should connect the model to tool position.

Level 3: independent problem

Create a similar problem from a real object near you. State assumptions, solve it, and include a reasonableness check.

Check yourself

A valid solution has a sketch, given/find list, governing relation, units, and a conclusion.

Level 4: transfer task

Turn the result into a design decision: what would you change if the output missed its target by 25 percent?

Check yourself

Name the design variable with the strongest influence and justify it from the equation.

Working with AI, and proving it yourself

Useful AI role

Ask for a critique of assumptions, units, diagram labels, and missing checks after you have attempted the solution.

Do not outsource

Do not paste the problem and accept a final answer. Your evidence is the model, the checks, and the explanation.

Retrieval and spaced review

Closed-notes prompts: define the joint frames, write the forward-kinematics map x = L1 c1 + L2 c12, evaluate a reachable pose, and state the actuator limit that would constrain it.

TodayRedo the worked example from a blank page.

+1 daySolve Level 1 without notes.

+3 daysSolve Level 2 with changed numbers.

+7 daysConnect this module to another course.

+30 daysAdd a portfolio artifact.

Mapping and portfolio task

Course mapping

Mechatronics is the integration course: it consumes dynamics (manipulator motion), controls (the loop), and circuits and sensors (perception) and forces them to work together on real hardware.

First-pass focus: definitions, model setup, units, and worked examples. Save edge cases for the second pass.

Portfolio task

Create a one-page forward-kinematics note for a 2-link arm with frames labeled: sketch, assumptions, equations, result, reasonableness check, limitation, and recommendation.