- Reaching a point: inverse kinematics of a two-joint armGiven where the hand should be, find the two joint angles. The law of cosines does it in four lines, and the arm has two answers.
- Workspace, singularities and joint limitsWhich points an arm can reach, where it gets stuck, and how servo limits shrink the reachable area. With a map you print yourself.
- Coordinate frames and transformsEvery position is measured from somewhere. Learn rotation matrices and 4x4 transforms so a point seen by a camera becomes a point your arm can reach.
- A real arm in 3D: the MeArmTurn a 3D target into base, shoulder and elbow angles for a three-servo arm, then into servo commands with offsets, directions and a calibration you do once.
- The Jacobian and numerical IKWhen there is no neat formula, let the computer search. The Jacobian links small joint moves to small tip moves, and a few lines of damped least squares solve IK for arms with any number of joints.
- Feedback: P, I and D explained with a cruise controlWhy open loop drifts, and what each of the three terms of a PID controller does, shown with a car on a hill that you simulate yourself.
- Measuring a DC motor: encoder, step response and a simple modelRead a motor's datasheet, count encoder pulses with an interrupt, record a step response on your laptop, and boil the motor down to two numbers you can control with.
- Tuning a motor speed loop on real hardwareA step-by-step method for choosing gains, with feedforward from your motor model, anti-windup, derivative on measurement, filtering and a stall guard, all checked with data you log yourself.
- Position over speed: cascaded loops and motion profilesMake a wheel turn an exact distance without jolts: a position loop that commands your tuned speed loop, fed by a trapezoidal motion profile.
- An arm that follows a target smoothlyStraight-line paths, slow-fast-slow timing, servo speed limits and a follower that chases a moving target: everything in the course combined on the MeArm.