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Joined 2026-09-21 Message
Incoming links: Sensor
Actuator 2026-11-05
An actuator turns supplied energy and a control input into a mechanical action, such as a displacement, force or torque. An electric motor produces rotation; a hydraulic cylinder converts fluid pressure into a linear push. The sensor reports a system's state, while the actuator changes it.
In an ideal cylinder with piston area and pressure difference , . Moving at speed requires volume flow , so mechanical power equals hydraulic power before losses. This relation shows why force capacity, speed and supply power must be considered together. In a controlled mechanism, actuator saturation and response time constrain achievable feedback control.
Christoph Gerber 2026-11-05
Christoph Gerber helped develop atomic force microscopy with Gerd Binnig and Calvin Quate. Their 1986 paper introduced an instrument that senses probe–sample forces through a compliant cantilever, enabling investigation of electrically insulating surfaces.[ref]
Atomic Force Microscope by Gerd Binnig and others. Original paper, byline, abstract and preliminary measurements
The mechanical probe makes a small interaction measurable through displacement: in a linear approximation, a cantilever of spring constant deflecting by carries force . Gerber's later research includes biochemical cantilever sensors, extending the same transduction principle from surface imaging to detection of molecular interactions.[ref]
A current-sign certificate with a curvature bound uses a bound on the second derivative of an electric current to certify the sign of an extrapolated current. An affine ramp is predicted exactly by two correctly timed samples, so its uncertainty should depend on curvature rather than counting the entire ramp as error. Current direction matters physically because it selects recirculation paths during switching dead time.[ref]
Let samples at and produce measurements and , with and . For a future time , use the linear extrapolationIf is twice continuously differentiable and throughout , the polynomial interpolation error givesThe model term follows by applying the remainder to the two-node interpolant: for some . The sample-error terms use absolute coefficients, as required by the signed-filter current-sign certificate. At , the model contribution is and equal sample bounds contribute .
For an original example, take , and each sample error bounded by . At ,If and , the predicted current is , certifying actual current at least at that future instant. To certify the entire interval , check everywhere. In this example the prediction decreases linearly and increases, so the minimum margin occurs at and the same lower bound applies throughout.
The curvature limit is a physical assumption. A switching event, sensor clipping or a slope discontinuity can invalidate it even when a fitted ramp looks smooth at the sample times. A bounded first derivative alone does not imply any finite . Timing uncertainty in a curvature-based current-sign certificate also matters: two accurate current values at incorrectly modeled times need not extrapolate an affine ramp correctly.
A proposed test supplies known smooth ramps and curved waveforms, records sample timestamps and checks the independently measured future waveform against the enclosure. Test transitions separately. The result is a deterministic sign guarantee only when the sample and curvature bounds are deterministic; substituting one standard uncertainty for an absolute error bound changes the claim.
Electrical engineer Created 2026-10-14 Updated 2026-11-05
An electrical engineer designs or analyzes systems involving electrical energy, electromagnetic fields and information-carrying signals. The work includes circuits, power conversion, communication, instrumentation and control. A sensor readout, for example, needs an amplifier that preserves the signal while accounting for noise, bandwidth, loading and supply limitations. The mathematical circuit model must be compared with component tolerances and measured behaviour, because an ideal amplifier equation does not capture every physical limit.
Hidden Markov model Created 2026-09-28 Updated 2026-11-05
Hot-wire anemometry 2026-11-05
Hot-wire anemometry is the measurement method that turns a hot-wire anemometer's heat-transfer signal into a flow velocity time series and its statistics. It is especially useful for resolving fluctuations, but the interpreted quantity depends on probe direction, spatial extent and dynamic response. The manufacturer's primary method requires known-flow calibration and separately describes directional and temperature sensitivity.[ref]
Measurement Principles of CTA by Dantec Dynamics. Velocity sensitivity, Directional sensitivity and Temperature sensitivity
The order of processing matters because a nonlinear calibration does not commute with averaging. For an original relation in numerical volts and metres per second, equal-duration speeds and give outputs and . Converting their average output giveswhereas converting each output first and then averaging gives the true two-level mean . A proposed processing chain therefore applies the validated instantaneous conversion before calculating statistics, subject to its bandwidth and direction limitations.
For equally spaced converted samples, define the record mean and root-mean-square fluctuation byThe stipulated record has mean and . Its ratio is about . This is the RMS fluctuation of that finite record, not automatically an unbiased estimate based on four independent observations; turbulence samples can be strongly correlated.
The measurement has both temporal and spatial filters. An electronic anti-aliasing filter must sufficiently attenuate unresolved fluctuations before digitization; a sampling rate of has Nyquist frequency regardless of the wire's faster response. Finite wire length produces hot-wire spatial averaging, so increasing sampling rate alone cannot recover spatial scales already averaged by the sensor. Flow direction changes can also be misread as speed changes by a single-wire calibration.
A useful proposed grid-turbulence experiment keeps the wire transverse to a positive mean flow, performs a reference-flow calibration before and after acquisition, records ambient temperature, and documents wire geometry, bridge settings, sample rate and filtering. Compare means and fluctuation spectra at different positions and repeat with a shorter wire or a changed electronic bandwidth. A changed high-frequency spectrum can reflect instrumental filtering as well as changed flow physics.
The electrical control loop should also be characterized rather than assigning a universal bandwidth to the wire alone; the primary description explicitly connects frequency response to wire and servo behavior.[ref] A measured time series is evidence for the flow only within the direction, spatial, thermal and frequency ranges actually tested.
Hot-wire spatial averaging 2026-11-05
Hot-wire spatial averaging is the loss or alteration of small-scale flow information because a heated sensing wire has finite spatial extent. Even a perfectly fast electronic readout observes a spatially distributed heat-transfer response. The manufacturer's practical guide relates spatial resolution to wire dimensions, flow and instrument frequency response.[ref]
An original small-perturbation model treats the inferred velocity fluctuation as a uniform line average over wire length . With measuring distance along the wire,For a spatial sinusoid , direct integration givesThis is a sinc function transfer factor. It follows from the stipulated uniform weighting and local linearity; a real wire's nonuniform temperature and nonlinear heat transfer require a more detailed spatial kernel.
For spatial wavelength , a fluctuation with has amplitude factor about and variance or power factor . At , the factors are and . At , one complete sinusoidal cycle lies along the wire and its line average is exactly zero. Raising the sample rate cannot restore a component that this spatial average has canceled.
For a wire, these illustrative wavelengths are , and . The result depends on the component of the spatial wavevector along the wire, rather than only on a temporal frequency. Orientation-dependent spatial filtering by a hot wire matters because a moving three-dimensional structure can have different projections along the wire and the mean flow. Under a frozen-advection model, temporal frequency obeys ; substituting into the wire-length factor requires an additional alignment assumption.
Spatial and temporal filters can both reduce measured fluctuation variance. In this single-sinusoid model, the measured variance is times the true variance even with noiseless electronics. A correction obtained by dividing by becomes unstable near its zeros, amplifying measurement noise without recovering independently lost information.
A proposed test compares probes of different active lengths in the same statistically repeatable flow, after separate steady calibrations and matched electronic filtering. Record wire orientation, support geometry, ambient temperature and traverse location; compare fluctuation spectra as well as mean velocity. A difference that tracks wire length supports a spatial-filtering interpretation, but changed thermal response or probe disturbance must also be checked. The observation establishes the filtered response of the actual apparatus over its characterized range, not an unqualified point measurement at every turbulent scale.
Measuring chain 2026-11-05
A measuring chain is one successive signal path through a measuring system, beginning at a sensor and ending at an output element. The VIM illustrates this with both an electro-acoustic chain and a mechanical chain; a measuring chain need not be electronic.[ref]
Consider an original force measurement: a load cell produces an electric potential difference, an amplifier scales that signal, an analog-to-digital converter encodes it, and software converts the code to a force value. This is one measuring chain within the larger measuring system, which also includes its excitation supply, references and mounting arrangements. The load cell acts as a measuring transducer.
In an ideal linear model, let sensor response be , amplifier gain , and converter step per code increment. If the additive output offset is increments, the numerical output isThus implies . These are stipulated teaching values, not measured equipment performance.
The example exposes why measurement calibration must describe the relevant path. Changing amplifier gain changes the relation between output and force even if the load cell is untouched. A saturated stage can also discard information that later conversion cannot restore. Gain uncertainty, offsets, instrumental drift and finite conversion steps contribute at different points; treating the final display's increment as the whole measurement uncertainty overlooks those contributions.
Measuring transducer 2026-11-05
A measuring transducer is a device whose output quantity has a specified relation to its input quantity and is used in measurement. VIM examples include a thermocouple, a strain gauge and a Bourdon tube.[ref] A measuring transducer provides a link in a measuring chain; it need not itself display a finished measurement result.
For an original pressure readout, choose a linear modelwith pressure , output electric potential difference , transducer sensitivity , and offset . An output then corresponds to . An amplifier, analog-to-digital converter and display can follow the transducer, each contributing to the whole measuring system.
The inverse calculation exposes distinct uncertainty contributions. Holding the other inputs fixed, a small output change changes inferred pressure by ; a small offset error changes it by . An output increment corresponds to for the stipulated sensitivity, but does not establish a total measurement uncertainty of that size.
Characterize the relevant range, temperature conditions, response time and possible instrumental drift during measurement calibration. The relation can be nonlinear, in which case local transducer sensitivity is the appropriate derivative rather than one gain valid everywhere. The definition also allows input and output quantities of the same kind; it does not require changing from a mechanical quantity to an electrical one. A sensor denotes the part directly affected by the phenomenon being sensed, whereas a complete measuring chain can contain further measuring transducers.
Microelectromechanical system Created 2026-10-20 Updated 2026-11-05
A microelectromechanical system combines small mechanical structures with electrical sensing or actuation. Fabrication methods related to semiconductor device fabrication can create suspended beams, membranes and movable masses together with their electrodes. Sensors and actuators can consequently be integrated into compact devices.
A capacitive accelerometer illustrates the mechanism. A suspended proof mass moves relative to its support under acceleration. In a simple spring model, a slowly varying support acceleration produces a relative displacement , where is the mass and is the spring constant. Measuring a change of capacitance then measures that displacement. The ADXL335 uses suspended polysilicon structures and a differential capacitor to turn motion into an electrical signal.[ref]
ADXL335 Data Sheet by Analog Devices. Revision B, page 10, Theory of Operation and Mechanical Sensor
For an idealized pair of parallel-plate capacitors with equal area and gaps , the capacitance difference isThis model explains why a small mechanical displacement can produce a signed electrical measurement; it is not a detailed model of every commercial MEMS geometry.
Optoelectronics Created 2026-10-18 Updated 2026-11-05
Optoelectronics combines electronic devices with generation, detection or control of light. A light-emitting diode converts carrier recombination into photons, while a photodiode converts absorbed photons into an electrical response. Semiconductor band structure determines which photon energies interact efficiently, but device geometry, recombination and transport also control speed and efficiency. Optical communication links, image sensors and photovoltaic devices use different parts of this interaction. Measuring an optical signal therefore often requires understanding both the light field and the electronic readout.
Maintain the latest five temperature readings in a circular buffer, together with their running sum. The following C programming language code spells out the message passing interface rather than assuming a particular library:
send(dst,&m) is a blocking synchronous message passing send; receive(src,&m) receives from the specified sender or ANY and returns the sender's identity; sendrec(dst,&m) atomically sends the request and waits for that sender's reply in the same message object. Successful, reliable operations are assumed. Message contents are copied by the interface.enum { ANY = -1, TIMER = 1, TEMP = 2 };
enum { PULSE, PING, REQUEST, REPLY };
typedef struct {
int type;
int period_ms;
double value;
} Message;
extern void send(int dst, const Message *m);
extern int receive(int src, Message *m);
extern void sendrec(int dst, Message *m);
void smooth(void) {
double history[5] = {0};
double sum = 0;
int count = 0, next = 0;
Message m = { .type = PULSE, .period_ms = 1000 };
send(TIMER, &m); /* subscribe once */
for (;;) {
int sender = receive(count < 5 ? TIMER : ANY, &m);
if (sender == TIMER && m.type == PING) {
Message t = { .type = REQUEST };
sendrec(TEMP, &t); /* matching REPLY contains t.value */
if (count == 5)
sum -= history[next];
else
++count;
history[next] = t.value;
sum += t.value;
next = (next + 1) % 5;
} else if (count == 5 && m.type == REQUEST) {
Message answer = { .type = REPLY, .value = sum / 5.0 };
send(sender, &answer);
}
}
}Before the fifth reading, selective reception from
TIMER prevents premature client requests from being accepted. Such clients wait at their synchronous sends; they are not given a partial arithmetic mean. Thereafter the operating-system process receives both timer messages and client requests. Each accepted PING initiates one measurement; each accepted client request returns the arithmetic mean of the five most recently completed measurements, without initiating another measurement or changing the circular buffer.The loop invariant is that
count is the number of valid readings, capped at five, sum is their sum, and next is the next unused slot during startup or the oldest slot afterwards. Removing the overwritten reading and adding the new one preserves this loop invariant. Each update and reply uses time complexity and storage, since the window length is fixed. Under timely sensor replies, timer delivery and process scheduling, measurements are initiated once per second. The next parts explain failures of these timing assumptions; the code does not promise one-second sampling when the sensor itself cannot sustain it.With synchronous message passing, the smoothing operating-system process can still be waiting for
TEMP when its next PING is due. If the timer service sends to subscribers serially, it blocks on this unready recipient and cannot deliver the other subscribers' ticks: one slow sensor can delay every timer client through head-of-line blocking. Once it resumes, implementations may deliver late ticks, drift from their schedule, or accumulate overdue work.The consequence depends on the delivery model. With buffered sends the timer need not block immediately, but its queue can grow or overflow; the smoothing operating-system process still cannot process readings at a sustained rate faster than the sensor. A nonblocking notification mechanism or separate timer-delivery workers can isolate other subscribers, while coalescing missed ticks prevents an unlimited backlog. These changes do not make an over-slow sensor meet the original sampling rate.
Rank-one update of pressure-map information 2026-11-05
A rank-one update of pressure-map information describes the extra constraint supplied by one independent scalar pressure measurement. Suppose the existing pressure-map information matrix is , and a new sensor reports with known variance , independent of the existing errors. Adding its squared residual to the weighted least squares objective givesThe added matrix has rank one when . It is positive semidefinite because its quadratic form is . Thus the new observation cannot reduce information in any direction under this fixed linear map and noise model. The noise normalization is the same whitening transformation used to express a correlated residual metric as an ordinary squared norm.[ref]
The update can remove a missing direction only if the new channel actually sees it. More precisely,This follows because a sum of two nonnegative quadratic forms is zero exactly when both are zero. Repeating an existing mixture improves its precision but cannot identify a pressure contrast that all mixtures annihilate.
When is positive definite, write . The Sherman–Morrison formula yields the updated estimator covariance matrixMultiplication by verifies the identity directly. For a particular quantity , its variance falls by . A small noise level is valuable only together with a useful sensitivity direction.
For an original calculation in kilopascal coordinates, let , and . ThenThe variance of the sum drops from to . The negative off-diagonal entry means the two inferred coefficients now have negatively correlated errors; it does not mean either individual variance is negative.
A correlated-channel update of pressure-map information needs the new channel's residual after predicting it from old channel noise. Simply adding double-counts information when a common amplifier or reference contributes correlated errors. A proposed array experiment uses repeated known loads to estimate sensitivity and noise separately, adds one channel, and compares withheld-load errors with . Agreement tests the full assumed model, including independence and unchanged sensor response, rather than the matrix identity alone.
Robotics 2026-11-05
Robotics studies the design, modelling and control of machines that interact with their surroundings through sensing and motion. A robot combines sensors, actuators, computation and a mechanical structure. A robot arm must relate joint motion to the position and orientation of its end effector; a mobile robot must also estimate where it is relative to its environment.[ref]
Modern Robotics: Mechanics, Planning, and Control by Kevin M. Lynch and Frank C. Park. Introductory scope; rigid-body configurations and motion
Kinematics asks which motions a mechanism permits. Dynamics determines the forces and torques needed to produce them, while feedback control corrects deviations using measurements. A desired path is useful only when the mechanism can realize it within constraints such as motor effort, contact and obstacles. These connections make robotics a meeting point of mechanics, geometry, statistical inference and control theory.
Sensor Created 2026-10-20 Updated 2026-11-05
A sensor converts a physical quantity into an observable signal. A temperature sensor might produce a voltage or resistance change that a measuring system converts into a temperature estimate. A useful model separates sensitivity, offset, noise, calibration and dynamic response: a large output change does not guarantee accuracy if the calibration drifts. Sensors also load the system they measure, for example by drawing heat or electrical current. The complete measurement chain includes the sensor, readout electronics and the model mapping the signal back to the intended quantity.
Stance phase 2026-11-05
The stance phase of a robot leg is the portion of a gait during which its foot is in the intended ground contact. It permits force transfer between the robot and its surroundings. Contact can occur with little load, and contact alone does not imply that the foot remains fixed without slipping. The swing phase instead transfers the foot toward another contact.
In an ideal rigid, nonadhesive contact model, let be the foot's normal gap above the ground and its normal contact force. The conditionsexclude penetration and tensile ground reaction. An open gap requires zero normal reaction; a zero gap permits a compressive reaction but does not require it to be strictly positive. The primary contact model distinguishes these unilateral constraints from the force/torque equations for equilibrium.[ref]
Robotic Systems by Kris Hauser. Chapter 12, Contact modeling and Equilibrium conditions
For an original level-ground example, take a robot supported by two stance feet, neglecting other external vertical forces. Newton's second law giveswhere is gravitational acceleration and is upward center of mass acceleration. With equal sharing and , each foot carries . With , each carries . Equal sharing is an additional symmetry assumption, not a consequence of knowing there are two contacts.
A simple Coulomb friction model constrains tangential force by . At zero vertical acceleration and , the two feet's combined horizontal-force capacity is at most in this planar model. Accelerating the body horizontally at would require and violate that bound. A stance-time schedule alone cannot remove this force limit. Individual contact geometry and torque balance can impose further constraints even when the combined bound passes.
For a periodic cycle, contact duration gives duty cycle . A proposed test records stance timing and forces separately, using calibrated sensors under the contacts together with body-motion measurements. It checks load transfer and slipping as well as touch timing. A support polygon is useful in an explicitly static planar model; dynamic stance additionally requires the changing force and momentum balance.
Swing phase 2026-11-05
The swing phase of a robot leg is the interval in which its foot moves between ground contacts without providing the intended ground support. It complements the stance phase. In a periodic gait with period and contact duty cycle , its duration is . The leg can still require substantial actuator effort: moving its own mass and controlling its trajectory are different from supporting the robot through ground contact.
An original planar foot path gives an explicit design example. Let parameterize a swing of duration , horizontal travel and desired swing-foot clearance over a flat reference plane. ChooseBoth components have zero endpoint velocity. At mid-swing the foot has moved halfway horizontally and reaches height . The maximum horizontal and vertical speed magnitudes areFor , and , these are and about . Halving the available swing time doubles the path's speed requirements and quadruples its acceleration requirements. A contact schedule can therefore be feasible in timing arithmetic but too demanding for the actual leg.
The path is only a foot-level specification. Inverse kinematics must find joint configurations that realize it, and joint motion, collision and actuator constraints must also hold. Zero endpoint velocity does not guarantee continuous acceleration when this segment is joined to another trajectory. An uncertain or uneven ground height changes the actual clearance and contact time.
The primary contact-planning treatment distinguishes choosing contacts from moving through configuration space between them.[ref]
Robotic Systems by Kris Hauser. Chapter 12, Manipulation planning and locomotion planning and Multi-modal motion planning
A proposed robot test measures the foot path, the contact transition and joint response while changing swing duration or clearance. Calibrated sensors can distinguish premature ground contact from a trajectory-tracking error. The example above is an original motion prescription; it is not a measured gait or a complete stability controller. Telemetry 2026-11-05
Telemetry transmits measurements from a remote system to a receiving system. A useful telemetry chain connects a sensor, signal conditioning, a data converter, an encoding and transmission system, and a receiver that reconstructs the reported quantities. Calibration, units and the time of measurement remain part of the scientific meaning of the received data.
Spacecraft illustrate why these stages are distinct. NASA's guide describes science and engineering measurements carried by a modulated downlink, then separated on the ground using their positions in frames or identifying information in packets. Locking a receiver onto the radio carrier is different from recognizing the data frames reliably.[ref]
Basics of Space Flight (2017 edition) by Dave Doody. Chapter 10, Uplink and Downlink; Multiplexing; Telemetry Lock; Channelization
For an original rate calculation, channels sampled at readings per second with transmitted bits per reading require at least bits per second for the raw measurements. Sixteen channels with twelve-bit readings at readings per second require bits per second before framing and other overhead. The receiving display must also distinguish the sample time from arrival time: transport delay and missing records otherwise make a remote process appear to evolve differently from the measured one.
Temperature sensor 2026-11-05
A temperature sensor is a sensor whose physical response is used to estimate temperature. A resistance thermometer and a thermistor use changes in electrical resistance; a thermocouple uses the Seebeck effect. The sensor element, its thermal contact and its electrical readout together determine what a temperature measurement means.[ref]
DOE Fundamentals Handbook Instrumentation and Control Volume 1 of 2. Module 1, printed pp. 1–7, resistance detectors and thermocouples
A contact sensor first responds to its own temperature, which need not immediately equal that of the object or fluid. A useful original lumped thermal model writes the first law of thermodynamics for a sensor with heat capacity , thermal conductance to an environment at , and internal heating power :For constant inputs, its thermal time constant and equilibrium are and . The temperature sensor response time and the bias from heating are different properties. Better thermal coupling both shortens and reduces in this model.
Take stipulated values and . Then . With and an environment step from to ,At the sensor reads about , despite a perfect electrical readout. Reaching of the step takes . A steady heating input would instead add at equilibrium. These are model calculations, not universal sensor specifications.
A proposed two-bath step test of a temperature sensor transfers a small probe between two well-stirred baths with independently established temperatures and records its readout against time. Repeating with a protective sleeve tests the thermal part of the measurement chain. The DOE handbook illustrates insulated sensor elements inside metal sheaths and protective wells; electrical accuracy alone does not describe that complete assembly.[ref]
Thermal loading by a contact temperature sensor is another limit: a probe exchanges heat with the object and can perturb the quantity it is meant to measure. A small object may require a coupled thermal model rather than a fixed . For a resistance thermometer, the excitation also causes Joule heating; checking several currents can distinguish that effect from a fixed readout offset.[ref]
Guide on Secondary Thermometry: Industrial Platinum Resistance Thermometers by Jonathan Pearce and others. §4.1, self-heating and excitation-current dependence