Construction of unwinding equation of motion for thin cable in spherical coordinate system

Author(s):  
Kun-Woo Kim ◽  
Jae-Wook Lee ◽  
Jin-Seok Jang ◽  
Joo-Young Oh ◽  
Ji-Heon Kang ◽  
...  

The transient-state unwinding equation of motion for a thin cable can be derived by using Hamilton’s principle for an open system, which can consider the mass change produced by the unwinding velocity in a control volume. In general, most engineering problems can be analyzed in Cartesian, cylindrical, and spherical coordinate systems. In the field of unwinding dynamics, until now, only Cartesian and cylindrical coordinate systems have been used. A spherical coordinate system has not been used because of the complexity of derivatives. Therefore, in this study, the unwinding motion of a thin cable was analyzed using a spherical coordinate system in both water and air, and the results were compared with the results in Cartesian and cylindrical coordinate systems. The unwinding motions in the spherical, Cartesian, and cylindrical coordinate systems were nearly same in both water and air. The error related to the total length was within 0.5% in water, and the error related to the maximum balloon radius was also within 0.5 % in air. Therefore, it can be concluded that it is possible to solve the transient-state unwinding equation of motion in a spherical coordinate system.

Author(s):  
Heather Johnston ◽  
Colleen Dewis ◽  
John Kozey

Objective The objectives were to compare cylindrical and spherical coordinate representations of the maximum reach envelope (MRE) and apply these to a comparison of age and load on the MRE. Background The MRE is a useful measurement in the design of workstations and quantifying functional capability of the upper body. As a dynamic measure, there are human factors that impact the size, shape, and boundaries of the MRE. Method Three-dimensional reach measures were recorded using a computerized potentiometric system for anthropometric measures (CPSAM) on two adult groups (aged 18–25 years and 35–70 years). Reach trials were performed holding .0, .5, and 1 kg. Results Three-dimensional Cartesian coordinates were transformed into cylindrical ( r, θ , Z) and spherical ( r, θ, ϕ) coordinates. Median reach distance vectors were calculated for 54 panels within the MRE as created by incremented banding of the respective coordinate systems. Reach distance and reach area were compared between the two groups and the loaded conditions using a spherical coordinate system. Both younger adults and unloaded condition produced greater reach distances and reach areas. Conclusions Where a cylindrical coordinate system may reflect absolute reference for design, a normalized spherical coordinate system may better reflect functional range of motion and better compare individual and group differences. Age and load are both factors that impact the MRE. Application These findings present measurement considerations for use in human reach investigation and design.


2011 ◽  
Vol 183-185 ◽  
pp. 1030-1034
Author(s):  
Xiao Ling Lei ◽  
Bo Tao

The development and application of the diffusion equations of water pollutants are synthetically discussed. Depending on Cartesian Coordinate system, the water pollutants diffusion equations in different waterflow states are reviewed. And further development of the water pollutants diffusion equations in different waterflow states is extended to Cylindrical Coordinate system and Spherical Coordinate system respectively. This makes the simulating and modeling of water pollutants diffusion much more accurate and convenient in various water areas with different waterflow states by using different coordinate systems.


2005 ◽  
Vol 128 (1) ◽  
pp. 4-10 ◽  
Author(s):  
Der-Form Chang ◽  
Jyhwen Wang

This paper presents an upper bound approach to analyze axisymmetric extrusion processes. A cylindrical and a spherical coordinate system are defined to represent the die geometry and the velocity field, respectively. For various curved dies, minimized upper bound results can be obtained by relating these two coordinate systems. Based on this modeling technique, the effects of die geometry, reduction ratio, and friction are investigated. Axisymmetric extrusion through various curved dies can be easily optimized with the proposed methodology.


2014 ◽  
Vol 705 ◽  
pp. 164-168
Author(s):  
Sang Wook Park ◽  
Hee Young Maeng ◽  
Ju Wook Park

Recently, automatic 3D scanning devices are commonly researched and developed for better productivity of the reverse engineering fields. In this paper, a 3D scanner utilizing a spherical coordinate system was designed and analyzed using FEM analysis. The system was designed for optimal performance, high precision, minimal deflection, and speed of data collection. FEM analysis allowed us to properly design the system to achieve these goals, with focus on the deflection of the cantilever arm. Results of the FEM analysis and figures showing the apparatus design are provided. Successive prototypes are shown to increase in overall performance and reliability through improved design and analysis.


Author(s):  
Debabrata Datta ◽  
T K Pal

Lattice Boltzmann models for diffusion equation are generally in Cartesian coordinate system. Very few researchers have attempted to solve diffusion equation in spherical coordinate system. In the lattice Boltzmann based diffusion model in spherical coordinate system extra term, which is due to variation of surface area along radial direction, is modeled as source term. In this study diffusion equation in spherical coordinate system is first converted to diffusion equation which is similar to that in Cartesian coordinate system by using proper variable. The diffusion equation is then solved using standard lattice Boltzmann method. The results obtained for the new variable are again converted to the actual variable. The numerical scheme is verified by comparing the results of the simulation study with analytical solution. A good agreement between the two results is established.


2016 ◽  
pp. 90-92
Author(s):  
A. G. Obukhov ◽  
R. E. Volkov

It is proved that complex flows of the viscous compressible heat-conducting gas, arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier-Stokes equations for description of such gas flows it are advisable to use a cylindrical coordinate system. This paper describes the transformation of the first projection of the equation of motion of the full Navier-Stokes equations system. The result of the transformation is a record of the first projection of the equation of a continuous medium motion in the cylindrical coordinate system.


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