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The Study of Geometry of the Selected Transition Curves in the Design of Circular Roads

Basak Agata

Advances in Science and Technology. Research Journal

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2022

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Vol. 16, no 4

270--278

EN

Transition curves connecting straight sections with circular curves and vice versa are present on all types of roads. They are designed to smooth the transition from rectilinear to circular motion. In numerous instances, they are hardly noticeable by road use. Although adequately selected, they increase the safety and comfort of driving. The research aimed to investigate the effectiveness of three most popular curves, in the design of road routes: clothoid, a parabola of the 3rd-degree and Bernoulli lemniscate. Starting from the permissible values of the increment of centripetal acceleration on the transition curves, the minimum lengths of the transition curves for the assumed speeds of the wheeled vehicle were determined. Then, based on the formulas of individual curves, their lengths were calculated, depending on the design speed and the radius of the circular arc. As a result of the research, the differences between the individual curves were obtained. Finally, it was found that due to the unconstrained movement of the vehicle on the road, all curves could be used as transition curves. By slightly adjusting their lengths, we can achieve the appropriate value of the increment of centripetal acceleration. The legitimacy of using different curves as transition curves lies primarily in their different geometric appearance. The choice of the curve to be used is based primarily on the terrain conditions and the type of the planned section of the route (serpentines, turnouts, etc.).

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Continuous-curvature trajectory planning

Roth Jörg

Journal of Automation Mobile Robotics and Intelligent Systems

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2021

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Vol. 15, No. 1

9--23

EN

Continuous-curvature paths play an important role in the area of driving robots: as vehicles usually cannot change the steering angle in zero-time, real trajectories must not have discontinuities in the curvature profile. Typical continuous-curvature paths are thus built of straight lines, arcs and clothoids. Due to the geometric nature of clothoids, some questions in the area of trajectory planning are difficult the answer – usually we need approximations here. In this paper we describe a full approach for continuous-curvature trajectory planning for mobile robots – it covers a maneuver-based planning with Viterbi optimization and geometric approximations required to construct the respective clothoid trajectories.

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Metoda wyznaczania zarysów zębów przekładni zębatej o krzywej tocznej zawierającej łuki klotoidy

Domański J., Bajkowski M.

Logistyka

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2014

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nr 6

3165--3173

PL

W artykule przedstawiono mechanizm zębatkowy, w którym zębnik odtacza się po krzywej zamkniętej (nazywanej tu „krzywą toczną”) składającej się z odcinków prostych, łuków okręgu oraz fragmentów klotoidy. Podano opisy matematyczne krzywych definiujących zarysy boków zębów na fragmencie uzębienia, którego krzywa toczna jest łukiem klotoidy. Zastosowanie klotoidy wynika z dążenia do wykonania takiego kształtu uzębienia, który pozwala na uzyskanie liniowego przyrostu przyśpieszenia dośrodkowego w trakcie zmiany kierunku ruchu osi zębnika przy stałej prędkości liniowej osi zębnika. Celem jest zredukowanie wartości przeciążeń udarowych podczas pracy urządzenia.

EN

In the paper, a gear mechanism wherein a pinion rolls on a closed curve (here named 'pitch curve') composed of straight sections, circular arcs and fragments of the clothoid (Cornu spiral) is presented. A mathematical description of curves defining a teeth outline based on the clothoid is given. The application of the clothoid stems from the desire to achieve such a shape of teeth which allows a linear increase of centripetal acceleration during the change of motion direction of the pinion axis while the pinion moves at a constant linear velocity. The aim is to reduce the impact of overload while the mechanism is in operation.

4

Rozjazdy do dużych prędkości o zmiennej krzywiźnie toru zwrotnego

Nowakowski M.

Przegląd Komunikacyjny

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2011

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Nr 9-10

88-91

PL

Na PKP rozjazdy o najnowocześniejszych konstrukcjach stosowane są na liniach przeznaczonych do prędkości 200 km/h. Umożliwiają one przejazd po torze zwrotnym z prędkością do 100 km/h. Koleje dużych prędkości stawiają przed konstruktorami rozjazdów jeszcze większe wymagania. Nie są im w stanie sprostać rozjazdy, w których tor zwrotny ma kształt łuku o stałej wartości promienia. W referacie przedstawiono wybrane typy rozjazdów, charakteryzujących się zmienną krzywizną toru zwrotnego.

EN

At Polish Railroads, most modern turnouts are used at railways suitable for 200 km/h speed. They enable transiting diverging track at speeds up to 100 km/h. For high-speed railroads, junction designers face even stricter requirements. Not even turnouts with diverging track of constant curvature can satisfy them. This paper presents selected turnouts types, characterized with variable diverging track curvature.