Editing Logarithmic spiral (section)

== In engineering applications ==
{{multiple image|total_width=400
|image1=A Kerf Canceling Mechanism (bearing).gif|caption1=A kerf-canceling mechanism leverages the self similarity of the logarithmic spiral to lock in place under rotation, independent of the kerf of the cut.<ref>{{Cite web|title=kerf-canceling mechanisms |url=https://hpi.de/baudisch/projects/kerf-canceling-mechanisms.html|access-date=2020-12-26 |website=hpi.de |language=en}}</ref>
|image2=ILA Berlin 2012 PD 128.JPG|caption2=A logarithmic spiral antenna}}
* Logarithmic [[Spiral antenna|spiral antennas]] are frequency-independent antennas, that is, antennas whose radiation pattern, impedance and polarization remain largely unmodified over a wide bandwidth.<ref>{{Cite journal|last=Mayes|first=P.E. |date=1992 |title=Frequency-independent antennas and broad-band derivatives thereof|url=https://ieeexplore.ieee.org/document/119570 |journal=Proceedings of the IEEE|volume=80|issue=1|pages=103–112|doi=10.1109/5.119570|bibcode=1992IEEEP..80..103M }}</ref>
* When manufacturing mechanisms by subtractive fabrication machines (such as [[Laser cutting|laser cutters]]), there can be a loss of precision when the mechanism is fabricated on a different machine due to the difference of material removed (that is, the [[kerf]]) by each machine in the cutting process. To adjust for this variation of kerf, the self-similar property of the logarithmic spiral has been used to design a kerf cancelling mechanism for laser cutters.<ref>{{Cite book|last1=Roumen|first1=Thijs |last2=Apel|first2=Ingo|last3=Shigeyama|first3=Jotaro|last4=Muhammad|first4=Abdullah|last5=Baudisch|first5=Patrick |title=Proceedings of the 33rd Annual ACM Symposium on User Interface Software and Technology |chapter=Kerf-canceling mechanisms: Making laser-cut mechanisms operate across different laser cutters |date=2020-10-20 |chapter-url=https://dl.acm.org/doi/10.1145/3379337.3415895|language=en |location=Virtual Event USA|publisher=ACM|pages=293–303|doi=10.1145/3379337.3415895 |isbn=978-1-4503-7514-6|s2cid=222805227 }}</ref>
*Logarithmic [[Spiral bevel gear|spiral bevel gears]] are a type of spiral bevel gear whose gear tooth centerline is a logarithmic spiral. A logarithmic spiral has the advantage of providing equal angles between the tooth centerline and the radial lines, which gives the meshing transmission more stability.<ref>{{Cite journal|last1=Jiang|first1=Jianfeng |last2=Luo | first2=Qingsheng |last3=Wang|first3=Liting|last4=Qiao|first4=Lijun|last5=Li|first5=Minghao|date=2020|title=Review on logarithmic spiral bevel gear|journal=Journal of the Brazilian Society of Mechanical Sciences and Engineering|language=en|volume=42|issue=8|pages=400|doi=10.1007/s40430-020-02488-y|issn=1678-5878 | doi-access=}}</ref>
{{CSS image crop|Image=Camalot number 6.JPG|bSize=400|cWidth=300|oLeft=60|cHeight=200|oTop=40|Description=A [[spring-loaded camming device]], with logarithmic spiral cam surfaces}}
*In [[rock climbing]], [[spring-loaded camming device]]s are made from metal cams whose outer gripping surfaces are shaped as arcs of logarithmic spirals. When the device is inserted into a rock crack, the rotation of these cams expands their combined width to match the width of the crack, while maintaining a constant angle against the surface of the rock (relative to the center of the spiral, where force is applied). The pitch angle of the spiral is chosen to optimize the friction of the device against the rock.<ref>{{cite book | last = Todesco | first = Gian Marco | editor1-last = Emmer | editor1-first = Michele | editor2-last = Abate | editor2-first = Marco | contribution = Weird gears | doi = 10.1007/978-3-319-93949-0_16 | isbn = 9783319939490 | pages = 179–193 | publisher = Springer International Publishing | title = Imagine Math 6: Between Culture and Mathematics | year = 2018}}</ref>
*Soft robots based on the logarithmic spiral were designed for scalable and efficient 3D printing. Using cable-driven actuation, they mimic octopus-like movements for stable and versatile object manipulation.<ref>{{Cite journal |last=Wang |first=Zhanchi |last2=Freris |first2=Nikolaos M. |last3=Wei |first3=Xi |date=2024 |title=SpiRobs: Logarithmic spiral-shaped robots for versatile grasping across scales |url=https://linkinghub.elsevier.com/retrieve/pii/S2666998624006033 |journal=Device |language=en |pages=100646 |doi=10.1016/j.device.2024.100646|arxiv=2303.09861 }}</ref>