Machine Design
Springs, seals and O-rings, power screws, cams, linkages, vibration and isolation, clutches and brakes, flywheels and balancing, and a complete press frame case study, with worked numbers.
Machine design turns calculations into a working, safe, durable machine. Gears, bearings and shafts are covered in Gears and Power Transmission, and stress, fatigue and fasteners in Structures and Strength of Materials; this guide covers the other machine elements and the way they are put together: springs, seals and O-rings, power screws, cams, linkages, vibration and isolation, clutches, brakes and couplings, flywheels and balancing, and a complete case study of the 80 kN press frame. The same press runs through every page, and every number is computed.
Start here: what do you need?
| I need to… | Go to |
|---|---|
| design or check a compression, extension or torsion spring | Springs: Design, Stress and Fatigue |
| choose an O-ring groove, a seal or a gasket | Seals, O-Rings and Gaskets |
| size a lead screw or a ball screw and its torque | Power Screws and Lead Screws |
| design a cam and find the follower motion and forces | Cams and Followers |
| analyze a four-bar, slider-crank or toggle linkage | Linkages and Mechanisms |
| mount a machine, avoid resonance, balance a rotor or limit noise | Vibration, Isolation and Noise |
| size a clutch, a brake or a shaft coupling | Clutches, Brakes and Couplings |
| size a flywheel or balance a rotor | Flywheels, Balancing and Rotors |
| design a whole machine frame, check fatigue and meet the standards | Machine Design Case Study: the 80 kN Press Frame |
A suggested order
The elements are independent, so go to the one you need. For a complete project read Machine Design Case Study: the 80 kN Press Frame first to see how they fit together, then the pages for the parts of your machine. Springs: Design, Stress and Fatigue, Seals, O-Rings and Gaskets and Power Screws and Lead Screws are the static elements; Cams and Followers and Linkages and Mechanisms the motion elements; Vibration, Isolation and Noise, Clutches, Brakes and Couplings and Flywheels, Balancing and Rotors the dynamics.
- Springs: Design, Stress and Fatigue: Compression, extension, torsion and disc springs: rate, stress, Wahl factor, buckling, surge and fatigue with a worked relief-valve spring.
- Seals, O-Rings and Gaskets: O-ring squeeze and groove fill, extrusion and back-up rings, rod and shaft seals, gaskets and flange bolting.
- Power Screws and Lead Screws: Thread geometry, torque to raise and lower a load, efficiency, self-locking and ball screws.
- Cams and Followers: Motion laws, velocity and acceleration, pressure angle, base circle and follower forces with a worked 20 mm rise.
- Linkages and Mechanisms: Mobility, the Grashof condition, four-bar and slider-crank kinematics, toggle mechanisms and transmission angle.
- Vibration, Isolation and Noise: Natural frequency, damping, resonance, transmissibility, rotor unbalance, critical speed and machinery limits.
- Clutches, Brakes and Couplings: Friction torque with uniform pressure and wear, engagement time and heating, brake sizing and flexible couplings.
- Flywheels, Balancing and Rotors: Energy storage and speed fluctuation, flywheel sizing and stress, balance grades and balancing of rotating masses.
- Machine Design Case Study: the 80 kN Press Frame: Frame stress and deflection, weld fatigue life, safety factors, standards and a design checklist for a complete machine.
One press, nine machine elements
Worked example: the elements of the press
- Spring (Springs: Design, Stress and Fatigue): the relief valve spring holds 452 N at 17.2 mm of compression, at 541 MPa.
- Seal (Seals, O-Rings and Gaskets): a 3.53 mm O-ring with 20 percent squeeze and 73 percent gland fill.
- Screw (Power Screws and Lead Screws): a Tr 30 × 6 stop screw needs 50 N·m for 10 kN; a ball screw would need 11.
- Cam (Cams and Followers): a 20 mm rise in 120° at 300 rpm peaks at 28 m/s² with the cycloidal law.
- Linkage (Linkages and Mechanisms): a crank-rocker for the guard door; a toggle clamp multiplies 400 N by 5.7.
- Vibration (Vibration, Isolation and Noise): 5 Hz mounts isolate the 25 Hz pump unit by 95 percent.
- Clutch (Clutches, Brakes and Couplings): a 144 N·m disc clutch for the 71.5 N·m motor torque with a 1.5 service factor.
- Flywheel (Flywheels, Balancing and Rotors): 1.22 kg·m² holds the speed within 10 percent over a 3 kJ stroke.
- Frame (Machine Design Case Study: the 80 kN Press Frame): 130 MPa at the throat is 2.7 times below yield, but a weld at that spot fails by fatigue in about 4 months.
Quick reference: the equations
| What you need | Equation |
|---|---|
| Spring rate and stress | k = G d⁴ ÷ (8 D³ Na), τ = Kw 8 F D ÷ (π d³) |
| O-ring squeeze | (cross-section − groove depth) ÷ cross-section |
| Screw torque | T = (W dm ÷ 2)(l + π μ dm) ÷ (π dm − μ l) |
| Cam peak acceleration | a = Ca h ω² ÷ β² |
| Grashof | s + l ≤ p + q; mobility M = 3(n − 1) − 2 j |
| Toggle | Fout = Fin ÷ (2 tan α) |
| Natural frequency | f = (1 ÷ 2π) √(k ÷ m) = 15.76 ÷ √(δ in mm) |
| Transmissibility | T = √(1 + (2ζr)²) ÷ √((1 − r²)² + (2ζr)²) |
| Clutch torque (uniform wear) | T = μ F n (ro + ri) ÷ 2 |
| Flywheel | I = ΔE ÷ (Cs ω²) |
| Rotor unbalance | e = G ÷ ω, F = m e ω² |
| Weld fatigue | N = 2 × 10⁶ (Δσc ÷ Δσ)³ |
Related guides and tools
- Gears and Power Transmission (shafts, bearings, belts, chains) and Structures and Strength of Materials (stress, fatigue, bolts, welds).
- Materials and Processes, Fits and Tolerances and GD&T.
- Spring Design, Natural Frequency and Bearing Life calculators.
- Motion Control and Actuators for drives and axes, and Hydraulics and Pneumatics.
- The Downloads library (a machine design formula sheet).
Safety first
- Stored energy kills: compressed springs, accumulators, flywheels, loaded frames and raised loads release their energy suddenly. Block, vent and lock out before work.
- Rotating parts (shafts, couplings, flywheels, screws) catch clothing and hair: guard them, and never run a machine with a guard removed.
- Crush and shear points in presses, linkages and cams: guards, interlocks, light curtains and two-hand controls to the machine safety standards.
- Design for failure: assume that a part can break; contain it with a guard, make failures safe and use a risk assessment.
- The numbers here are for study and preliminary design. A real machine needs a full design review, tests and the standards of its country.
FAQ
Where do I start a machine design?
With the requirements and the load path (the case study shows the method), then the elements.
Where are gears, bearings and shafts?
In Gears and Power Transmission; fasteners, stress and fatigue are in Structures and Strength of Materials.
Do I need to run the calculations by hand?
To understand them, yes once; then use a calculator or a spreadsheet and always sanity-check the result with a rough hand estimate.
What is the last guide in this series?
Fundamentals: statics, dynamics, mathematics, statistics and economics for engineers.
References
- Shigley, J. E., Mischke, C. R., Budynas, R. G., Mechanical Engineering Design, McGraw-Hill; Norton, R. L., Machine Design: An Integrated Approach, Pearson; Norton, R. L., Design of Machinery, McGraw-Hill.
- Machinery’s Handbook, Industrial Press; Rao, S. S., Mechanical Vibrations; Wahl, A. M., Mechanical Springs; Parker O-Ring Handbook.
- ISO, EN, DIN and ASME standards for machine elements and safety (cited on each page).
Last reviewed: November 2026. Values are typical; check the standard, the maker’s data and the requirements that apply to your machine.