Focused, exact video lessons that walk through the GATE 2027 Robotics & Automation (RA) and Physics (PH) syllabi one idea at a time, with every number checked in Python. Each episode links to the matching hands-on AIHUB lesson so you can practise straight after watching.
How does a robot know which way it is pointing? Frames and orientation, the derivation of the 2D rotation matrix (columns = new axes), its properties (RᵀR = I, R⁻¹ = Rᵀ, det R = +1; reflections have det −1), 3D Rx/Ry/Rz, why rotation order matters (fixed vs current axes), a solved GATE-style NAT problem and the common traps.
RA · A.1 Linear Algebra
RA · A.3 Coordinate systems & DOF
RA · Rotation matrices in 2D/3D
RA · Homogeneous transformations
PH · Sec 2 Linear vector spaces, similarity transformations
Most arrows turn when a matrix acts on them, but a few only stretch: those are eigenvectors, and the stretch factors are eigenvalues (A v = λ v). Finding them with det(A − λI) = 0, the trace and determinant checks, symmetric matrices and diagonalization (PᵀAP = D), why every 3D rotation has eigenvalue 1 along its axis, the physics link to principal axes of inertia, a GATE-style solved problem (eigenvalues of A²) and a numerical (NAT) question.
Why can a small push at the right rhythm make something shake very hard? The spring-mass natural frequency ωn = √(k/m), the small-angle pendulum, the damping ratio ζ and the three damping cases (under, critical, over), the link to eigenvalues (λ = −ζωn ± jωd, from episode 2), forced vibration and the resonance peak 1/(2ζ), why robot arms care, a GATE-style solved problem and a numerical (NAT) question.
RA · Engineering Mathematics: differential equations
RA · Control systems: second-order response, natural frequency, damping ratio
How can a sharp square wave be built from smooth sine waves? Harmonics of the base frequency ω0 = 2π/T, how the coefficients come from averaging (orthogonality), the square-wave series (4/π)(sin t + sin 3t/3 + sin 5t/5 + …), the Gibbs phenomenon, even/odd/half-wave symmetry shortcuts, Parseval's theorem for power, how a low-pass filter cleans a noisy robot sensor signal, a GATE-style solved problem and a numerical (NAT) question.
RA · Engineering Mathematics: Fourier series
RA · Signals & systems: harmonics, filtering
RA · Sensor signal conditioning (low-pass filter, FFT)
How does a robot joint hold still against gravity? The error e = r − y, proportional control and its steady-state error 1/(1 + Kp), integral action that removes the step offset (type-1 loop), derivative action as damping and why it needs a filter, the full PID law C(s) = Kp + Ki/s + Kd s, a side-by-side P vs PI vs PID step response, Ziegler–Nichols ultimate-gain tuning, a GATE-style solved problem and a numerical (NAT) question.
RA · Control systems: feedback, steady-state error
RA · PID controllers and tuning (Ziegler–Nichols)
RA · Robot joint position control
PH · Electronics: feedback and control basics
PH · Differential equations of first/second-order systems
Why do you jerk forward when an auto brakes suddenly? The first law (inertia: no net force, constant velocity), the second law F_net = dp/dt = m a for constant mass, the third law (equal and opposite forces on two different bodies), a GATE-style solved problem on the scale reading in an accelerating lift (N = m(g + a) = 708 N), and the common trap that weight and normal force are not a third-law pair.
Every robot runs on circuits, and every circuit obeys two rules. Kirchhoff's current law (current in = current out at every node) and voltage law (voltages around any closed loop sum to zero), a GATE-style node-voltage problem solved with KCL (12 V, 4 Ω into node A, 6 Ω and 12 Ω to ground gives V_A = 6 V), a check with both laws and mesh analysis, and the most common KVL sign trap.
RA · Electrical circuits: KCL, KVL
RA · Node and mesh analysis
RA · DC circuits in motor drivers and sensor boards
Why a capacitor never charges instantly. The RC charging curve v(t) = V(1 − e^(−t/RC)), the time constant τ = RC (63% after one τ, practically full after five), a GATE-style problem with 5 V, 10 kΩ and 100 µF (τ = 1 s, v(2 s) ≈ 4.32 V), checks at t = 0 and t → ∞, and the common trap: a capacitor is a short at the first instant and an open at DC steady state.
RA · Electrical circuits: RC transients
RA · Time constant and first-order response
RA · Decoupling and power stability on robot boards
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