2inch Slackline Kits Aggroline Designed to achieve dynamic movement and bounce at great distances, the AGGRO LINE is ideal for large trees, water lines, tricks or challenging walks. Featuring trampoline-style webbing with rubber grip, Alpha Ratchet with mechanical advantage at long lengths and a backup line system, this kit allows for progression to long lines and advanced tricks. Two-piece Slackline is fully adjustable and easily installed between trees or other sturdy anchor points.Improve balance skills, core strength, and coordination while having fun.Kit includes slackline, Alpha Ratchet, tree protection and safety backup line.Custom-designed trampoline-style webbing is made for slacklining and provides extra bounce for dynamic tricks. Slackline Kits Aggroline,Zen Monkey Slackline,Ourdoor Playing Slackline Training WINNERLIFTING SAFETY EQUIPMENT CO., LTD. , https://www.cargostrapfactory.com
INTRODUCTION Whether it is a CAE based on finite element analysis for a single gear or a motion simulation based on virtual simulation (VS) for the entire gear train, the gear 3D geometric model is a foundation. Because the geometric modeling functions of software platforms such as CAE and VS are relatively weak, it is not possible to provide accurate part models directly or difficultly. For this reason, the 3D model of the parts is usually built using the mainstream CAD software platform, and then imported through the data conversion interface. Analyze or simulate in CAE software or virtual environment (VE).
Although this method is widely used, it is not without its drawbacks. First, the mainstream CAD software platform generally does not directly provide the 3D geometric modeling function of the gear. On some CAD software platforms, to build a gear 3D geometric model, you must use the development tools that the platform itself to carry out secondary development. The convenience brought by the modeling function of the CAD software platform may be offset by the workload of secondary development. Secondly, in the process of model data conversion, because of different application fields, the model accuracy and file size after conversion may be difficult to meet the requirements of subsequent software. For example, finite element analysis software focuses on the mechanical analysis of gears, which has higher accuracy requirements for geometric models. The virtual simulation software usually analyzes the motion process of the entire gear mechanism, emphasizing real-time rather than accuracy. A more common situation is to replace the involute of the tooth with a straight line, replace the tooth surface with a flat surface, or even replace the solid model with a surface model. This is especially true when performing virtual simulations of integrated mechanisms including gear mechanisms. Secondly, the model transformation is actually the transformation of the expression. The idea is to convert from the special format related to the CAD platform to the common or standard format. The same primitive in the CAD model often uses different in the subsequent software. The primitives are expressed, which may deviate from the original design intent of the CAD model. For example, the desired rectangular surface is often divided into two triangles, so there is a sudden change in illumination on the same rectangular platform during illumination calculation. This unnatural effect is not conducive to the visualization emphasized by virtual simulation technology. It can be seen that model conversion is not a very ideal technical means when it can not effectively meet the requirements of subsequent software models.
To this end, this paper proposes a method for accurately constructing a three-dimensional model of a gear. This method is independent of the CAD software platform and directly constructs the gear 3D model by using points, lines, polygons and other primitives in OpenGL, thus avoiding the adverse effects of the data conversion tool on the geometric model. Using this method, the user can construct a geometric model that satisfies CAE and virtual simulation requirements by specifying the number of vertices from the accuracy of the control gear geometry model. The OpenGL graphics library was chosen because it is an efficient software interface that can be connected to graphics hardware but is hardware independent.
A tooth geometry definition complex geometry model is usually obtained by performing a series of stretching, array, symmetry, etc. on a basic graphic model. The symmetry of the shape of the gear determines that it must contain the most basic graphic model. This basic graphic model is called a gear tooth. It must meet two requirements: 1) The entire gear geometry can be completed by performing array operations on the tooth elements. Modulus; 2) The tooth element is indistinguishable, that is, any part inside the tooth element cannot be obtained by geometric transformation of another part.
Gear teeth are not suitable for these two requirements. The gear teeth generally refer to the protruding portion higher than the root, that is, the FAMAF segment in Fig. 1a, and does not include the cogging EF and EF portions. Therefore, the array transformation of the gear FAMAF cannot obtain the entire gear outer shape, which does not satisfy the requirement 1) . If the teeth contain EF and EF segments, although the entire gear can be built by array transformation, it is not the basic unit for building gears, because it contains symmetrical EFAM segments and MAFE segments. From the above analysis, it can be seen that the EFAM segment is the tooth element. When the gear is cut by the standard rack-shaped cutter, there is a circular arc transition between the top edge and the side edge of the rack, and a non-involute line F1F2 corresponding to the gear is also a component of the tooth element. EF2F1AM, 2 tooth descriptions are described as facilitating the operation of the logarithm in OpenGL. It is necessary to describe the segments of the curve that are part of the tooth in a uniform coordinate system. For this purpose, different coordinate systems and segments of the tooth elements are involved in these coordinate systems. Analytic expression in .
The 21 coordinate system setting is done by geometrically transforming the tooth elements. For the convenience of coordinate transformation, it is better to place the tooth elements in the appropriate position of the coordinate system. To this end, a Cartesian coordinate system O-XY is established, OE is the X-axis, and E is the midpoint of the cogging.
Each segment of the tooth element is ultimately described in this coordinate system. To facilitate the description of the involute F1A and the non-involute segment F1F2, a Cartesian coordinate system O-XY and a polar coordinate system OX are established, and OF1 is an X-axis. It is also contemplated that the involute F1A is F1B at the root portion, as indicated by the dashed line in Fig. 2, and the point B is on the base circle, which is the point at which the involute occurs. In the polar coordinate system with OB as the polar axis, the involute BF1A is a standard equation, so that there are two Cartesian coordinate systems and two polar coordinate systems.
22 tooth top part (MA) non-involute part F1F2 is usually replaced by a circular arc, replaced by a simple usable straight line F1F2, and it is tangent to the involute F1A at point F1, intersecting the cogging at point F2, and OE Intersect at point G.
Through the above steps, the segments constituting the tooth elements are unified in the O-XY coordinate system description.
3 Geometry Model Construction 31 Two Modeling Strategies After determining the unified description of the tooth elements, the coordinates of each point on the tooth element can be calculated and stored in the vertex array according to the accuracy requirements, and then the geometry of the tooth element can be drawn by using the OpenGL function.
There are two modeling strategies to choose from when building gears from the tooth. First, the axial priority method, that is, the tooth element contour EF2F1AM and the coordinate origin O form a closed polygon, and the polygon is axially stretched to form a three-dimensional tooth element. The circular tooth is then circularly arrayed around the axis. The second is the circumferential priority method, which performs mirror transformation on the tooth element EF2F1AM to obtain a complete tooth profile. On this basis, the tooth profile is circumferentially arrayed to obtain the entire gear face shape. The end face shape is further stretched in the axial direction to obtain a three-dimensional model of the complete gear.
Both of these modeling strategies have their own characteristics, but the circumferential priority method is better. Because the transition region is replaced by a straight line or an arc, the contour of the tooth element and the origin are both non-convex polygons, while OpenGL can only deal with the convex polygon, and the data of the end faces of the gear can be reasonably organized by the circumferential priority method. For example, all the teeth are placed in the same array, which facilitates the meshing of the end faces and even the entire gear.
The 32-week-first method modeling process describes the circumferential-first method modeling process. First, the calculation is prepared according to the modulus, the number of teeth, and the required accuracy. For example, the pressure angle and the spread are the discrete tooth involute, the tooth top arc, and the number of root arcs, which are equal here. In addition, l is the axial length of the gear.
The gear end faces are expressed by a three-dimensional array Contour[z][N][k].
Where z is the number of teeth; N is the number of discrete points, which is the modeling accuracy index; k0, 1, 2, corresponding to the three-dimensional coordinate components x, y, z.
It must be noted that in order to facilitate the illumination processing, when the three-dimensional array of the tooth elements is mirrored to obtain a three-dimensional array of teeth, the mirrored array elements must be rearranged so that they are placed in the same hour sequence, so that the front side of the corresponding polygon Consistent with the back, this will ensure the desired lighting effect.
Because OpenGL is independent of the window operating system, it does not have a function for managing windows. For this reason, OpenGL's toolkit glut is used, which simplifies window management.
4 Conclusion This paper combines the different follow-up applications of the three-dimensional model of gears, analyzes the necessity of directly establishing its three-dimensional geometric model, and proposes a method to construct a three-dimensional model of gears using tooth elements. To facilitate the organization of the data structure, different parts of the tooth element are described in the same coordinate system. Two modeling strategies based on tooth elements are proposed and analyzed, and a modeling example of the circumferential priority method is given. This method controls the accuracy of the model by specifying the number of vertices, which makes it easier to meet the requirements of gear CAE and virtual simulation.