Mathematical and Computer Simulation of Hex Head Screws for Implementation on a 3D Printer

In this paper, based on the R-functions theory, methods have been developed and equations have been constructed for the 3D printing of hex-head screws with Bristol, Pentalobe, Polydrive and other types of screw slots. Such screws are used both in personal computers and other high-end equipment. The Bristol slot has four or six radial grooved beams. The advantage of the design of this slot is the correct perpendicular, rather than tangential, vector of force application when the slot is rotated by a tool, which minimizes the risk of stripping out the slot. For this reason, the Bristol slot is used in soft metal screws. Compared to the internal hex, the Bristol slot allows a noticeably higher torque, only slightly higher than that of the Torx slot. This type of slot is used in aviation, high-end telecommunications equipment, cameras, air brakes, agricultural equipment, astronomical equipment, and foreign military equipment. Variations with a pin in the center are found in game consoles to prevent the use of a flat-blade screwdriver as an improvised key. The Pentalobe slot is a five-point slot designed by Apple and used in its products to limit unauthorized disassembly. It was first used in mid 2009 to mount MacBook Pro batteries. Its miniature version was used in the iPhone 4 and later models, in the MacBook Air (available since late 2010 models), and the MacBook Pro with Retina screens. The Polydrive slot is a starlike slot with rounded star points, used in the automotive industry for applications requiring high tightening torque. The Torq-set slot is a cross slot for fasteners requiring high tightening torque. The grooves are slightly offset, not intersecting at one point. Fasteners with this type of slot are used in military aviation, for example, in E-3, P-3, F-16, Airbus, Embraer, and Bombardier Inc. The Phillips Screw Company owns the trademark and manufactures fasteners with this type of slot. The slot design standards are National Aerospace Standard NASM 3781 and NASM 4191 for the ribbed version. The resulting equations for the surfaces of screws were checked during the modeling of the screws before 3D printing. The 3D printing technology allows us to reduce the cost and labor intensity of manufacturing products, including complex slot screws. The analytical recording of designed objects makes it possible to use alphabetic geometric parameters, complex superposition of functions, which, in turn, allows us to quickly change their design elements. The positivity property of the constructed functions at the internal points of an object is very convenient for the implementation of 3D printing.

New method for determining singularities on enveloped surface and its application to study curvature interference theory of involute worm drive

In this paper, a more computationally convenient singularity condition of the enveloped surface is proposed using the theory of linear algebra. Its preconditions are only the tangential vector of the enveloping surface, the relative velocity vector, and the total differential of the meshing function. It avoids calculating the curvature parameters of the enveloping surface. It is proved that the singularity conditions of enveloped surface from different references are equivalent to each other and the relational equations among them are obtained. The curvature interference theory for the involute worm drive is established using the proposed singularity condition. The equation for the singularity trajectory is obtained. The calculation method for the singularity trajectory is proposed and its numerical result is obtained. The influence of the design parameters on the singularity trajectory is studied using the proposed curvature interference theory. The study results show that the risk of curvature interference is high when the transmission ratio is too small, especially in the case of the single-threaded worm and large modulus. The proposed singularity condition can also be applied to study the curvature interference mechanism in other types of the worm drive and to study the undercutting mechanism when machining the worm drive.

Three-Dimensional Path Planning of Constant Thrust Unmanned Aerial Vehicle Based on Artificial Fluid Method

In this paper, a three-dimensional path planning problem of an unmanned aerial vehicle under constant thrust is studied based on the artificial fluid method. The effect of obstacles on the original fluid field is quantified by the perturbation matrix, the streamlines can be regarded as the planned path for the unmanned aerial vehicle, and the tangential vector and the disturbance matrix of the artificial fluid method are improved. In particular, this paper addresses a novel algorithm of constant thrust fitting which is proposed through the impulse compensation, and then the constant thrust switching control scheme based on the isochronous interpolation method is given. It is proved that the planned path can avoid all obstacles smoothly and swiftly and reach the destination eventually. Simulation results demonstrate the effectiveness of this method.

Perancangan dan Analisis Antena Dipole Pada Frekuensi 2,4 GHz Untuk Modul Xbee S2 Pro Menggunakan HFFS 14.0

Xbee s2 pro module works at 2,4 Ghz using IEEE 802.15.4 standard and polarization are linear. There are many types of antennas that can be used, which one is the dipole antenna. The simulation model implemented in this study uses Ansoft HFSS 14.0 software. HFSS stands for high frequency structure simulator is a pioneer in the use of finite element method for electromagnetic wave simulators that implement tangential vector finite elements, adaptive meshing and Adaptive Lanczos-Pade Sweep (ALPS) technology. By using HFSS 14.0 simulation, the axial ratio value of 35.0359 dB that means linier polarization. For the value of s-parameter -21,1851 db and VSWR value approaches 1, that is 1.5195 db. The gain value obtained is 0.7469 dB, the gain value needs to be optimized by using a metamaterial to get a good gain.

Analysis of finite element methods for vector Laplacians on surfaces

We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in ${\mathbb{R}}^3$. Closely related operators arise in models of flow on surfaces as well as elastic membranes and shells. The method is based on standard continuous parametric Lagrange elements that describe a ${\mathbb{R}}^3$ vector field on the surface, and the tangent condition is weakly enforced using a penalization term. We derive error estimates that take into account the approximation of both the geometry of the surface and the solution to the partial differential equation. In particular, we note that to achieve optimal order error estimates, in both energy and $L^2$ norms, the normal approximation used in the penalization term must be of the same order as the approximation of the solution. This can be fulfilled either by using an improved normal in the penalization term, or by increasing the order of the geometry approximation. We also present numerical results using higher-order finite elements that verify our theoretical findings.

A fundamental solution for a nonelliptic partial differential operator, II

Let [Formula: see text] denote the holomorphic tangential vector field to the generalized upper-half plane [Formula: see text]. In our terminology, [Formula: see text]. Consider the [Formula: see text] operator on the boundary of [Formula: see text], [Formula: see text]; note that [Formula: see text] is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution [Formula: see text] to [Formula: see text]. Our approach is based on special functions and their properties.