![]() The coils of watch balance springs and the grooves of very early gramophone records form Archimedean spirals, making the grooves evenly spaced (although variable track spacing was later introduced to maximize the amount of music that could be cut onto a record). ![]() Scroll compressors, used for compressing gases, have rotors that can be made from two interleaved Archimedean spirals, involutes of a circle of the same size that almost resemble Archimedean spirals, or hybrid curves.Īrchimedean spirals can be found in spiral antenna, which can be operated over a wide range of frequencies. The Archimedean spiral has a variety of real-world applications. Sometimes the term Archimedean spiral is used for the more general group of spirals Taking the mirror image of this arm across the y-axis will yield the other arm.įor large θ a point moves with well-approximated uniform acceleration along the Archimedean spiral while the spiral corresponds to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity (see contribution from Mikhail Gaichenkov).Īs the Archimedean spiral grows, its evolute asymptotically approaches a circle with radius | v| / ω. Only one arm is shown on the accompanying graph. The two arms are smoothly connected at the origin. ![]() The Archimedean spiral has two arms, one for θ > 0 and one for θ < 0. In contrast to this, in a logarithmic spiral these distances, as well as the distances of the intersection points measured from the origin, form a geometric progression. The Archimedean spiral has the property that any ray from the origin intersects successive turnings of the spiral in points with a constant separation distance (equal to 2 πb if θ is measured in radians), hence the name "arithmetic spiral". Archimedean spiral represented on a polar graph
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