1. Performance Criteria

The height adjustment subsystem is evaluated against the following performance criteria, derived from the system-level requirements and specific actuation specifications:

ID	Criterion	Target
RM-5	Vertical stroke & speed	≥ 400 mm stroke completed in ≤ 32 s
RM-1	Structural stability	Remain upright and maintain alignment under combined punch loads
HA-AC-1	Actuation reliability	5 consecutive full cycles under 60 kg payload without stalling
HA-AC-2	Delrin wear & backlash	Pad wear < 1 mm, lateral backlash < 2 mm after 200 cycles

2. Test Procedures

Test 1: Stroke Length & Speed Test RM-5, HA-AC-1

• Setup: Fully assembled height adjustment stage with the upper structure payload attached. Note: Due to physical cable length constraints connecting the top electronics to the bottom power units, the maximum safe extension was limited.
• Procedure: Command the screw jack motor to drive the column downwards from its maximum permitted extension to its lowest position. Record the total vertical stroke distance achieved and time the duration of the descent.
• Success Criteria: The vertical stroke achieves ≥ 40 cm (to accommodate users 150-190 cm) and the duration is ≤ 32 seconds.

Test 2: Structural Deflection under Punching Loads RM-1

• Setup: To numerically measure the deflection of the robot structure with increasing punching forces (without a direct force load cell), a self-made wireless IMU is utilized. The IMU is systematically pasted at four different elevations to measure vibration and sway:
  • Level 1 (Base): 15.2 cm from bottom non-friction pad to top of IMU holder.
  • Level 2 (Circular Plate): 20.8 cm from bottom non-friction pad.
  • Level 3 (Bottom of Steel Tube): 46.0 cm from bottom non-friction pad.
  • Level 4 (Top of Steel Tube): 106.0 cm from bottom non-friction pad.
• Procedure: At each IMU mounting position, deliver the following strike matrix (45 total strikes per height) to capture structural responses across different torque arms:
  • Center Pad: 5 light taps, 5 medium punches, 5 hard punches
  • Right Pad: 5 light taps, 5 medium punches, 5 hard punches
  • Left Pad: 5 light taps, 5 medium punches, 5 hard punches
• Success Criteria: The captured CSV data processed through DSP confirms that the telescopic lift column effectively dissipates punching forces without resonant amplification, maintaining alignment without structural failure.

Test 3: Delrin Wear & Backlash Endurance HA-AC-2

• Setup: Fully assembled telescopic column with micrometer instrumentation on the Delrin wear pads.
• Procedure: Perform 200 standard vertical adjustment cycles. Post-test, measure the physical wear on the Delrin pads and the lateral play (backlash) at the top of the stroke.
• Success Criteria: Pad surface wear < 1 mm, lateral backlash < 2 mm.

3. Results & Discussion

Test 1: Stroke Length & Speed Test RM-5, HA-AC-1

Results

The height adjustment stage achieved a maximum vertical stroke of 28 cm (accommodating a user height range of 150–178 cm, short of the 190 cm target) before being constrained by the internal cable length connecting the top and bottom electronics. The stroke descent was timed at 1 minute 26 seconds (86 s), which exceeded the 32-second target. This slower speed was due to utilizing an alternative motor rather than the originally specified screw-jack motor.

Discussion & Limitations

• Slow Speed: The recorded stroke duration of 1 minute 26 seconds (86 s) significantly exceeds the ≤ 32 s target. This limitation arose from using a different motor than the one originally specified for the screw jack.
• User Height Unmet: The maximum vertical stroke was constrained to 28 cm (limiting the maximum accommodated user height to 178 cm instead of the targeted 190 cm). This restriction was due to the physical cable length being too short to connect the top electronics to the bottom power units at full extension.

Test 2: Structural Deflection under Punching Loads RM-1

Results

At present, the height-adjustment subsystem has been validated structurally through load-path reasoning and empirical impact recording. The raw wireless IMU data was processed through a custom Python Digital Signal Processing (DSP) pipeline (using a 4th-order Butterworth low-pass filter with a 0.5 Hz cutoff) to isolate the true low-frequency structural sway from the high-frequency impact shockwaves and horizontal sliding artifacts.

Graph Interpretation: The DSP analysis (Figure below) illustrates the system's dynamic response to the 45-strike matrix. The Impact Vibration graph (left) captures the kinetic energy propagating through the frame. The distinct repeating pattern of "low, medium, high" clusters corresponds perfectly to the test procedure: the 5 light, 5 medium, and 5 hard punches were delivered sequentially to the Center pad, then repeated on the Right pad, and finally repeated on the Left pad. The Structural Sway graph (right) tracks the calculated angular deflection. While the top tube (Level 4) shows a controlled sway of around 3.5° under hard center impacts, the base (Level 1) occasionally exhibits massive spikes that exceed the top tube. As detailed in the Discussion below, these base spikes are not true angular tipping; rather, they are horizontal sliding artifacts caused by the base jolting and slipping on the floor, particularly when struck on the off-center (Right and Left) pads which introduce a sudden twisting moment.

Discussion & Limitations

Upon rigorous mechanical engineering review, the DSP methodology utilized to derive the angular sway presents inherent limitations associated with accelerometer-based tilt calculations during dynamic impacts.

The analytical script calculated the absolute tilt angle by taking the arc-cosine of the dot product between the low-pass filtered instantaneous acceleration vector and the resting gravity baseline. This mathematical approach relies on the quasi-static assumption that the only low-frequency acceleration acting on the sensor is the 1g downward pull of gravity.

When subjected to a hard punch, the robot experiences violent lateral translational acceleration. Because accelerometers cannot distinguish between true angular tilt and horizontal acceleration (Einstein's equivalence principle), the initial raw data exhibited physically impossible >16° spikes at the base. These were horizontal sliding jolts misidentified as tilt.

While applying a strict 0.5 Hz Butterworth low-pass filter successfully eliminated these high-frequency sliding artifacts, a 0.5 Hz cutoff (representing a 2-second vibration period) is almost certainly below the natural resonant frequency of the steel cantilever column. As a result, the filter likely attenuated the true peak dynamic bending of the structure along with the noise. The 3.5° value recorded at the top tube should therefore be interpreted as a heavily damped, quasi-static deflection rather than the absolute instantaneous dynamic peak.

Recommendation: For future dynamic deflection testing, the true angular sway should be calculated by integrating the IMU's gyroscope data (angular velocity) over the brief impact window, fused with the accelerometer data via a Complementary or Kalman filter to correct for drift, making the calculation immune to horizontal sliding jolts.

Overall Structural Implications: Despite the instrumentation limitations in capturing the exact instantaneous peak deflection, the empirical test demonstrated the physical robustness of the height-adjustment assembly. While the structure exhibits noticeable transient vibrations and shaking under heavy impact, it remained upright throughout the extensive strike matrix without experiencing plastic deformation, tipping, or mechanical binding. This practically validates that the telescopic steel column and Delrin pad interfaces are effectively absorbing the overturning moments, shielding the internal screw-jack actuator from harmful lateral shear forces as intended by requirement RM-1.

Test 3: Delrin Wear & Backlash Endurance HA-AC-2

Results

Pending 200-cycle mechanical endurance test.

Discussion & Limitations

To be evaluated upon completion of the physical endurance test.

Overall Subsystem Assessment

ID	Criterion	Measured Result	Status
RM-5 / HA-AC-1	Stroke & Reliability	Vertical Stroke: 28 cm achieved (Target: 40 cm) Stroke Duration: 1 min 26 s / 86 s (Target: ≤ 32 s) User Height: 150–178 cm accommodated (Target: 150–190 cm)	Partial
RM-1	Structural deflection	DSP analysis confirmed acceptable structural stability within operational limits. While visible shaking and vibration occur under impact, the peak quasi-static structural sway remained under 4° at the top of the steel tube (106.0 cm) during the hardest punching loads. Impact vibration data showed kinetic energy is safely dissipated down the column without causing base lift-off or permanent plastic deformation.	Passed
HA-AC-2	Delrin wear & backlash	Pending 200-cycle mechanical endurance test.	Partial

4. Cross-References

• Robot Mechanism — Verification Results — System-level integration testing and the overall performance assessment against all RM requirements.
• 5.2 Robot Mechanism — Definitions of the system-level requirements (RM-5, RM-1) that this height adjustment subsystem satisfies.

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