CENEVAL EGEL Plus Ingeniería Mecatrónica (EGEL Plus IMECATRO)

A planar packaging mechanism consists of 4 moving rigid links (excluding the fixed ground link) connected by 5 lower kinematic pairs (revolute and prismatic joints, each with 1 degree of freedom) and 1 higher kinematic pair (cam-follower rolling contact with 2 degrees of freedom). According to Grübler's mobility formula for planar mechanisms (M = 3(n - 1) - 2*j1 - j2, where n is total links including ground), what is the net mobility (degrees of freedom) of the mechanism?

• A1 degree of freedom
• B2 degrees of freedom
• C3 degrees of freedom
• D0 degrees of freedom (statically determinate structure)

A coordinate frame {B} is attached to a robotic wrist that is rotated by +90° counterclockwise around the Z-axis of the base reference frame {A} and translated by position vector ^A P_B_org = [100, 50, 0]^T mm. A sensor detects a workpiece located at coordinates ^B P = [20, 10, 0]^T mm relative to frame {B}. What are the coordinates of this workpiece in the base frame {A} (^A P = ^A T_B * ^B P)?

• A[120, 60, 0]^T mm
• B[90, 70, 0]^T mm
• C[110, 30, 0]^T mm
• D[80, 50, 0]^T mm

In standard Denavit-Hartenberg (DH) kinematic modeling of serial robot manipulators, how are the link length (a_i) and link twist (alpha_i) parameters defined between joint axis i-1 (z_{i-1}) and joint axis i (z_i)?

• Aa_i is measured along z_{i-1}, and alpha_i is the angle between x_{i-1} and x_i measured…
• Ba_i is the distance along z_i, and alpha_i is the angle between z_{i-1} and z_i measured…
• Ca_i is the distance along the common normal x_i, and alpha_i is the angle between z_{i-1}…
• Da_i is the direct Euclidean distance between link centers of mass, and alpha_i is the act…

A planar two-link revolute manipulator with link lengths l1 and l2 has end-effector position equations x = l1*cos(q1) + l2*cos(q1 + q2) and y = l1*sin(q1) + l2*sin(q1 + q2). Under which joint configuration does this manipulator reach a kinematic singularity where the Jacobian determinant det(J) vanishes?

• Aq1 = 90° and q2 = 45°
• Bq1 = 0° and q2 = 90°
• Cq2 = 90° or q2 = 270°
• Dq2 = 0° or q2 = 180°

A mechatronic positioning axis has a total moment of inertia J_total = 0.005 kg·m² reflected to the servomotor shaft. The mechanism experiences a continuous frictional and load resistance torque T_load = 1.20 N·m. What electromagnetic torque T_motor must the servomotor deliver to accelerate the axis from rest to an angular speed of 1500 RPM in exactly 0.20 seconds with constant acceleration?

• A5.13 N·m
• B3.93 N·m
• C2.73 N·m
• D1.20 N·m

A rotary indexing table has a load inertia J_load = 0.18 kg·m² and is coupled to an electric servomotor with rotor inertia J_motor = 0.00020 kg·m² through a speed-reducing gearbox with gear ratio N = 30:1 (where N = omega_motor / omega_load). What is the total effective moment of inertia seen by the motor shaft, and does this system satisfy the classical inertia matching condition for maximum acceleration?

• A0.00620 kg·m²; it does not satisfy inertia matching
• B0.00040 kg·m²; it satisfies exact 1:1 inertia matching
• C0.18020 kg·m²; it suffers from excessive load mismatch
• D0.00020 kg·m²; it satisfies matching by eliminating load inertia

In a standard three-op-amp instrumentation amplifier used for sensor signal conditioning, the first buffer stage has feedback resistors R1 = 25 kΩ and gain-setting resistor Rg = 1.0 kΩ. The second stage differential amplifier has input resistors R2 = 10 kΩ and feedback resistors R3 = 50 kΩ. What is the total differential voltage gain A_d = V_out / (V2 - V1)?

• A255
• B250
• C130
• D51

A second-order active low-pass Sallen-Key filter uses an operational amplifier with matched resistors R1 = R2 = 10 kΩ and matched capacitors C1 = C2 = 15.9 nF. What is the cutoff frequency (-3 dB point) and the high-frequency attenuation roll-off rate of this filter topology?

• A500 Hz with -20 dB/decade roll-off
• B2.0 kHz with -60 dB/decade roll-off
• C1.0 kHz with -40 dB/decade roll-off
• D10 kHz with -40 dB/decade roll-off

In an H-bridge circuit driving a DC motor with PWM, what critical condition causes a catastrophic 'shoot-through' (cross-conduction) fault, and how is it prevented in gate driver hardware/firmware?

• ABoth low-side switches turn on simultaneously; prevented by reversing motor polarity
• BFreewheeling diodes conduct in forward bias; prevented by adding series chokes
• CPWM duty cycle drops below 10%; prevented by enforcing a minimum frequency limit
• DBoth high-side and low-side switches on the same half-bridge leg conduct simultaneously;…

When designing a solid-state power driver for an industrial mechatronic system, what fundamental trade-off governs the selection between power MOSFETs and Insulated Gate Bipolar Transistors (IGBTs)?

• AIGBTs operate at switching frequencies above 500 kHz, whereas MOSFETs are limited to low-…
• BMOSFETs exhibit lower conduction losses at lower voltages (<200 V) and permit high switch…
• CMOSFETs are current-controlled bipolar devices, whereas IGBTs are purely voltage-controll…
• DIGBTs possess zero turn-off tail current, making them superior for ultra-fast PWM modulat…

In the analytical dynamic modeling of a multi-DOF mechatronic mechanism using the Euler-Lagrange method, the Lagrangian function is defined as L = K - P. What is the fundamental Euler-Lagrange equation of motion governing each generalized coordinate q_i?

• Ad/dt(dL/dq_i) + dL/d(dot{q}_i) = tau_i
• Bd²/dt²(dL/d(dot{q}_i)) - dL/dq_i = tau_i
• Cd/dt(dL/d(dot{q}_i)) - dL/dq_i = tau_i
• DdL/d(dot{q}_i) * dL/dq_i = tau_i

A mechanical translational system consists of a mass m, viscous damper with damping coefficient c, and linear spring with stiffness k driven by an external force u(t): m*x'' + c*x' + k*x = u(t). Defining state variables x1 = x and x2 = x', what is the state matrix A and input vector B in the continuous state-space representation [x1'; x2'] = A*[x1; x2] + B*u?

• AA = [[0, 1], [-k/m, -c/m]], B = [0; 1/m]
• BA = [[1, 0], [-c/m, -k/m]], B = [1/m; 0]
• CA = [[0, 1], [k/m, c/m]], B = [0; m]
• DA = [[-c/m, -k/m], [1, 0]], B = [1/m; 1/m]

A four-bar planar linkage has link lengths: shortest link s = 30 mm, longest link l = 80 mm, and remaining intermediate links p = 50 mm and q = 70 mm. According to Grashof's theorem, what type of mechanism behavior will be obtained if the shortest link (s) is selected as the input crank adjacent to the fixed ground link (p)?

• ADouble-rocker mechanism with no link capable of full revolution
• BDrag-link (double-crank) mechanism where both input and output links revolve fully
• CNon-Grashof triple-rocker linkage
• DCrank-rocker mechanism where the input link revolves 360° continuously while the output l…

A CNC linear slide is driven by a ground precision ball screw with a lead (pitch) p = 10 mm/rev and a mechanical efficiency eta = 0.90 (90%). If the slide must exert a continuous axial cutting force F_axial = 1800 N against a workpiece during machining, what motor torque T_drive is required to overcome this axial thrust?

• A2.86 N·m
• B3.18 N·m
• C2.58 N·m
• D20.0 N·m

In the kinematic design of 6-DOF articulated industrial robot arms, what geometric condition allows the inverse kinematics problem to be solved analytically in closed form via Pieper's kinematic decoupling?

• AAll six joint axes must be strictly parallel to one another
• BThe robot must possess at least two prismatic joints in the wrist assembly
• CThree consecutive joint axes intersect at a single common point (such as a spherical wris…
• DThe links must have identical link lengths and zero twist angles

An analog sensor conditioning circuit employs a differential amplifier with differential gain A_d = 1000 and common-mode gain A_cm = 0.05. What is the Common-Mode Rejection Ratio (CMRR) in decibels (dB), and what primary design factor degrades CMRR in discrete op-amp implementations?

• A86 dB; degraded primarily by resistor tolerance mismatch in the bridge network
• B26 dB; degraded primarily by op-amp input bias currents
• C40 dB; degraded primarily by supply rail ripple
• D106 dB; degraded primarily by thermal Johnson noise

A DC solenoid coil with inductance L = 250 mH and internal resistance R = 12 Ω is switched at 24 V DC using a low-side N-channel MOSFET. When the MOSFET turns off abruptly, what phenomenon occurs across the drain terminal if no freewheeling clamp diode is present, and why?

• AThe drain voltage drops to -24 V, causing forward conduction of the body diode
• BThe coil current instantly reverses, generating an electrostatic charge on the gate
• CThe drain terminal remains at 24 V due to capacitive decoupling
• DA massive positive inductive voltage spike (V = L*di/dt) appears at the drain, risking av…

In precision robotic arm joints, Harmonic Drive (strain wave gearing) mechanisms are widely used instead of conventional spur gear trains. Which set of attributes correctly describes the operating principle and mechanical features of a harmonic drive?

• AThree rigid planetary gears rotating around a sun gear, featuring high backlash and low t…
• BAn elliptical wave generator, flexible external-toothed flexspline, and rigid internal-to…
• CA worm and worm gear pair operating strictly on hydrodynamic fluid film sliding contact
• DA bevel gear differential requiring external preloading springs to eliminate backlash

A CNC mill working in the XY plane (G17), in absolute coordinates (G90) and millimeters, executes the block G02 X40 Y20 I10 J0 F200. What does this block command?

• AA clockwise circular arc from the current position to X40 Y20, with the arc center offset…
• BA counterclockwise circular arc to X40 Y20 with a radius of 10 mm at 200 mm/min
• CA rapid (non-cutting) move to X40 Y20, ignoring the feed rate
• DA straight-line cutting move to X40 Y20, with I and J applying a tool-length offset

A finite element analysis of a robot bracket is repeated with successively refined meshes. The maximum von Mises stress is 182 MPa (coarse mesh), 205 MPa (medium) and 207 MPa (fine), and the peak lies in a filleted region. What should the engineer conclude?

• AThe result has converged (about a 1% change between the last two meshes), so about 207 MP…
• BThe coarse mesh is the most accurate because it averages out numerical noise
• CThe stress should be reported as the average of the three meshes (198 MPa)
• DMesh refinement should never change the result, so the differences indicate a software er…

An operational amplifier with a Gain-Bandwidth Product (GBWP) of 10 MHz is configured as a non-inverting amplifier with input resistor R1 = 1.0 kΩ and feedback resistor Rf = 39 kΩ. What is the closed-loop voltage gain A_v and the resulting -3 dB small-signal bandwidth f_bw of the circuit?

• AA_v = 39 V/V, f_bw = 256 kHz
• BA_v = 40 V/V, f_bw = 250 kHz
• CA_v = 40 V/V, f_bw = 10 MHz
• DA_v = 39 V/V, f_bw = 390 kHz

A packaging machine utilizes an external 4-slot Geneva mechanism (Maltese cross) driven by a pin rotating at a constant angular speed of 60 RPM. What is the indexing angle of the driven wheel per cycle, and what fraction of each driver revolution is spent in dwell (stationary rest)?

• A45° indexing angle; 1/4 dwell time fraction
• B60° indexing angle; 1/2 dwell time fraction
• C180° indexing angle; 3/4 dwell time fraction
• D90° indexing angle; 3/4 dwell time fraction

A linear mechatronic system has the state matrix A = [[0, 1], [-6, -5]] and input matrix B = [0; 2]. To determine if the system states can be driven to arbitrary values via state feedback u = -K*x, what is the controllability matrix C_o and is the system completely state controllable according to the Kalman rank criterion?

• AC_o = [[0, 0], [2, -10]]; rank is 1, so the system is uncontrollable
• BC_o = [[2, 0], [-10, 2]]; rank is 2, so the system is controllable
• CC_o = [[0, 2], [2, -10]]; rank is 2, so the system is completely controllable
• DC_o = [[1, 0], [0, 1]]; rank is 2, but controllability depends on eigenvalues

An automation retrofit project has these activities: A, design (4 weeks); B, procure parts (6 weeks, after A); C, write the PLC program (3 weeks, after A); D, assemble the cell (2 weeks, after B); E, integration and testing (2 weeks, after C and D). Using the critical path method, what is the project duration, and how much total float does activity C have?

• A14 weeks; C has 5 weeks of float
• B17 weeks; C has no float
• C9 weeks; C is on the critical path
• D14 weeks; C has 3 weeks of float

In precision cam-follower kinematic synthesis, how does a cycloidal motion profile compare to a simple harmonic motion (SHM) profile during rise-dwell transitions?

• ACycloidal motion has infinite jerk at dwell boundaries, causing severe vibrations at high…
• BCycloidal motion has continuous acceleration that starts and ends at zero, resulting in f…
• CSimple harmonic motion provides strictly zero jerk throughout the entire stroke
• DSimple harmonic motion eliminates jerk discontinuities at dwell boundaries, resulting in…

Compliant flexure mechanisms are commonly incorporated into nanometer-scale mechatronic micro-positioning stages (such as atomic force microscope scanners). What is the primary operational advantage and primary mechanical limitation of flexure mechanisms compared to conventional rolling-element linear bearings?

• AInfinite range of travel; excessive frictional hysteresis during reversal
• BImmunity to thermal expansion; high wear due to continuous sliding contact
• CZero manufacturing cost; requirement for continuous oil lubrication
• DComplete absence of friction, stiction, and mechanical backlash; severely limited travel…

A robotic palletizing cell costs MXN 1,800,000 installed. It is expected to save MXN 600,000 per year in labor and to add MXN 150,000 per year in maintenance and energy costs. Ignoring the time value of money, what is the simple payback period?

• A4.0 years
• B3.0 years
• C12.0 years
• D2.4 years

A power MOSFET driving a DC motor dissipates P_loss = 15 W of average power in continuous conduction. The junction-to-case thermal resistance is R_th(j-c) = 1.2 °C/W, and the thermal interface pad resistance is R_th(c-s) = 0.5 °C/W. If the maximum ambient operating temperature inside the control enclosure is T_amb = 50 °C and the silicon junction temperature must not exceed T_j_max = 125 °C, what is the maximum allowable thermal resistance of the heatsink R_th(s-a)?

• A3.3 °C/W
• B5.0 °C/W
• C1.7 °C/W
• D6.7 °C/W

A simple pendulum actuator has the non-linear equation of motion: J*theta'' + b*theta' + m*g*L*sin(theta) = u(t). To design a linear state-space controller around the stable downward vertical equilibrium operating point (theta_0 = 0, theta'_0 = 0, u_0 = 0), what is the resulting linearized system equation using small-angle Taylor series approximation?

• AJ*theta'' + b*theta' + m*g*L = u(t)
• BJ*theta'' + b*theta' + (m*g*L)*theta = u(t)
• CJ*theta'' + b*theta' - (m*g*L)*theta = u(t)
• DJ*theta'' + b*theta' + (m*g*L)*(theta - theta³/6) = u(t)

A planetary (epicyclic) gearbox consists of a sun gear with N_s = 20 teeth, three identical planet gears, and a fixed stationary outer ring gear with N_r = 80 teeth. If the input motor drives the sun gear at 1500 RPM, what is the output rotational speed and direction of the planet carrier arm according to Willis's epicyclic formula?

• A375 RPM in the opposite direction
• B300 RPM in the opposite direction
• C500 RPM in the same direction
• D300 RPM in the same direction

An incremental optical encoder outputs two square wave channels, Channel A and Channel B, in phase quadrature (electrically separated by 90°). When decoded using a microcontroller hardware quadrature decoder set to 4x (four-edge) counting mode, how does the system establish rotational direction and achieve resolution multiplication?

• ADirection is decoded by comparing the phase relationship (which channel leads), and resol…
• BDirection is decoded by measuring the pulse width, and resolution is doubled by counting…
• CDirection is decoded by channel voltage amplitude, and resolution is increased by analog…
• DDirection is determined by the index Z pulse, while 4x counting multiplies the motor volt…

A high-speed CNC milling spindle has an incremental optical encoder with a resolution of 1024 pulses per revolution (PPR). During high-speed machining, the spindle rotates at 3000 RPM. What is the fundamental square wave output frequency f on Channel A, and what edge frequency must the microcontroller capture timer support in 4x quadrature decoding mode?

• Af = 204.8 kHz; capture edge rate = 819.2 kHz
• Bf = 51.2 kHz; capture edge rate = 204.8 kHz
• Cf = 30.7 kHz; capture edge rate = 122.8 kHz
• Df = 853 Hz; capture edge rate = 3.41 kHz

A metal foil strain gauge with nominal resistance R = 120 Ω and gauge factor GF = 2.00 is bonded to a robotic gripper finger in a quarter-bridge Wheatstone circuit excited by V_ex = 10.0 V. When a gripping force is applied, the beam experiences a tensile strain epsilon = 1000 microstrain (1.00 × 10⁻³ mm/mm). Assuming ideal bridge linearity for small strains (V_out ≈ (V_ex / 4) * GF * epsilon), what differential voltage V_out is produced across the bridge terminals?

• A20.0 mV
• B10.0 mV
• C5.00 mV
• D2.50 mV

A mobile robot uses a triaxial MEMS capacitive accelerometer to measure chassis pitch angle (inclination) relative to the horizontal plane. If the robot is completely stationary on an incline and the accelerometer reads a_x = +4.905 m/s² along its longitudinal axis and a_z = +8.496 m/s² along its vertical normal axis (with gravity g = 9.81 m/s²), what is the measured pitch angle theta?

• A15.0°
• B45.0°
• C60.0°
• D30.0°

A standard two-phase hybrid stepper motor has a permanent magnet rotor with 50 teeth (Nr = 50). What is its full-step angle theta_s in degrees, and how many full steps are required for the motor shaft to complete exactly one 360° revolution?

• Atheta_s = 1.8°; 200 steps per revolution
• Btheta_s = 3.6°; 100 steps per revolution
• Ctheta_s = 0.9°; 400 steps per revolution
• Dtheta_s = 7.2°; 50 steps per revolution

When controlling a two-phase hybrid stepper motor in microstepping mode (such as 1/16 microstepping), how are the stator phase currents regulated, and what primary operational benefits are achieved compared to full-step mode?

• APhase currents are pulsed as square waves at double voltage; increases top speed by 400%
• BPhase currents are modulated as sine and cosine waves (I_A = I_max * cos(theta), I_B = I_…
• COne phase is energized with pure DC while the second is grounded; provides maximum holdin…
• DBoth phases are driven by variable frequency 3-phase AC; eliminates the need for current…

In standard six-step (trapezoidal) commutation of a three-phase Brushless DC (BLDC) motor with three digital Hall-effect sensors spaced 120° electrical apart, how many inverter power switches conduct at any given state, and how many motor phases carry current simultaneously?

• AAll six switches conduct simultaneously; all three phases carry continuous current
• BOnly one switch conducts; current flows through one phase to ground
• CExactly two switches conduct (one high-side switch on one leg and one low-side switch on…
• DThree high-side switches conduct while all low-side switches are held off

In Field-Oriented Control (FOC) of Permanent Magnet Synchronous Motors (PMSM), what is the function of the mathematical Clarke and Park transformations applied to the measured three-phase stator currents (i_a, i_b, i_c)?

• ATo convert AC voltages into mechanical shaft vibrations for resonance analysis
• BTo transform frequency-domain Fourier components into discrete wavelet coefficients
• CTo filter out high-frequency PWM switching harmonics using numerical averaging
• DClarke transforms stationary 3-phase currents (abc) into a stationary 2-phase frame (alph…

For a permanent magnet DC motor operating in steady state, the torque constant is specified as K_t = 0.080 N·m/A. In consistent SI units (radians per second), what is the numerical value of the back-EMF constant K_e (in V·s/rad), and why?

• AK_e = 0.080 V·s/rad, because conservation of energy dictates that mechanical power (T * o…
• BK_e = 0.0084 V·s/rad, due to the 2*pi / 60 unit conversion from RPM
• CK_e = 0.0013 V·s/rad, because voltage and torque are inversely proportional
• DK_e = 12.5 V·s/rad, because K_e is defined as 1 / K_t

A 12-bit successive approximation register (SAR) ADC on a microcontroller has a full-scale analog input range from 0 V to 3.30 V (V_ref = 3.30 V). What is the ideal voltage resolution corresponding to 1 LSB, and what decimal digital code will be produced for an analog sensor input of exactly 1.65 V?

• A3.22 mV; digital code = 512
• B0.806 mV; digital code = 2048
• C0.403 mV; digital code = 4096
• D1.61 mV; digital code = 1024

An analog vibration sensor produces signals containing frequency components up to f_signal = 1200 Hz. If this signal is sampled by an ADC at f_sample = 2000 samples/second without an analog anti-aliasing pre-filter, what aliased artifact frequency will appear in the digitized spectrum?

• A1200 Hz without distortion
• B1000 Hz
• C800 Hz
• D400 Hz

In embedded C firmware development for microcontrollers, why must global variables modified inside an Interrupt Service Routine (ISR) and monitored inside the main loop be declared with the 'volatile' type qualifier?

• ATo allocate the variable in non-volatile flash memory instead of volatile SRAM
• BTo automatically protect the variable with an atomic hardware mutex lock
• CTo prevent stack overflow by storing the variable in the CPU register file
• DTo instruct the C compiler not to optimize or cache the variable in a CPU register, ensur…

In bare-metal embedded C firmware controlling a mechatronic valve on GPIO port register PORTB, which bitwise C statement sets Bit 4 to logic HIGH without modifying any other bits in PORTB?

• APORTB |= (1 << 4);
• BPORTB &= ~(1 << 4);
• CPORTB ^= (1 << 4);
• DPORTB = (1 << 4);

In an ARM Cortex-M microcontroller equipped with a Nested Vectored Interrupt Controller (NVIC), what is the difference between interrupt preempt priority and subpriority?

• ASubpriority determines whether an ISR can execute floating-point instructions, whereas pr…
• BPreempt priority allows a higher-priority interrupt to preempt (nest inside) a currently…
• CPreempt priority is set in software, whereas subpriority is hardwired permanently in sili…
• DPreempt priority applies only to external GPIO pins, while subpriority applies exclusivel…

A microcontroller hardware timer peripheral is clocked at f_clk = 72 MHz. The engineer needs to configure a center-aligned PWM channel to drive a motor inverter with an exact PWM switching frequency f_pwm = 10.0 kHz. If the timer prescaler register is configured with PSC = 0 (1:1 clock division, f_timer = 72 MHz), what Auto-Reload Register (ARR) value must be programmed?

• AARR = 7199
• BARR = 7200
• CARR = 3600
• DARR = 3599

A three-phase inverter driving a BLDC motor uses complementary PWM with dead-time insertion. The power stage uses MOSFETs with a turn-off delay time t_d(off) = 120 ns, fall time t_f = 60 ns, turn-on delay t_d(on) = 40 ns, and rise time t_r = 30 ns. What is the minimum recommended dead-time delay t_dead that must be programmed into the microcontroller's PWM dead-time generator to guarantee zero shoot-through?

• At_dead = 40 ns
• Bt_dead = 70 ns
• Ct_dead = 120 ns
• DAt least t_d(off) + t_f − t_d(on) = 140 ns, plus a margin for temperature and driver skew…

A mechanical limit switch on an automated gantry axis triggers an external interrupt on a microcontroller. Due to mechanical contact bounce, the signal oscillates for 5 ms upon closure. Which approach represents the most robust engineering method for contact debouncing without wasting microcontroller processing cycles?

• AA hardware low-pass RC filter (tau ≈ 2 ms) followed by a Schmitt trigger buffer, or an in…
• BCalling a blocking delay loop (e.g., delay_ms(10)) directly inside the Interrupt Service…
• CIncreasing the microcontroller clock frequency so that bounce pulses occur faster than th…
• DPolling the pin in an infinite while(1) loop without sleep or interrupts

Absolute optical rotary encoders frequently encode shaft positions using Gray code rather than natural binary code on their optical disk tracks. What critical physical phenomenon justifies the use of Gray code in position sensing?

• AGray code uses fewer phototransistors than binary code for the same resolution
• BIn Gray code, exactly one bit changes state between any two consecutive position incremen…
• CGray code signals can travel ten times farther over RS-485 cables without termination
• DGray code eliminates optical diffraction across the grating slits