In geometry, an epitrochoid (/ɛpɪˈtrɒkɔɪd/ or /ɛpɪˈtroʊkɔɪd/) is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle.
The parametric equations for an epitrochoid are:
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In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes. On a basic level, it is the path traced by a curve while rolling on another curve without slipping.
In the 16th century, Nicolaus Copernicus proposed a major shift in the understanding of the cycle of the heavenly spheres. Driven by a desire for a more perfect (i.e. circular) description of the cosmos than the prevailing Ptolemaic model - which posited that the Sun circled a stationary Earth - Copernicus instead advanced a heliostatic system where a stationary Sun was located near, though not precisely at, the mathematical center of the heavens. In the 20th century, the science historian Thomas Kuhn characterized the "Copernican Revolution" as the first historical example of a paradigm shift in human knowledge. Both Arthur Koestler and David Wootton, on the other hand, have disagreed with Kuhn about how revolutionary Copernicus' work should be considered.
In the 16th century, Nicolaus Copernicus proposed a major shift in the understanding of the cycle of the heavenly spheres. Driven by a desire for a more perfect (i.e. circular) description of the cosmos than the prevailing Ptolemaic model - which posited that the Sun circled a stationary Earth - Copernicus instead advanced a heliostatic system where a stationary Sun was located near, though not precisely at, the mathematical center of the heavens. In the 20th century, the science historian Thomas Kuhn characterized the "Copernican Revolution" as the first historical example of a paradigm shift in human knowledge,. Both Arthur Koestler and David Wootton, on the other hand, have disagreed with Kuhn about how revolutionary Copernicus' work should be considered.
The Wankel engine (/ˈvʌŋkəl/, VAHN-kəl) is a type of internal combustion engine using an eccentric rotary design to convert pressure into rotating motion. The concept was proven by German engineer Felix Wankel, followed by a commercially feasible engine designed by German engineer Hanns-Dieter Paschke. The Wankel engine's rotor is similar in shape to a Reuleaux triangle, with the sides having less curvature. The rotor spins inside a figure-eight-like epitrochoidal housing around a fixed gear. The midpoint of the rotor moves in a circle around the output shaft, rotating the shaft via a cam.
In its basic gasoline-fuelled form, the Wankel engine has lower thermal efficiency and higher exhaust emissions relative to the four-stroke reciprocating engine. This thermal inefficiency has restricted the Wankel engine to limited use since its introduction in the 1960s. However, many disadvantages have mainly been overcome over the succeeding decades following the development and production of road-going vehicles. The advantages of compact design, smoothness, lower weight, and fewer parts over reciprocating internal combustion engines make Wankel engines suited for applications such as chainsaws, auxiliary power units (APUs), loitering munitions, aircraft, personal watercraft, snowmobiles, motorcycles, racing cars, and automotive range extenders.