Sweeping Surfaces Research Articles

Design and Strength Analysis of a New Construction of a Sweeper with an Independent Surface Copying System Dedicated to Small Loaders and Front Loaders

Most enterprises and farms have paved parking lots, yards, warehouses, or sidewalks that need to be cleaned or cleaned. There are many sweepers available on the Polish and European markets, but there is still a lack of a solution that would be mounted on pallet forks and would have an independent copying system to support sweeping surfaces with different inclinations. The aim of the work was to develop a conceptual design for a new sweeper equipped with an independent surface copying system dedicated to small loaders and front loaders, as a well as strength analysis of the main frame. The conceptual design included an analysis of available solutions, development of a 3D CAD model of the new sweeper, and a detailed strength analysis of the sweeper’s main frame using the finite element method (FEM). The sweeper model was made in the Autodesk Inventor program, while the FEM strength analysis was made in the Siemens NX program. The designed frame model did not have nodes in which the stresses would be greater than 25% of the allowable stress in the material structure and 33% of the maximum allowable stress in the structure of the joints. The sweeper developed new design fulfills all the assumed functions and has a good chance of application.

Involutive sweeping surfaces with Frenet frame in Euclidean 3-space

In this paper we first define the involutive sweeping surfaces as a new surface form. We then investigate singularity, Gaussian and mean curvatures of these surfaces. By calculating the Gaussian and mean curvatures of the involutive sweeping surfaces, we find necessary conditions of being flat or minimal of these surfaces. Also, we analyze the necessary and sufficient conditions for parameter curves on the surface to be asymptotic, geodesic. Then we investigate the special case that the parameter curves are lines of curvature on the surface. Finally, we illustrate our method of calculation by presenting an example.

Sweeping Surfaces Due to Conjugate Bishop Frame in 3-Dimensional Lie Group

In this work, we present a new Bishop frame for the conjugate curve of a curve in the 3-dimensional Lie group G3. With the help of this frame, we derive a parametric representation for a sweeping surface and show that the parametric curves on this surface are curvature lines. We then examine the local singularities and convexity of this sweeping surface and establish the sufficient and necessary conditions for it to be a developable ruled surface. Additionally, we provide detailed explanations and examples of its applications.

Designing and Studying Darboux Sweeping Surface in Isotropic Space I^1_3

This research aims to study Darboux sweeping surface in isotropic space I1 3 . We went through the geometric characteristics of sweeping surfaces in I1 3 . The first and second fundamental forms of the sweeping surface were evaluated. Furthermore, we investigate the mean and Gaussian curvature of the sweeping surface. We also show that the parametric curves on these surfaces are non-geodesic and non-asymptotic. Then, we derive the necessary and sufficient conditions for the sweeping surface to become a developable sweeping surface, minimal sweeping surface, and Weingarten surface. Finally, an example to illustrate the application of the results is introduced.

Sweeping Surfaces according to Type-3 Bishop Frames in Euclidean 3-Space

The aim of this work is to investigate sweeping surfaces and their local singularities due to type-3 Bishop frames in Euclidean 3-space, E3. A sweeping surface a is surface that is designed from a section curve positioned along a path, which acts as the vertebral column or spine curve, and it has symmetrical characteristics. In this work, we have specified a sweeping surface and have examined its geometry and singularity. Thereafter, we deduced the circumstances required for this surface to be a developable surface. In great detail, we concentrated on the fundamental discussion on whether the resulting developable surface is a cylindrical, cone or tangent surface. Meanwhile, examples are detailed to explain the applications of the notional outcomes.

Sweeping surface due to rotation minimizing Darboux frame in Euclidean 3-space $ \mathbb{E}^{3} $

<abstract><p>In this paper, we address a new version of Darboux frame using a common tangent vector field to a surface along a curve and call this frame the rotation minimizing Darboux frame (RMDF). Then, we give the parametric equation due to the RMDF frame for a sweeping surface and show that the parametric curves on this surface are curvature lines. Consequently, necessary and sufficient conditions for sweeping surfaces to be developable ruled surfaces are derived. Also, we analyze the conditions when the resulting developable surface is a cylinder, cone or tangential surface. We also provide some examples to illustrate the main results.</p></abstract>

Sweeping Surfaces in theThree-Dimensional Lie Group

This paper investigated the rotation minimizing frames that are related to the space curves and the sweeping surfaces that are traced by these frames in the three-dimensional Lie group. Then, the sufficient and necessary conditions for the sweeping surface to be a developable ruled surface were obtained. In particular, we mostly focused on the study of the resulting developable surface is a cylinder, cone, or tangent surface. Meanwhile, to support the results in the paper, some illustrative examples are presented.

Developable Surfaces through Spacelike Sweeping Surfaces in Minkowski 3–Space

Developable Surfaces through Spacelike Sweeping Surfaces in Minkowski 3–Space

Sweeping surfaces according to type-2 Bishop frame in Euclidean 3-space

This work is concerned with the study of the kinematic-geometry of a special kind of tube surfaces, so-called sweeping surface in Euclidean 3-space [Formula: see text]. It is generated by a plane curve moving through space such that the movement of any point on the surface is always orthogonal to the plane. In particular, the type-2 Bishop frame is considered and some important theorems are obtained. Also, the problem of singularity and convexity of such sweeping surface is discussed. Finally, an application is presented and plotted using computer aided geometric design.

Timelike sweeping surfaces and singularities

We consider a timelike sweeping surface with rotation minimizing frames in Minkowski 3-Space [Formula: see text]. We introduce a new geometric “invariant”, which demonstrates the geometric properties and local singularities of the surface. Subsequently, we give the sufficient and necessary conditions for this surface to be a developable ruled surface. Finally, the singularities of these ruled surfaces are investigated.

Sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-Space

In this paper, we introduce the notion of sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-space E3 . We also show that the parametric curves on these surfaces are lines of curvature. Then, we derive the necessary and sufficient condition for the sweeping surface to become a developable ruled surface. In particular, we analyze the necessary and sufficient conditions when the resulting developable surface is a cylinder, cone or tangent surface. Finally, some representative curves are chosen to construct the corresponding developable surfaces which possessing these curves as lines of curvature.

Timelike Sweeping Surfaces According to Type-2 Bishop Frame in Minkowski 3–space

In this paper, we express timelike sweeping surfaces using rotation minimizing frames in Minkowski 3–Space E3 1 . Necessary and sufficient conditions for timelike sweeping surfaces to be developable ruled surfaces are derived. Using these, we analyze the conditions when the resulting timelike developable surface is a cylinder, cone or tangential surface.

Ceramic 3D printed sweeping surfaces

Ceramic 3D printing has gained rapid development in recent years. Especially, desktop ceramic 3D printers get more and more popular for designers, artists, and makers to work with clays. As a highly viscous pseudoplastic liquid, the printing material clay produces featured aesthetics, and also indicates several manufacturing constraints. There are barely customized modeling tools for ceramic printing. Targeting for ceramic printing, we present a user-interactive modeling and fabricating framework using sweeping lines as the design tool. We integrate the ceramic printing constraints like self-supporting and collision-free in the modeling stage. Then we propose a customized method for generating the printing file, with the guarantee that the extruder traces a single continuous path without starts and stops. To fulfill this goal, we compute an adaptive zig-zag path along the sweeping surface. During the fabrication, our continuous path avoids the potential collision between the printing head and the physical model. Moreover, we optimize the extrusion amount along with the extruder movement, such that overlap between neighboring layers is appropriate in terms of both model stability and cost-effectiveness. We demonstrate the fabrication process and physical results to validate our method.

Developable Surfaces Through Sweeping Surfaces

This paper studies the rotation minimizing frames that are associated with spatial curves and the sweeping surfaces which are generated by these frames. Then the necessary and sufficient condition for sweeping surface to be developable ruled surface is derived. In particular, we focused for the resulting developable surface is a cylinder, cone or tangent surface.

Cubic Pythagorean hodograph spline curves and applications to sweep surface modeling

This article is devoted to cubic Pythagorean hodograph (PH) curves which enjoy a number of remarkable properties, such as polynomial arc-length function and existence of associated rational frames. First we derive a construction of such curves via interpolation of G 1 Hermite boundary data with Pythagorean hodograph cubics. Based on a thorough discussion of the existence of solutions we formulate an algorithm for approximately converting arbitrary space curves into cubic PH splines, with any desired accuracy. In the second part of the article we discuss applications to sweep surface modeling. With the help of the associated rational frames of PH cubics we construct rational representations of sweeping surfaces. We present sufficient criteria ensuring G 1 continuity of the sweeping surfaces. This article concludes with some remarks on offset surfaces and rotation minimizing frames.

Rocketships, Rayguns and UFOs

Rocketships, Rayguns and UFOs

Curves with rational Frenet-Serret motion

This paper examines a special type of rational curves called rational Frenet-Serret (RF) curves distinguished by the property that the motion of their Frenet-Serret frame is rational. It is shown that a rational curve is an RF curve if and only if it has rational speed and rational curvature. The paper derives a general representation formula for RF curves suitable for geometric design and provides a geometric survey of special RF curves. The special case of a cubic helix is examined thoroughly. Additionally the paper discusses several applications including examples for the design of rational sweeping surfaces, rational pipe surfaces and rational transition surfaces joining sweeps with G 1 continuity.

Sweeping with all graphical ingredients in a topological picturebook

Sweeping is a powerful method to generate 3-D shapes in geometric modeling. In this paper we formulate a general matrix to give a mathematical definition of twisted-profiled sweep objects as a discrete approximation. While conceptually simple, our result is, to our best knowledge, the first precise formulation of sweeping with all graphical ingredients, viz. twisting, scaling, rotation, and translation. Twisted-profiled sweeping surfaces defined by contour, profile, trajectory, and guide curves are thus represented in concatenated matrix formulation. In addition, we give interactive methods to generate sweep objects and present sample figures produced within the framework of our implementation Tb, a topological picturebook.