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  1. Atomic force microscope
  2. Atomic nanoscope
  3. Atom probe
  4. Ballistic conduction
  5. Bingel reaction
  6. Biomimetic
  7. Bio-nano generator
  8. Bionanotechnology
  9. Break junction
  10. Brownian motor
  11. Bulk micromachining
  12. Cantilever
  13. Carbon nanotube
  14. Carbyne
  15. CeNTech
  16. Chemical Compound Microarray
  17. Cluster
  18. Colloid
  19. Comb drive
  20. Computronium
  21. Coulomb blockade
  22. Diamondoids
  23. Dielectrophoresis
  24. Dip Pen Nanolithography
  25. DNA machine
  26. Ecophagy
  27. Electrochemical scanning tunneling microscope
  28. Electron beam lithography
  29. Electrospinning
  30. Engines of Creation
  31. Exponential assembly
  32. Femtotechnology
  33. Fermi point
  34. Fluctuation dissipation theorem
  35. Fluorescence interference contrast microscopy
  36. Fullerene
  37. Fungimol
  38. Gas cluster ion beam
  39. Grey goo
  40. Hacking Matter
  41. History of nanotechnology
  42. Hydrogen microsensor
  43. Inorganic nanotube
  44. Ion-beam sculpting
  45. Kelvin probe force microscope
  46. Lab-on-a-chip
  47. Langmuir-Blodgett film
  48. LifeChips
  49. List of nanoengineering topics
  50. List of nanotechnology applications
  51. List of nanotechnology topics
  52. Lotus effect
  53. Magnetic force microscope
  54. Magnetic resonance force microscopy
  55. Mechanochemistry
  56. Mechanosynthesis
  57. MEMS thermal actuator
  58. Mesotechnology
  59. Micro Contact Printing
  60. Microelectromechanical systems
  61. Microfluidics
  62. Micromachinery
  63. Molecular assembler
  64. Molecular engineering
  65. Molecular logic gate
  66. Molecular manufacturing
  67. Molecular motors
  68. Molecular recognition
  69. Molecule
  70. Nano-abacus
  71. Nanoart
  72. Nanobiotechnology
  73. Nanocar
  74. Nanochemistry
  75. Nanocomputer
  76. Nanocrystal
  77. Nanocrystalline silicon
  78. Nanocrystal solar cell
  79. Nanoelectrochemistry
  80. Nanoelectrode
  81. Nanoelectromechanical systems
  82. Nanoelectronics
  83. Nano-emissive display
  84. Nanoengineering
  85. Nanoethics
  86. Nanofactory
  87. Nanoimprint lithography
  88. Nanoionics
  89. Nanolithography
  90. Nanomanufacturing
  91. Nanomaterial based catalyst
  92. Nanomedicine
  93. Nanomorph
  94. Nanomotor
  95. Nano-optics
  96. Nanoparticle
  97. Nanoparticle tracking analysis
  98. Nanophotonics
  99. Nanopore
  100. Nanoprobe
  101. Nanoring
  102. Nanorobot
  103. Nanorod
  104. Nanoscale
  105. Nano-Science Center
  106. Nanosensor
  107. Nanoshell
  108. Nanosight
  109. Nanosocialism
  110. Nanostructure
  111. Nanotechnology
  112. Nanotechnology education
  113. Nanotechnology in fiction
  114. Nanotoxicity
  115. Nanotube
  116. Nanovid microscopy
  117. Nanowire
  118. National Nanotechnology Initiative
  119. Neowater
  120. Niemeyer-Dolan technique
  121. Ormosil
  122. Photolithography
  123. Picotechnology
  124. Programmable matter
  125. Quantum dot
  126. Quantum heterostructure
  127. Quantum point contact
  128. Quantum solvent
  129. Quantum well
  130. Quantum wire
  131. Richard Feynman
  132. Royal Society's nanotech report
  133. Scanning gate microscopy
  134. Scanning probe lithography
  135. Scanning probe microscopy
  136. Scanning tunneling microscope
  137. Scanning voltage microscopy
  138. Self-assembled monolayer
  139. Self-assembly
  140. Self reconfigurable
  141. Self-Reconfiguring Modular Robotics
  142. Self-replication
  143. Smart dust
  144. Smart material
  145. Soft lithography
  146. Spent nuclear fuel
  147. Spin polarized scanning tunneling microscopy
  148. Stone Wales defect
  149. Supramolecular assembly
  150. Supramolecular chemistry
  151. Supramolecular electronics
  152. Surface micromachining
  153. Surface plasmon resonance
  154. Synthetic molecular motors
  155. Synthetic setae
  156. Tapping AFM
  157. There's Plenty of Room at the Bottom
  158. Transfersome
  159. Utility fog


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From Wikipedia, the free encyclopedia

The cantilevered beam (green) projects out into space from its supports (blue). In this case the beam is balanced by a load over the structure (red block) which counteracts the force of gravity (red arrow).  The orange arrow indicates the location of the maximum bending and shear forces on the cantilever at the support.
The cantilevered beam (green) projects out into space from its supports (blue). In this case the beam is balanced by a load over the structure (red block) which counteracts the force of gravity (red arrow). The orange arrow indicates the location of the maximum bending and shear forces on the cantilever at the support.

A cantilever is a beam anchored at one end and projecting into space. This beam may be fixed at the support, or extend to another support as illustrated. The beam carries the load to the support where it is resisted by bending moment and shear. Cantilever construction allows for long structures without external bracing.

This is in contrast to a post and lintel system where the beam is supported at both ends and loads applied between them.

The Forth Bridge, a cantilever railway bridge with three balanced (double) cantilevers
The Forth Bridge, a cantilever railway bridge with three balanced (double) cantilevers

In bridges, towers, and buildings

Less obvious examples are free-standing radio towers without cable stays and chimneys, which resist being blown over by the wind through cantilever action at their base.

Arguably the most famous cantilever in architecture, a balcony at Fallingwater.
Arguably the most famous cantilever in architecture, a balcony at Fallingwater.

In aircraft

Another use of the cantilever is in aircraft design, pioneered by Hugo Junkers in 1915. Early aircraft wings bore their loads by building two (or more) wings, and bracing them with wires. They were similar to truss bridges in some aspects, the wings on each side of the plane were braced with crossed wires both along their length, so they would stay parallel, as well as front-to-back to resist twisting. The cables generated considerable drag however, and there was constant experimentation on ways to eliminate them.

A British Hawker Hurricane from World War II with cantilever wings
A British Hawker Hurricane from World War II with cantilever wings

It was also desirable to build a monoplane aircraft, as additional drag is formed by having a stack of wings. Early monoplanes used either struts (as do some modern personal aircraft), or cables (as do some modern home-built aircraft). The advantage in using struts or cables is a reduction in weight for a given strength, but with the penalty of additional drag, which reduces maximum speed (for a given power) and increases fuel consumption (for a given speed).

The most successful wing design was the cantilever. A single large beam, referred to as the spar, runs through the wing, and often right through the aircraft. Looking at a plane from the front, the wings are both trying to rotate up at the tips, a force that is resisted either by mounting the two spars to each other (each one is twisting in the opposite direction) or to a strong box-like structure in the middle, or by a shell like structure forward of the spar that forms the aerodynamic shape and resists twisting (this is called a D tube).

Cantilever wings require a much heavier spar than would otherwise be needed in cable-stayed designs. However as the size of aircraft grew, this additional weight dropped in comparison to the overall weight, as well as the growing weight of the cables needed to brace larger wings. Eventually a line was crossed in the 1920s, and designs increasingly turned to the cantilever design. By the 1940s almost all larger aircraft used the cantilever exclusively, even on smaller surfaces such as the horizontal stabilizer.


Cantilevered beams are the most ubiquitous structures in the field of microelectromechanical systems (MEMS). MEMS cantilevers are commonly fabricated from Si, SiN or polymers. The fabrication process typically involves undercutting the cantilever structure to release it, often with an anisotropic wet or dry etching technique. Without cantilever transducers, atomic force microscopy would not be possible. A large number of research groups are attempting to develop cantilever arrays as biosensors for medical diagnostic applications. MEMS cantilevers are also finding application as radio frequency filters and resonators.

Two equations are key to understanding the behavior of MEMS cantilevers. The first is Stoney's formula, which relates cantilever end deflection δ to applied stress σ:

\delta = \frac{3\sigma\left(1 - \nu \right)}{E} \left(\frac{L}{t}\right)^2

where ν is Poisson's ratio, E is Young's modulus, L is the beam length and t is the cantilever thickness. Very sensitive optical and capacitive methods have been developed to measure changes in the static deflection of cantilever beams used in dc-coupled sensors.

The second is the formula relating the cantilever spring constant k to the cantilever dimensions and material constants:

k = \frac{F}{\delta} = \frac{Ewt^3}{4L^3}

where F is force and w is the cantilever width. The spring constant is related to the cantilever resonant frequency ω0 by the usual harmonic oscillator formula \omega_0 = \sqrt{k/m}. A change in the force applied to a cantilever can shift the resonant frequency. The frequency shift can be measured with exquisite accuracy using heterodyne techniques and is the basis of ac-coupled cantilever sensors.

The principal advantage of MEMS cantilevers is their cheapness and ease of fabrication in large arrays. The challenge for their practical application lies in the square and cubic dependences of cantilever performance specifications on dimensions. These superlinear dependences mean that cantilevers are quite sensitive to variation in process parameters. Controlling residual stress can also be difficult.

See also

  • cantilever bridge
  • cantilever chair
  • cantilever mechanics (orthodontics)
  • engineering mechanics
  • moment (physics)
  • statics

External links

  • cantilever beam calculation.


  • Roth, Leland M (1993). Understanding Architecture: Its Elements History and Meaning. Oxford, UK: Westview Press. ISBN 0-06-430158-3. pp. 23-4
  • Madou, Marc J (2002). Fundamentals of Microfabrication. Taylor & Francis. ISBN 0-8493-0826-7.
  • Sarid, Dror (1994). Scanning Force Microscopy. Oxford University Press. ISBN 0-19-509204-X.
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