The NTC thermistor's resistance varies non-linearly with temperature. The β-parameter form of the Steinhart–Hart equation gives absolute temperature in kelvin, which is then converted to Celsius.

The flex sensor's conductive ink increases in resistance as it bends. A voltage divider converts this to analog voltage; linear calibration gives angle in degrees.

Raw EMG signals are bandpass-filtered to isolate muscle activation frequencies (20–450 Hz), then converted to an RMS envelope that represents contraction intensity. Higher RMS indicates stronger muscle engagement.

The MAX30102 emits red (660 nm) and infrared (880 nm) light through the skin. Oxygenated and deoxygenated hemoglobin absorb these wavelengths differently. The ratio R of the AC/DC components at each wavelength is mapped to SpO₂ via an empirical linear calibration derived from the Beer–Lambert law.

The infrared PPG waveform tracks blood volume changes with each heartbeat. After low-pass filtering to remove motion artifacts, peaks are detected to find inter-beat intervals. Heart rate is computed as 60 seconds divided by the mean interval between peaks.

Torque at the elbow joint is the load force times the moment arm (forearm length times sine of the elbow angle). Cross-referenced with safe thresholds to warn about dangerous combinations of weight and joint angle.

float computeNtcResistanceOhms(int adcValue) {
  if (adcValue <= 0) return -1.0f;
  float ratio = ADC_MAX / (float)adcValue;
  return NTC_FIXED_RESISTOR_OHMS * (ratio - 1.0f);
}

float computeTemperatureCFromResistance(float resistanceOhms) {
  if (resistanceOhms <= 0.0f) return -1000.0f;
  float inverseT = (1.0f / NTC_T0_KELVIN)
                  + (log(resistanceOhms / NTC_R25_OHMS) / NTC_BETA);
  return (1.0f / inverseT) - 273.15f;
}

float mapFlexRawToAngleDeg(float rawValue) {
  float slope = (FLEX_BENT_ANGLE_DEG - FLEX_STRAIGHT_ANGLE_DEG)
              / (FLEX_BENT_RAW - FLEX_STRAIGHT_RAW);
  float angle = FLEX_STRAIGHT_ANGLE_DEG
              + (rawValue - FLEX_STRAIGHT_RAW) * slope;
  return clampFloat(angle, FLEX_BENT_ANGLE_DEG, FLEX_STRAIGHT_ANGLE_DEG);
}

// Called at 50 Hz — computes ω and α from successive angle readings
void updateFlexKinematics(unsigned long nowMs) {
  float dt = (nowMs - lastKinematicsSampleAtMs) / 1000.0f;
  filteredFlexRaw += FLEX_FILTER_ALPHA * ((float)flexRaw - filteredFlexRaw);
  float previousAngleDeg = currentAngleDeg;
  currentAngleDeg = mapFlexRawToAngleDeg(filteredFlexRaw);
  angularVelocityDegPerSec = (currentAngleDeg - previousAngleDeg) / dt;
}

// Triggered when bend speed exceeds 200°/s for 2 consecutive samples
enum MotorProtectionState : uint8_t {
  MOTOR_STATE_IDLE    = 0,
  MOTOR_STATE_FORWARD = 1,   // tighten sleeve
  MOTOR_STATE_SETTLE  = 2,   // hold 2 seconds
  MOTOR_STATE_REVERSE = 3    // release
};

void maybeStartMotorProtectionCycle(unsigned long nowMs) {
  if (motorProtectionState != MOTOR_STATE_IDLE) return;
  if (bendClosingSpeedDegPerSec >= BEND_SPEED_TRIGGER_DEG_PER_SEC)
    bendSpeedTriggerSamples++;
  else
    bendSpeedTriggerSamples = 0;
  if (bendSpeedTriggerSamples >= BEND_SPEED_TRIGGER_CONFIRM_SAMPLES) {
    motorCycleCount++;
    enterMotorProtectionState(MOTOR_STATE_FORWARD, nowMs,
                              getMotorPhaseDurationMs());
  }
}

// Three BLE characteristics, each ≤20 bytes (BLE 4.2 MTU limit)
BLECharacteristic vitalsPacketChar("19B10011-...", BLERead|BLENotify, 20);
BLECharacteristic motionPacketChar("19B10012-...", BLERead|BLENotify, 20);
BLECharacteristic imuPacketChar   ("19B10013-...", BLERead|BLENotify, 14);

// Fixed-point encoding: heartRate × 10, temperature × 100
int16_t heartRateX10 = clampToInt16((int32_t)(heartRateBpm * 10.0f));
int16_t tempX100     = clampToInt16((int32_t)(temperatureC * 100.0f));

uint8_t vitalsPacket[20] = {0};
writeU16LE(vitalsPacket, 0, packetSequence);
vitalsPacket[2] = buildStatusFlags();
writeI16LE(vitalsPacket, 4, heartRateX10);
writeI16LE(vitalsPacket, 6, spo2X10);
writeI16LE(vitalsPacket, 8, tempX100);