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Exercise set

Biomedical Device Design and Biomechanics Exercises

Worked biomedical engineering exercises for device design and biomechanics covering axial stress, contact pressure, bending stress, fatigue, fracture screening, corrosion, strain sensing, leakage current, RPN, actuator force, and validation evidence.

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Biomedical Engineering
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Exercise set
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v1.1.0 ยท reviewed

These exercises practise biomedical device design and biomechanics at the interface between engineered components and living systems. They cover stress, contact pressure, bending, fatigue, fracture screening, corrosion, strain sensing, leakage current, risk ranking, actuator force, and validation evidence.

The purpose is not only to calculate a mechanical number. The purpose is to decide whether the device, body interface, material, sensor, user task, and risk control are credible under intended-use and foreseeable-use conditions.

Assume simplified geometry and project-specific criteria unless an exercise states otherwise. Real biomedical device design should also check anatomy, tissue tolerance, material processing, surface condition, cleaning, sterilization, biocompatibility, fatigue scatter, corrosion environment, usability, software, manufacturing variation, and validation evidence.

How to Use These Exercises

For each design calculation, define:

  1. the intended use and body interface;
  2. the load path, motion, contact, or sensing path;
  3. the material and manufacturing assumptions;
  4. the failure mode and risk control being tested;
  5. the evidence needed before the device can support its claim.

The common mistake is treating a device as a standalone part. Biomedical design performance depends on the coupled system of device, tissue, user, workflow, manufacturing, and lifecycle exposure.

For each answer, separate the numerical screen from the release decision. A calculation can show that a concept is plausible, but device release still depends on verified requirements, representative test conditions, manufacturing controls, usability evidence, and risk acceptability.

A handheld surgical accessory contains a polymer link that may carry tensile load:

F=180\ \text{N}

The minimum cross-sectional area is:

A=24\ \text{mm}^2

Calculate axial stress:

\displaystyle \sigma=\frac{F}{A}

Solution

Convert area:

A=24\ \text{mm}^2=24\times10^{-6}\ \text{m}^2

Stress:

\displaystyle \sigma=\frac{180}{24\times10^{-6}}=7.5\times10^6\ \text{Pa}=7.5\ \text{MPa}

Engineering Comment

The axial stress is 7.5 MPa under the stated load. That is only one part of the design review. The link may also see bending, impact, cleaning exposure, stress concentration, aging, assembly preload, and user misuse.

For biomedical devices, stress calculations should be connected to material lot, geometry tolerance, surface condition, sterilization or cleaning history, and failure consequence.

Exercise 2: Contact Pressure Under a Wearable Pad

A wearable sensor is held against skin with strap force:

F=18\ \text{N}

The pad contact area is:

A=30\ \text{cm}^2

Estimate average contact pressure.

Solution

Convert area:

A=30\ \text{cm}^2=30\times10^{-4}\ \text{m}^2=0.0030\ \text{m}^2

Pressure:

\displaystyle p=\frac{F}{A}=\frac{18}{0.0030}=6000\ \text{Pa}=6.0\ \text{kPa}

Engineering Comment

The average pressure is 6.0 kPa. Average pressure can hide local peaks at pad edges, seams, sensor housings, cable exits, or stiff inserts. Sustained pressure, shear, heat, moisture, and patient sensitivity may matter more than the average value.

Contact design should be evaluated with realistic placement, motion, duration, and user adjustment.

Exercise 3: Bending Stress in a Reusable Instrument Arm

A reusable instrument arm is modeled as a rectangular section with:

b=8\ \text{mm},\quad h=4\ \text{mm}

The bending moment at the critical section is:

M=0.9\ \text{N m}

For a rectangular section:

\displaystyle I=\frac{bh^3}{12},\quad c=\frac{h}{2},\quad \sigma=\frac{Mc}{I}

Calculate bending stress.

Solution

Convert dimensions:

b=0.008\ \text{m},\quad h=0.004\ \text{m}

Second moment of area:

\displaystyle I=\frac{0.008(0.004)^3}{12}=4.27\times10^{-11}\ \text{m}^4

Outer-fiber distance:

c=0.002\ \text{m}

Bending stress:

\displaystyle \sigma=\frac{0.9(0.002)}{4.27\times10^{-11}}=4.22\times10^7\ \text{Pa}=42.2\ \text{MPa}

Engineering Comment

The simplified bending stress is 42.2 MPa. The actual maximum may be higher if there are fillets, holes, threads, surface scratches, welds, printed-layer boundaries, or contact notches.

Reusable instruments should also be checked after cleaning, sterilization, drops, repeated loading, and inspection limits.

Exercise 4: Static Safety Factor Against Yield

A component has yield strength:

S_y=220\ \text{MPa}

The maximum calculated stress from combined loading is:

\sigma_{max}=74\ \text{MPa}

Calculate static safety factor:

\displaystyle n=\frac{S_y}{\sigma_{max}}

Solution

Safety factor:

\displaystyle n=\frac{220}{74}=2.97

Engineering Comment

The static safety factor is about 3.0. Whether that is sufficient depends on risk, uncertainty, fatigue, material scatter, geometry tolerance, environment, and failure consequence.

For a biomedical device, static yield margin does not replace fatigue testing, fracture assessment, corrosion review, usability validation, or manufacturing process control.

Exercise 5: Fatigue Stress-Amplitude Screen

A wearable hinge sees cyclic stress between:

\sigma_{min}=8\ \text{MPa}

and:

\sigma_{max}=48\ \text{MPa}

Calculate stress amplitude and mean stress:

\displaystyle \sigma_a=\frac{\sigma_{max}-\sigma_{min}}{2}
\displaystyle \sigma_m=\frac{\sigma_{max}+\sigma_{min}}{2}

Solution

Stress amplitude:

\displaystyle \sigma_a=\frac{48-8}{2}=20\ \text{MPa}

Mean stress:

\displaystyle \sigma_m=\frac{48+8}{2}=28\ \text{MPa}

Engineering Comment

The hinge sees a 20 MPa alternating component with 28 MPa mean stress. Fatigue review should consider surface finish, polymer aging, humidity, cleaning chemicals, temperature, notch effects, assembly preload, and user cycling profile.

The mean stress matters because fatigue life is not controlled by amplitude alone.

Exercise 6: Fracture-Toughness Screening

A machined component may contain a surface flaw with characteristic depth:

a=0.30\ \text{mm}

The maximum tensile stress is:

\sigma=95\ \text{MPa}

Use a simplified stress-intensity estimate:

K=Y\sigma\sqrt{\pi a}

with:

Y=1.1

Calculate K. Use meters for flaw depth.

Solution

Convert flaw depth:

a=0.30\ \text{mm}=0.00030\ \text{m}

Stress intensity:

K=1.1(95\times10^6)\sqrt{\pi(0.00030)}
K=1.1(95\times10^6)(0.0307)=3.21\times10^6\ \text{Pa}\sqrt{\text{m}}

In MPa square-root meters:

K=3.21\ \text{MPa}\sqrt{\text{m}}

Engineering Comment

This is a simplified screen. It should be compared with an appropriate fracture toughness value for the actual material, processing state, environment, and flaw geometry. If the calculated K approaches the material limit, inspection sensitivity and acceptance criteria become critical.

Biomedical components can fail from small flaws when the consequence is high and repeated loading or corrosion assists crack growth.

Exercise 7: Corrosion Penetration from Rate

A metallic component has measured corrosion rate:

r=0.018\ \text{mm/year}

The intended service interval before replacement is:

t=4\ \text{years}

Estimate material penetration over the interval.

Solution

Penetration:

d=rt=0.018\times4=0.072\ \text{mm}

Engineering Comment

The estimated penetration is 0.072 mm over four years. That value may be acceptable or unacceptable depending on wall thickness, stress concentration, surface function, fatigue sensitivity, crevice geometry, galvanic coupling, and biological exposure.

Corrosion review should consider not only material loss but also debris, surface chemistry, electrical contact, fatigue crack initiation, and cleaning or sterilization effects.

Exercise 8: Strain-Gauge Signal from Device Flexure

A strain gauge on a device flexure reads:

\epsilon=650\ \text{microstrain}

The gauge factor is:

GF=2.1

Bridge excitation is:

V_{ex}=3.3\ \text{V}

For a quarter bridge:

\displaystyle V_o\approx\frac{V_{ex}GF\epsilon}{4}

Calculate bridge output.

Solution

Convert strain:

\epsilon=650\times10^{-6}

Output:

\displaystyle V_o\approx\frac{3.3(2.1)(650\times10^{-6})}{4}=0.00113\ \text{V}=1.13\ \text{mV}

Engineering Comment

The bridge signal is about 1.13 mV, so amplifier noise, offset, temperature drift, bridge completion tolerance, lead strain, and calibration fixture quality matter.

If the strain signal is used for alarm, feedback, or usage logging, the design also needs failure detection for open gauge, loose bond, saturation, and signal drift.

Exercise 9: Leakage Current Screening

A patient-connected device path has measured insulation resistance:

R=95\ \text{MOhm}

at applied voltage:

V=250\ \text{V}

Estimate leakage current:

\displaystyle I=\frac{V}{R}

Compare with a project screening limit of 4 microA.

Solution

Convert resistance:

R=95\ \text{MOhm}=95{,}000{,}000\ \Omega

Leakage current:

\displaystyle I=\frac{250}{95{,}000{,}000}=2.63\times10^{-6}\ \text{A}=2.63\ \text{microA}

Comparison:

2.63<4

Engineering Comment

The screen passes the project limit. Full electrical safety evidence still needs test method, applied part configuration, humidity conditioning, accessories, single-fault conditions, enclosure condition, and production control.

For patient-connected devices, electrical safety evidence must stay tied to the exact configuration being released.

Exercise 10: RPN for a Body-Interface Failure Mode

A wearable device can be strapped too tightly, creating excessive local pressure. Initial FMEA ratings are:

RatingValue
Severity6
Occurrence5
Detection5

The design team adds a force-limiting buckle, pad-edge redesign, and on-screen placement feedback. Revised ratings are:

RatingValue
Severity6
Occurrence2
Detection3

Calculate initial and revised RPN.

Solution

Initial RPN:

RPN_0=6\times5\times5=150

Revised RPN:

RPN_1=6\times2\times3=36

Relative reduction:

\displaystyle \frac{150-36}{150}\times100=76.0\%

Engineering Comment

The controls reduce occurrence and detection rating, but severity remains unchanged. The engineering evidence should verify buckle force limiting, pressure distribution, pad wear, usability of placement feedback, and field complaints after release.

RPN reduction is not proof of safety unless controls are implemented and validated.

Exercise 11: Actuator Force Margin

A handheld device actuator must overcome a maximum tissue-interface resistance:

F_r=32\ \text{N}

The actuator can deliver:

F_a=46\ \text{N}

The project requires at least 25 percent force margin:

\displaystyle M=\frac{F_a-F_r}{F_r}\times100

Calculate the margin.

Solution

Force margin:

\displaystyle M=\frac{46-32}{32}\times100=43.75\%

Engineering Comment

The actuator has about 43.8 percent margin against the stated resistance, so it passes the 25 percent project criterion. The validation should still cover worst-case tissue conditions, user angle, battery state, friction, wear, software limits, sterilization effects, and failure response.

Force margin is useful only when the resistance model represents the intended use.

Review Checklist

When reviewing biomedical device design calculations, ask:

  • Is the load path connected to the real body interface and user workflow?
  • Are contact pressure, local peaks, duration, shear, heat, and motion represented?
  • Are material properties tied to processing, surface condition, cleaning, and sterilization?
  • Are fatigue, fracture, corrosion, and wear considered for repeated use?
  • Are sensors and electronics reviewed as risk controls, not only as features?
  • Are usability controls validated under realistic placement and handling conditions?
  • Do inspection and manufacturing controls detect the failure modes that matter?
  • Are acceptance criteria stated before test data are reviewed?
  • Can the calculation be traced to the released device configuration, material condition, software state, and intended-use scenario?
  • Does lifecycle feedback update the design basis after field use?

Biomedical device design is credible when mechanics, materials, sensing, safety, usability, manufacturing, and validation all support the intended body-interface function.

REF

See also

  1. Biomedical Device Design and Biomechanics Biomedical Engineering
  2. Biomaterials and Implantable Medical Devices Biomedical Engineering
  3. Biomaterials and Implantable Medical Devices Exercises Biomedical Engineering
  4. Biomedical Signal Acquisition and Instrumentation Biomedical Engineering
  5. Biomedical Signal Acquisition and Instrumentation Exercises Biomedical Engineering
  6. Biomedical Imaging and Diagnostic Systems Biomedical Engineering
  7. Biomedical Imaging and Diagnostic Systems Exercises Biomedical Engineering
  8. Biomedical Instrumentation Formula Sheet Biomedical Engineering
  9. Clinical Engineering and Healthcare Technology Management Biomedical Engineering
  10. Clinical Engineering and Healthcare Technology Management Exercises Biomedical Engineering
  11. Medical Device Verification, Validation, and Risk Management Biomedical Engineering
  12. Medical Device Verification, Validation, and Risk Management Exercises Biomedical Engineering
  13. Materials Selection and Mechanical Properties Materials Engineering
  14. Materials Selection and Mechanical Properties Exercises Materials Engineering
  15. Mechanical Stress Analysis Mechanical Engineering
  16. Mechanical Stress Analysis Exercises Mechanical Engineering
  17. Machine Design and Power Transmission Systems Exercises Mechanical Engineering
  18. Material Fatigue and Fracture Materials Engineering
  19. Material Fatigue and Fracture Exercises Materials Engineering
  20. Corrosion and Surface Protection Engineering Materials Engineering
  21. Corrosion and Surface Protection Engineering Exercises Materials Engineering
  22. Human Factors and Usability Engineering Industrial and Management Engineering
  23. Human Factors and Usability Engineering Exercises Industrial and Management Engineering
  24. Quality Engineering and Process Improvement Industrial and Management Engineering
  25. Quality Engineering and Process Improvement Exercises Industrial and Management Engineering
  26. Medical Device Biomedical Engineering device
  27. Sterilization Biomedical Engineering process
  28. Biomechanics Biomedical Engineering concept
  29. Biocompatibility Biomedical Engineering concept
  30. Bioinstrumentation Biomedical Engineering term
  31. Transducer Electronic Engineering device
  32. Strain Gauge Mechanical Engineering device
  33. Stress Mechanical Engineering quantity
  34. Elastic Modulus Materials Engineering quantity
  35. Young's Modulus Materials Engineering quantity
  36. Shear Modulus Materials Engineering quantity
  37. Poisson Ratio Materials Engineering quantity
  38. Yield Strength Materials Engineering quantity
  39. Ultimate Tensile Strength Materials Engineering quantity
  40. Fatigue Materials Engineering phenomenon
  41. Fracture Toughness Materials Engineering quantity
  42. Corrosion Rate Materials Engineering metric
  43. Galvanic Corrosion Materials Engineering phenomenon
  44. Non-Destructive Testing Materials Engineering method
  45. X-Ray Computed Tomography Materials Engineering method
  46. Signal-to-Noise Ratio Telecommunications Engineering metric
  47. Leakage Current Electrical Engineering quantity
  48. Error Budget Electronic Engineering method
  49. Uncertainty Analysis Mathematical Engineering method
  50. Validation Industrial and Management Engineering method
  51. Reliability Industrial and Management Engineering metric
  52. Failure Mode Industrial and Management Engineering concept
  53. Risk Priority Number Industrial and Management Engineering metric
  54. Usability Engineering Industrial and Management Engineering method
  55. Interlock Industrial and Management Engineering device
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