Key Principles of Mechanics

Why This Matters

Mechanical prototyping isn't just about building things—it's about building things that work. Every prototype you create will succeed or fail based on how well you understand the underlying mechanics: force equilibrium, material behavior, energy transfer, and motion dynamics. These aren't abstract concepts you'll forget after the exam; they're the diagnostic tools you'll use every time a prototype breaks, binds, overheats, or doesn't move the way you expected.

You're being tested on your ability to connect physical principles to real design decisions. Can you look at a failed part and identify whether it was a stress concentration issue or a material selection problem? Can you predict how changing a gear ratio will affect both speed and torque? Don't just memorize formulas—know what concept each principle illustrates and when to apply it in the design process.

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Forces and Equilibrium

Before anything moves (or doesn't), you need to understand how forces balance and what happens when they don't. These foundational concepts determine whether your structure stands or collapses.

Statics and Force Analysis

• Equilibrium conditions—a body at rest has all forces and moments summing to zero ($\Sigma F = 0$, $\Sigma M = 0$)
• Free-body diagrams isolate objects to visualize all external forces, reactions, and moments acting on them
• Internal force analysis reveals how structures distribute loads, critical for identifying weak points in your prototype

Kinematics and Dynamics

• Kinematics describes motion through displacement, velocity, and acceleration without considering what causes it
• Dynamics adds forces to the picture, governed by Newton's laws ($F = ma$) to predict how objects accelerate under load
• Rotational analogs apply the same principles to spinning components—essential for anything with motors, gears, or wheels

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Material Behavior Under Load

Materials don't just "break"—they deform, yield, and fail in predictable ways based on their properties. Understanding this lets you choose the right material and predict how your parts will perform.

Stress and Strain

• Stress ($\sigma = F/A$) measures internal resistance to applied force, expressed in Pascals or psi
• Strain ($\epsilon = \Delta L / L$) quantifies deformation as a ratio—dimensionless but critical
• Hooke's Law ($\sigma = E\epsilon$) defines the linear elastic region where materials spring back; beyond this lies permanent deformation

Material Properties and Selection

• Tensile strength indicates maximum stress before failure; yield strength marks the onset of permanent deformation
• Ductility vs. brittleness determines whether materials bend before breaking—crucial for impact-loaded prototypes
• Material selection charts (Ashby plots) let you compare stiffness-to-weight or strength-to-cost ratios systematically

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Energy and Thermal Systems

Energy doesn't disappear—it transfers, converts, and sometimes causes problems. These principles govern everything from motor efficiency to thermal management in your prototypes.

Thermodynamics

• First Law (energy conservation): energy entering a system equals energy leaving plus any stored—$Q = W + \Delta U$
• Second Law establishes that heat flows from hot to cold naturally; reversing this requires work input
• Cycle efficiency (like the Carnot cycle) sets theoretical limits on how much useful work you can extract from heat engines

Heat Transfer

• Conduction moves heat through solid materials, governed by Fourier's Law ($q = -k \nabla T$)
• Convection transfers heat via fluid motion; Newton's law of cooling relates heat flux to temperature difference
• Radiation requires no medium and dominates at high temperatures—think electronics cooling and thermal management

Fluid Mechanics

• Hydrostatics analyzes fluids at rest (pressure increases with depth: $P = \rho g h$)
• Bernoulli's equation ($P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$) relates pressure, velocity, and elevation in flowing fluids
• Viscosity describes fluid resistance to flow—low viscosity fluids move easily; high viscosity fluids resist and generate heat

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Machine Components and Assemblies

Individual parts must work together precisely. These principles ensure your moving components mesh correctly, spin freely, and transmit power efficiently.

Machine Elements (Gears, Bearings, Shafts)

• Gear ratios trade speed for torque—a 3:1 ratio triples torque but cuts output speed to one-third
• Bearing selection depends on load type: ball bearings handle radial loads, thrust bearings handle axial loads
• Shaft design must account for both torsional stress (twisting) and bending stress from mounted components

Tolerances and Fits

• Tolerances specify acceptable dimensional variation (e.g., $25.00 \pm 0.05$ mm)—tighter tolerances cost more
• Clearance fits allow parts to slide freely; interference fits create friction-locked assemblies
• Tolerance stackup analysis prevents assemblies where individual acceptable parts combine into unacceptable results

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Design for Reality

Great designs on paper fail in the real world if you ignore manufacturing constraints, safety margins, and failure modes. These principles bridge the gap between concept and functional prototype.

Design for Manufacturability

• Process compatibility means designing features your available machines can actually produce—no internal sharp corners for milling
• Part consolidation reduces assembly complexity, cost, and potential failure points
• Draft angles and radii prevent parts from sticking in molds and reduce stress concentrations

Manufacturing Processes

• Subtractive methods (CNC machining) remove material—excellent precision, higher waste, works with metals and plastics
• Additive methods (3D printing) build layer-by-layer—complex geometries possible, but with anisotropic strength
• Formative methods (casting, molding) shape material in cavities—economical at volume, requires tooling investment

Prototyping Techniques

• Rapid prototyping (FDM, SLA printing) prioritizes speed over strength—ideal for fit checks and visual models
• Functional prototypes (CNC, SLS) must survive real loads and should use production-representative materials
• Fidelity tradeoffs balance time, cost, and accuracy—know when "good enough" testing beats perfect parts

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Reliability and Failure Prevention

Everything fails eventually—your job is to control when, how, and whether it matters. These principles help you design robust systems and learn from failures.

Safety Factors and Reliability

• Safety factor ($SF = \text{Allowable Stress} / \text{Actual Stress}$) provides margin against uncertainties—typically 1.5–4 depending on consequences
• Reliability quantifies probability of failure-free operation over time, often expressed as MTBF (mean time between failures)
• Load uncertainty and material variability both justify higher safety factors in critical applications

Failure Analysis

• Root cause analysis traces failures backward from symptom to origin—don't just fix what broke, fix why it broke
• FMEA (Failure Mode Effects Analysis) proactively identifies potential failures before they occur
• Failure modes include fatigue, corrosion, wear, and overload—each leaves distinct evidence and requires different prevention strategies

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Documentation and Communication

A prototype nobody else can understand, reproduce, or modify has limited value. These skills ensure your work is usable by others—including future you.

Engineering Drawings and CAD

• Orthographic projections show front, top, and side views with true dimensions—the universal language of manufacturing
• CAD parametric modeling lets you modify designs by changing driving dimensions rather than redrawing
• GD&T (Geometric Dimensioning and Tolerancing) communicates not just size but form, orientation, and position requirements

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Quick Reference Table

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Self-Check Questions

1. A prototype shaft keeps failing at the same location after repeated use. Which two principles would you apply to diagnose whether this is a fatigue failure or a stress concentration issue?

2. You need to connect a motor to a wheel that should spin slower but with more force. Which machine element concept determines the relationship, and what tradeoff are you making?

3. Compare and contrast 3D printing and CNC machining for creating a functional load-bearing bracket. When would you choose each?

4. Your prototype assembly has five parts, each within tolerance, but the final assembly doesn't fit. Which principle explains this, and how would you prevent it in future designs?

5. If an FRQ asks you to evaluate a thermal management system for an electronics enclosure, which three heat transfer mechanisms would you analyze, and what design features address each?