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Special Design Problems in Gear Drives
Published in Stephen P. Radzevich, Dudley's Handbook of Practical Gear Design and Manufacture, 2021
The tooth profile in involute gears is the involute of the base circle. Figure 9.1, where 1 is the base circle and 2 is its involute, demonstrates the features of the involute. The most important feature is that in each point of the involute, the normal to it is tangent to the base circle. The length of arc ab of the base circle equals the length of line segment bc. Angle θ is denoted “invα” and called involute function. It is one of the parameters used often in the gear geometry calculations. From Figure 9.1 we can see that θ = φ – α. Since: φ=ab0.5db=bc0.5db=tanα,rad,θ=invφ=tanφ−φ,rad.
Urban 3D Building Extraction Through LiDAR and Aerial Imagery
Published in Guoqing Zhou, Urban High-Resolution Remote Sensing, 2020
If the Curvature0 is greater than the given threshold, the pixel is determined as a corner; otherwise, it is not a corner pixel. Sometimes, it is necessary to suppress the local non-maximum since the multiple Curvature0 surrounding the central pixel simultaneously meets the condition of Equation 6.9. With the proposed method here, the result of the detected corners is displayed in Figure 6.19.Determination of straight line or curve. When using the aspect or aspect graph for house interpretation, the property of a line segmentation, either a straight line or a curve, has to be determined. To this end, the curvature of the line segmentation between two corners is calculated. If the curvature is close to zero, the line segment is considered as a straight line, otherwise, as a curve.Face-coding. With the operations above, the face-coding is conducted in terms of the coding regulation formulated in Sections 2.3 and 2.4. When the above operations are finished, the face codes are completed. An example is depicted in Figure 6.19.
Onion-Like Inorganic Fullerenes from a Polyhedral Perspective
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
Ch. Chang, A. B. C. Patzer, D. Sülzle, H. Bauer
A general polyhedron in three-dimensional space is a solid bounded by a number of polygons (faces), which, two by two have a side in common (edges), while three or more polygonal faces join in common vertices. There is a solid angle Ω associated with each vertex. Broadly, all polyhedra fall into two categories: Convex or non-convex (concave). A convex polyhedron is a polyhedron with the property that for any two points inside of it, the line segment joining them is completely contained within the polyhedron. In general, any polyhedron subtending a solid angle Ω < 2π sr at each of its vertices is called convex while any polyhedron subtending a solid angle Ω > 2π sr at any of its vertices is concave. In other words, a convex polyhedron has each of its vertices protruding outward while a concave polyhedron has any of its vertices indented inwards the surface. Any polyhedron in three-dimensional space can be thoroughly characterized by the total number of its faces f, vertices v, and edges e, which are commonly related by Euler’s theorem: υ−e+f=χ=2(1−g).
A new global toolpath linking algorithm for different subregions with Travelling Saleman problem solver
Published in International Journal of Computer Integrated Manufacturing, 2021
Qirui Hu, Zhiwei Lin, Jianzhong Fu
In this structure, the integer pair property is the index of the current-line segment. Each line segment is made up of two endpoints. The pair value of the two points from the same segment must be identical. For example, for two line segments S1 and S2, S1 has two endpoints P1 and P2 while S2 has two endpoints P3 and P4. If the pair value of P1 and P2 are set as 1, then the pair value for other points must not be 1. Although the pair value can be used to recognize line segments from points, it is still not wise to retrieve all the points every time to find a line segment. To solve this problem, the data structure of the line segment is constructed as follows.