A new method for characterizing axis of rotation radial error motion: Part 1. Two-dimensional radial error motion theory

2011 ◽  
Vol 35 (1) ◽  
pp. 73-94 ◽  
Author(s):  
Xiaodong Lu ◽  
Arash Jamalian
Keyword(s):  
New Method ◽  
Two Dimensional ◽  
Radial Error ◽  
Axis Of Rotation ◽  
Error Motion

scholarly journals On the 3D → 2D Isomerization of Hexaborane(12)

Chemistry ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 28-38
Author(s):  
Josep M. Oliva-Enrich ◽  
Ibon Alkorta ◽  
José Elguero ◽  
Maxime Ferrer ◽  
José I. Burgos
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Transition States ◽  
Three Dimensional ◽  
Reaction Coordinate ◽  
Intrinsic Reaction Coordinate ◽  
Limiting Factor ◽  
Two Dimensional ◽  
Axis Of Rotation

By following the intrinsic reaction coordinate connecting transition states with energy minima on the potential energy surface, we have determined the reaction steps connecting three-dimensional hexaborane(12) with unknown planar two-dimensional hexaborane(12). In an effort to predict the potential synthesis of finite planar borane molecules, we found that the reaction limiting factor stems from the breaking of the central boron-boron bond perpendicular to the C2 axis of rotation in three-dimensional hexaborane(12).

scholarly journals Three-Dimensional Coordination Number from Two-Dimensional Measurements: A New Method

1986 ◽  
Vol 32 (112) ◽  
pp. 391-396 ◽  
Author(s):  
Richard B. Alley
Keyword(s):  
Coordination Number ◽  
Three Dimensional ◽  
New Method ◽  
Two Dimensional ◽  
Shape Factors ◽  
Important Measure ◽  
Dimensional Measurements ◽  
Average Bond

AbstractThe average three-dimensional coordination number, n3, is an important measure of firn structure. The value of n3 can be estimated from n2, the average measured two-dimensional coordination number, and from a function, Γ, that depends only on the ratio of average bond radius to grain radius in the sample. This method is easy to apply and does not require the use of unknown shape factors or tunable parameters.

scholarly journals FOUR-DIMENSIONAL BALL IN A GRAPHIC REPRESENTATION

2021 ◽  
pp. 37-46
Author(s):  
Helena Bidnichenko
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Modelling ◽  
Vector Model ◽  
Original Position ◽  
Two Dimensional ◽  
Axis Of Rotation ◽  
Dimensional Ball ◽  
Three Dimensional Space ◽  
Horizontal Vector

The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection. It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image during rotation forms a body of a higher dimension, that is, one that belongs to (n + 1) -dimensional space. Identified regularities are extended to the four-dimensional space in which the ball is placed. It is shown that the axis of rotation of the ball will be a degenerate projection in the form of a circle, and the ball, when rotating, changes its size from a volumetric object to a flat circle, then increases again, but in the other direction (that is, it turns out), and then in reverse order to its original position. This rotation is more like a deformation, and such a ball of four-dimensional space is a hypersphere. For geometric modelling of the hypersphere and the possibility of its projection image, the article uses the vector model proposed by P.V. Filippov. The coordinate system 0xyzt is defined. The algebraic equation of the hypersphere is given by analogy with the three-dimensional space along certain coordinates of the center a, b, c, d. A variant of hypersection at t = 0 is considered, which confirms by equations obtaining a two-dimensional ball of three-dimensional space, a point (a ball of zero radius), which coincides with the center of the ball, or an imaginary ball. For the variant t = d, the equation of a two-dimensional ball is obtained, in which the radius is equal to R and the coordinates of all points along the 0t axis are equal to d. The variant of hypersection t = k turned out to be interesting, in which the equation of a two-dimensional sphere was obtained, in which the coordinates of all points along the 0t axis are equal to k, and the radius is . Horizontal vector projections of hypersection are constructed for different values of k. It is concluded that the set of horizontal vector projections of hypersections at t = k defines an ellipse.  

A Synthesis Method for Placing Workpieces in RPR Planar Robotic Workcells in Which Large Rotations Are Required at the Workpiece

1996 ◽  
Author(s):  
K. D. Chaney ◽  
J. K. Davidson
Keyword(s):  
Reference Frame ◽  
Synthesis Method ◽  
Analytical Representation ◽  
New Method ◽  
Two Dimensional ◽  
End Effector ◽  
Radial Location ◽  
Practical Applications ◽  
Full Turn ◽  
Large Rotations

Abstract A new method is developed for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar RPR robots that can provide dexterous workspace. The method is an analytical representation of the geometry of the robot and the task, and is particularly well suited to applications in which the task requires large rotations of the end-effector. It is determined that, when the task requires that the end-effector rotate a full turn at just two locations and when the first or third joint in the robot is rotatable by one turn, then the radial location of the workpiece is fixed in the workcell but its angular location is not fixed. When the mounting-angle of the tool is also a variable, the method accommodates tasks in which the tool must rotate a full turn at three locations on the workpiece. The results are presented as coordinates of points in a two-dimensional Cartesian reference frame attached to the workcell. Consequently, a technician or an engineer can determine the location for the workpiece by laying out these coordinates directly in the workcell. Example problems illustrate the method. Practical applications include welding and deposition of adhesives.

Introduction of a new method for two-dimensional NMR quantitative analysis in metabolomics studies

2020 ◽  
Vol 597 ◽  
pp. 113692 ◽  
Author(s):  
Lin Jiang ◽  
Kevin Howlett ◽  
Kristen Patterson ◽  
Bo Wang
Keyword(s):  
Quantitative Analysis ◽  
New Method ◽  
Two Dimensional

Study on the influence of machine tool spindle radial error motion resulted from bearing outer ring tilting assembly

2018 ◽  
Vol 233 (9) ◽  
pp. 3246-3258 ◽  
Author(s):  
Xiaohu Li ◽  
Ke Yan ◽  
Yifa Lv ◽  
Bei Yan ◽  
Lei Dong ◽  
...  
Keyword(s):  
Rotation Speed ◽  
Total Error ◽  
Experimental System ◽  
Outer Ring ◽  
Operation Condition ◽  
Thermal Displacement ◽  
Radial Error ◽  
Spindle Rotation ◽  
Motion Characteristics ◽  
Error Motion

To reveal the spindle radial error motion characteristics in condition of bearing outer ring tilting assembly, mathematical method on spindle radial error motion were analyzed. Then, in real operation condition the natural frequency of the test rig was investigated. Experimental system and methods were designed to test axial thermal displacement, radial error motion and modal characteristic of spindle in condition of bearing outer ring tilting assembly. Results show that axial thermal extension and radial vertical rising of spindle front-end occurs during thermal displacement test. With the same outer spacer nonparallelism, the synchronous error motion and total error motion generally increase with spindle rotation speed, and reach a peak at certain rotation speed.

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