Arc-length-based axial deformation and length preserved animation

2002 ◽  
Author(s):  
Qunsheng Peng ◽  
Xiaogang Jin ◽  
Jieqing Feng
Keyword(s):  
Arc Length ◽  
Axial Deformation

Analysis of Large-Sag Extensible Catenary with Free Horizontal Sliding at One End by Variational Approach

2017 ◽  
Vol 17 (07) ◽  
pp. 1750070 ◽  
Author(s):  
Thongchai Phanyasahachart ◽  
Chainarong Athisakul ◽  
Somchai Chucheepsakul
Keyword(s):  
Variational Approach ◽  
Equilibrium Configuration ◽  
Virtual Work ◽  
Stationary Condition ◽  
Arc Length ◽  
Axial Deformation ◽  
Vertical Coordinate ◽  
The One ◽  
Equilibrium Consideration ◽  
Work Done

A variational approach for the static equilibrium configuration analysis of a large-sag extensible catenary with free horizontal sliding at one end is developed, considering the virtual work done by the catenary self-weight and the horizontal tension at the free sliding end support. The virtual work of the cable system is expressed in terms of the vertical coordinate, which is a function of the unstrained arc length of the cable. The stationary condition is applied to the virtual work functional to obtain the equilibrium configuration of the catenary. The validity of the variational approach is ensured by Euler’s equation, which is identical to the one derived by the force equilibrium consideration of a catenary segment. The finite element method is used to evaluate the numerical results. A parametric study is performed to demonstrate the effect of axial deformation on the equilibrium configuration of a large-sag extensible free horizontal sliding catenary. The results indicate that as the axial deformation increases, the total arc-length and horizontal span length of the cable also increase. Particularly, the very large-sag catenary configurations are studied and exhibited in this study.

The visual perception of arc length on a real surface

1997 ◽  
Author(s):  
J. Farley Norman ◽  
Joseph S. Lappin ◽  
Hideko F. Norman
Keyword(s):  
Visual Perception ◽  
Real Surface ◽  
Arc Length

Dimensions of plane and solid angles and their units in the International System of Units (SI)

2020 ◽  
pp. 26-32
Author(s):  
M. I. Kalinin ◽  
L. K. Isaev ◽  
F. V. Bulygin
Keyword(s):  
Solid Angle ◽  
International System ◽  
International Committee ◽  
Plane Angle ◽  
Arc Length ◽  
Weights And Measures ◽  
International System Of Units ◽  
System Of Units ◽  
In Series ◽  
Solid Angles

The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.

Choice of Noncircular Gears Hobbing Linkage Methods

2019 ◽  
Vol 13 (1) ◽  
pp. 69-74
Author(s):  
Wang Yazhou ◽  
Xiao Junfeng ◽  
Liu Yongping ◽  
An Jianmin
Keyword(s):  
Machine Tools ◽  
High Density ◽  
Arc Length ◽  
Linkage Methods ◽  
High Uniformity ◽  
Linkage Method ◽  
Noncircular Gears

Background: Various relevant patents and papers which have reported noncircular gears synthesize the advantages of circular gears and cam mechanisms, and are widely used in many types of mechanical instruments. Hobbing is a better method for fabricating noncircular gears. There are 4 linkagemethods to hob noncircular gears. However, which linkage method should be chosen practically has not yet been reported. Objective: The goal of this work is to choose the best linkage method for hobbing noncircular gears. Method: Firstly, the hobbing models of noncircular gears was deduced. Then, based on the model, hobbing linkage methods of noncircular gears were obtained. Thirdly, under different hobbing linkage methods, their aspects (developing regularity of hobbing cutter trace, arc length of program blocks and motion axes of machine tools) were compared. Results: Finally, with the best characteristics of a high density of shaping cutter trace, high uniformity of arc length of program blocks and ease of control, the equal arc-length of gear billet (EALGB) is obtained. It has been proven that EALGB is an excellent linkage method to hob noncircular gears. Conclusion: It has been proven that EALGB is an excellent linkage method to hob noncircular gears.

scholarly journals Affine Subspaces of Curvature Functions from Closed Planar Curves

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese
Keyword(s):  
Arc Length ◽  
Planar Curves ◽  
Affine Subspaces ◽  
Planar Curve ◽  
Real Functions ◽  
Discrete Counterpart ◽  
Equivalent Conditions

AbstractGiven a pair of real functions (k, f), we study the conditions they must satisfy for $$k+\lambda f$$ k + λ f to be the curvature in the arc-length of a closed planar curve for all real $$\lambda $$ λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.

scholarly journals A Feedrate Planning Method for the NURBS Curve in CNC Machining Based on the Critical Constraint Curve

2021 ◽  
Vol 11 (11) ◽  
pp. 4959
Author(s):  
Peng Guo ◽  
Yijie Wu ◽  
Guang Yang ◽  
Zhebin Shen ◽  
Haorong Zhang ◽  
...  
Keyword(s):  
Planning Method ◽  
Cnc Machining ◽  
Arc Length ◽  
Kinematic Constraint ◽  
Nurbs Curve ◽  
Planning Strategy ◽  
Feedrate Planning ◽  
Curvature Constraint ◽  
Planning Methods ◽  
The Relationship

The curvature of the NURBS curve varies along its trajectory, therefore, the commonly used feedrate-planning method, which based on the acceleration/deceleration (Acc/Dec) model, is difficult to be directly applied in CNC machining of a NURBS curve. To address this problem, a feedrate-planning method based on the critical constraint curve of the feedrate (CCC) is proposed. Firstly, the problems of existing feedrate-planning methods and their causes are analyzed. Secondly, by considering both the curvature constraint and the kinematic constraint during the Acc/Dec process, the concept of CCC which represents the relationship between the critical feedrate-constraint value and the arc length is proposed. Then the CCC of a NURBS curve is constructed, and it has a concise expression conforming to the Acc/Dec model. Finally, a feedrate-planning method of a NURBS curve based on CCC and the Acc/Dec model is established. In the simulation, a comparison between the proposed method and the conventional feedrate-planning method is performed, and the results show that, the proposed method can reduce the Acc/Dec time by over 40%, while little computational burden being added. The machining experimental results validate the real-time performance and stability of the proposed method, and also the machining quality is verified. The proposed method offers an effective feedrate-planning strategy for a NURBS curve in CNC machining.

scholarly journals Aspects of Vibration-Based Methods for the Prestressing Estimate in Concrete Beams with Internal Bonded or Unbonded Tendons

2021 ◽  
Vol 6 (6) ◽  
pp. 83
Author(s):  
Angelo Aloisio
Keyword(s):  
Elastic Modulus ◽  
Structural Reliability ◽  
Natural Frequencies ◽  
Concrete Beams ◽  
Experimental Testing ◽  
Hybrid Approach ◽  
Reliable Estimate ◽  
Axial Deformation ◽  
Dynamic Identification ◽  
Concrete Girders

The estimate of internal prestressing in concrete beams is essential for the assessment of their structural reliability. Many scholars have tackled multiple and diverse methods to estimate the measurable effects of prestressing. Among them, many experimented with dynamics-based techniques; however, these clash with the theoretical independence of the natural frequencies of the forces of internally prestressed beams. This paper examines the feasibility of a hybrid approach based on dynamic identification and the knowledge of the elastic modulus. Specifically, the author considered the effect of the axial deformation on the beam length and the weight per unit of volume. It is questioned whether the uncertainties related to the estimate of the elastic modulus and the first natural frequency yield reasonable estimates of the internal prestressing. The experimental testing of a set of full-scale concrete girders with known design prestressing supports a discussion about its practicability. The author found that the uncertainty in estimating the natural frequencies and elastic modulus significantly undermines a reliable estimate of the prestressing state.

scholarly journals Solitons of the midpoint mapping and affine curvature

2021 ◽  
Vol 112 (1) ◽  
Author(s):  
Christine Rademacher ◽  
Hans-Bert Rademacher
Keyword(s):  
Differential Equation ◽  
Large Class ◽  
Affine Group ◽  
Arc Length ◽  
Smooth Curves ◽  
Affine Map ◽  
Affine Curvature

AbstractFor a polygon $$x=(x_j)_{j\in \mathbb {Z}}$$ x = ( x j ) j ∈ Z in $$\mathbb {R}^n$$ R n we consider the midpoints polygon $$(M(x))_j=\left( x_j+x_{j+1}\right) /2.$$ ( M ( x ) ) j = x j + x j + 1 / 2 . We call a polygon a soliton of the midpoints mapping M if its midpoints polygon is the image of the polygon under an invertible affine map. We show that a large class of these polygons lie on an orbit of a one-parameter subgroup of the affine group acting on $$\mathbb {R}^n.$$ R n . These smooth curves are also characterized as solutions of the differential equation $$\dot{c}(t)=Bc (t)+d$$ c ˙ ( t ) = B c ( t ) + d for a matrix B and a vector d. For $$n=2$$ n = 2 these curves are curves of constant generalized-affine curvature $$k_{ga}=k_{ga}(B)$$ k ga = k ga ( B ) depending on B parametrized by generalized-affine arc length unless they are parametrizations of a parabola, an ellipse, or a hyperbola.

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