clothoid

clothoid

[′klȯth·ȯid]
(mathematics)
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The superelevation of the first curve is equal to 60 mm with a clothoid curve transition 30 m long, the second curve has the same transition curve but a superelevation equal to 70 mm.
To be able to achieve the remarkable horsepower and torque on such a small engine, Isuzu gave it a host of advanced technological features, such as a well-designed combustion system-composed of Diamond Like Coated piston pins, coupled with a clothoid curve combustion chamber, new fracture split design connecting rods and DLC fuel-injector needles, which were all engineered to reduce friction, resulting in a better fuel economy and lesser exhaust emissions.
Finally, a dynamic analysis of a wheel approaching a chock is provided, to illustrate the advantage of using a clothoid chock profile to reduce structural loads, in particular when the vehicle has an initial velocity before contacting the chock surface.
From Figure 9(a), we can see that the vehicle can track the preplanned reference path composed of arcs, clothoid curves and straight lines.
The clothoid is defined to be a spiral whose curvature is a linear function of its arc length.
Euler spiral is also known as Cornu's spiral or clothoid. The Euler spiral is widely applied in highway/railway or robotic trajectories design due to its linear curvature property (curvature varies linearly with respect to arc length).
We refer to the methods for clothoid designing and, particularly to the observance of the minimum development of the residual arc that could be brought from a formal point of view to unjustified designing solutions incompatible with territorial pre-existences and costs.
Clothoid is often prefered for highways and railway route design (Meek, Walton 2004a; 2004b).
The IPA plans the turning curvature in accordance with the vehicle movement by using a clothoid curve and determining the minimized steering angle.
Leite, "Smooth trajectory planning for fully automated passengers vehicles: Spline and clothoid based methods and its simulation," Informatics in control automation and robotics, pp.