Kinematics: A Key to Solving the Angle Trisection Problem | Chapter 8 | Mathematics and Computer Science: Contemporary Developments Vol. 10

This paper is a sequel to its forerunner entitled, “A Procedure for Trisecting an Acute Angle,” published earlier where it presented a construction capable of dividing any arbitrary acute angle into three exactly equal parts using an unmarked straightedge and compass only. This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem. It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics, to arrive at the desired construction, using an unmarked straightedge and a compass only. In presenting this construction, since there was no requirement to provide a detailed logic behind the procedure, this information was not provided. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis, in graphical detail, that formed the basis of the long-sought solution to the age-old Angle Trisection Problem, that goes back to the period of Archemedes (around 250 B.C.). The study concluded that this long-sought solution has been finally accomplished, notwithstanding the theoretical proofs of Wantzel, Dudley, and others.

 

Author (s) Details

Lyndon O. Barton
Department of Mathematics and Physics, Delaware State University, Dover, Delaware, USA.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v10/3304

Grounding of the Longitudinal Distance from the Plow Corps to the Center of the Disk Skimmer | Chapter 2 | Innovations in Science and Technology Vol.8

  The theoretical grounding of the longitudinal distance from the plough corps to the centre of the disc skimmer is discussed in this article. The longitudinal distance (I) from the tip of the ploughshare to the centre (Od) of the disc and the determination of the distance (y) of the soil discarding were theoretically substantiated. The angle () of attack, depth (hg) stroke, radius (r) of the sphere, radius (R) of the disc, and angle (k) of the ploughshare installation to the furrow wall are all factors that influence the longitudinal distance.

Author(s) Details:

A. R. Normirzayev,
Namangan Engineering Construction Institute (NECI), Namangan, Republic of Uzbekistan.


A. D. Nuriddinov,
Namangan Engineering Construction Institute (NECI), Namangan, Republic of Uzbekistan.

Please see the link here: https://stm.bookpi.org/IST-V8/article/view/6243

Investigating the Effect of Rotor Angle to Characteristic Amplitudo Vibration Shaft on Wind Turbine Horizontal Axis Testing | Chapter 6 | New Approaches in Engineering Research Vol. 4

 The vibrations that occur in the wind turbine's axis are a result of the unstable wind velocity caused by the angle of the wind attacked by the wind turbine's blade. Because abundant energy sources such as wind and water have not been fully utilized, this study will seek to improve efficiency. Vibration is a popular tool for analyzing machines with both rotational and translational motion. Vibration is a popular tool for analyzing machines with both rotational and translational motion. Data and vibration knowledge will be of critical importance for the treatment of repair analysis and also. This knowledge can help technicians. reduce the occurrence of downtime and can improve advantage from both the aspect of peroduksi and the longer wind turbine age Vibration caused by the effect of the style of siklik [pass/through] existing machine elements, where the elements are displaying each other and didesifikasienergi [pass/through] structure in the form of vibration. The impact of vibration is the occurrence of clunk, a decrease in wind turbine performance, and the destruction of wind turbine components, particularly at the pad and axis. This study of angle includes corner variation of blade (sudu / wind turbine rotor) to axis as well as variation of incoming wind speed. With a change in can perceive an known by the vibration behavior that occurred by measuring with appliance mengunakan agree vibration of vibrometer VQ-400-A OMETRON which in circuit with U3-Lv labjak distribute to PC in the form of digital voltage to analogous voltage This model measures vibration along the horizontal axis of the abscis or along the rotatory wind turbine axis. To present the results of measurements taken by labjak, which is connected to a PC laptop via a circuit. This study found that for wind speeds [among/between] 3 - 4,5 m/s with the smallest deviation, use angle; corner of blade 30o [so that/to be] vibration that happened more minimal, which is [among/between] 0,2353425 mm to 0,356839 mm. According to the critical frequency calculation, if the turbine rotation frequency is 9,464226 Hz and the simulation software ANSYS is used, the frequency is 4,1854 Hz.

Author (S) Details

Aston Sianipar
Department Mechanical Engineering FT-UHN, Jl.Sutomo No.4-A, Medan 20234, Indonesia.

View Book :- https://stm.bookpi.org/NAER-V4/article/view/1882