scholarly journals A Contribution to Avalanche Dynamics: A Formal and an Exact Solution of the Voellmy/Perla Two-Parametric Equation of Motion (Abstract only)

1983 ◽  
Vol 4 ◽  
pp. 304-304
Author(s):  
Bonsak Schieldrop
Keyword(s):  
Exact Solution ◽  
Velocity Profile ◽  
Average Velocity ◽  
Equation Of Motion ◽  
Centrifugal Effect ◽  
Circular Arcs ◽  
Straight Line ◽  
Abrupt Changes ◽  
Friction Parameters ◽  
Straight Lines

The two-parameter equation of motion for snow avalanches proposed by Voellmy in 1955 was later formally derived by Perla in 1979. It has been the object of numerous investigations, mainly to its applications. It has been solved for tracks approximated by straight lines, and this solution has, in some countries, been used extensively with a two-segment approximation. Perla and Cheng programmed such a solution for digital computation by matching an arbitrary number of straight line segments. This solution can also include impact losses due to abrupt changes in the track.In the first part of this paper a formal integration of the Voellmy/Perla equation is carried out for the general case of a track. The averaged values of the different terms are discussed and evaluated as to their relative orders of magnitude. It is shown that the “centrifugal” effect, which is, of course, automatically omitted in the straight-line solution, can be neglected in most cases. As a conclusion it is shown that all avalanche motions governed by the Voellmy/Perla equation will have the same average velocity on all tracks having the same vertical drop H, the same horizontal extension L, and the same set of “friction” parameters, as long as the length S of the track is the same, regardless of the shape of the tracks. The shape will only determine the velocity profile along the track.The second part of the paper shows the exact solution of the equation for the special case of tracks with constant curvature, i.e. circular arcs. If the conclusion of the first part of the paper holds true, this solution can be used to determine the average velocity on other shaped tracks of the same length, etc.It is finally shown that a number of well-known avalanches described in the literature can well be approximated by a circular arc. In these cases even the velocity profile is determined by the exact solution.

scholarly journals A Contribution to Avalanche Dynamics: A Formal and an Exact Solution of the Voellmy/Perla Two-Parametric Equation of Motion (Abstract only)

1983 ◽  
Vol 4 ◽  
pp. 304
Author(s):  
Bonsak Schieldrop
Keyword(s):  
Exact Solution ◽  
Velocity Profile ◽  
Average Velocity ◽  
Equation Of Motion ◽  
Centrifugal Effect ◽  
Circular Arcs ◽  
Straight Line ◽  
Abrupt Changes ◽  
Friction Parameters ◽  
Straight Lines

The two-parameter equation of motion for snow avalanches proposed by Voellmy in 1955 was later formally derived by Perla in 1979. It has been the object of numerous investigations, mainly to its applications. It has been solved for tracks approximated by straight lines, and this solution has, in some countries, been used extensively with a two-segment approximation. Perla and Cheng programmed such a solution for digital computation by matching an arbitrary number of straight line segments. This solution can also include impact losses due to abrupt changes in the track. In the first part of this paper a formal integration of the Voellmy/Perla equation is carried out for the general case of a track. The averaged values of the different terms are discussed and evaluated as to their relative orders of magnitude. It is shown that the “centrifugal” effect, which is, of course, automatically omitted in the straight-line solution, can be neglected in most cases. As a conclusion it is shown that all avalanche motions governed by the Voellmy/Perla equation will have the same average velocity on all tracks having the same vertical drop H, the same horizontal extension L, and the same set of “friction” parameters, as long as the length S of the track is the same, regardless of the shape of the tracks. The shape will only determine the velocity profile along the track. The second part of the paper shows the exact solution of the equation for the special case of tracks with constant curvature, i.e. circular arcs. If the conclusion of the first part of the paper holds true, this solution can be used to determine the average velocity on other shaped tracks of the same length, etc. It is finally shown that a number of well-known avalanches described in the literature can well be approximated by a circular arc. In these cases even the velocity profile is determined by the exact solution.

Experiments for Performance Evaluation of a Mobile Robot Trajectory Tracking

2012 ◽  
Vol 162 ◽  
pp. 302-307 ◽  
Author(s):  
Mircea Nitulescu
Keyword(s):  
Mobile Robot ◽  
Tracking Control ◽  
Smooth Curve ◽  
Robot Trajectory ◽  
Circular Arcs ◽  
Straight Line ◽  
Turning Motion ◽  
Polygonal Shape ◽  
Path Planner ◽  
Straight Lines

Generally, the path given by the 2D global path planner is a complex trajectory concerning straight lines, circular arcs, quick turning motion or lane change motion, but in the simplest case, the trajectory can be a polygonal shape. For the case of a differential wheeled mobile robot without spin motions, this paper presents and analyzes the real continuous evolution of the robot between two adjacent straight line of a polygonal rote, concerning different angles. For the same model of the robot, the control uses alternatively two different algorithms: the first one is a classical solution in path tracking control and the second one is an algorithm based on a smooth curve function.

Development of Knowledge Base for Designing Linkage-Type Dwell Mechanisms: Part 1—Theory

1987 ◽  
Vol 109 (3) ◽  
pp. 308-315 ◽  
Author(s):  
Sridhar Kota ◽  
Arthur G. Erdman ◽  
Donald R. Riley
Keyword(s):  
Expert System ◽  
Circular Arc ◽  
Design Charts ◽  
Circular Arcs ◽  
Straight Line ◽  
Parallel Motion ◽  
Curvature Theory ◽  
Path Curvature ◽  
Motion Characteristics ◽  
Straight Lines

Linkage-type mechanisms have certain advantages over cams for dwell applications. The design of a typical six-link dwell mechanism involves adding an output dyad to the basic four-bar mechanism that generates either a circular arc or a straight line portion of the coupler curve. The entire motion characteristics of these four-bar mechanisms should be considered in order to design a suitable dwell linkage. Part 1 of this paper is devoted to the study of four-bar linkages which generate straight line, circular arc and symmetrical curves. Part 2 discusses how the design experience gained in this study can be applied to develop an expert system for designing linkage-type dwell mechanisms. Using path curvature theory and design charts developed by Tesar, et al., hundreds of four-bar straight-line mechanisms are systematically investigated. Based on the typical shapes of coupler curves these mechanisms are then classified. A synthesis technique has been developed to design four-bar mechanisms for circular arc generation. Symmetrical coupler curves with straight-line or circular-arc segments, which are required for designing double-dwell mechanisms, are studied. This paper is part of the research that is underway to develop an “expert system” for designing mechanisms to generate straight lines, circular arcs, symmetrical curves, parallel motion and dwell.

Automatic Tread Gaging Machine

1979 ◽  
Vol 7 (1) ◽  
pp. 31-39
Author(s):  
G. S. Ludwig ◽  
F. C. Brenner
Keyword(s):  
Experimental Tests ◽  
Automatic Machine ◽  
Wear Rates ◽  
Handling Device ◽  
Straight Line ◽  
Component Systems ◽  
Before And After ◽  
Good Repeatability ◽  
The Difference ◽  
Straight Lines

Abstract An automatic tread gaging machine has been developed. It consists of three component systems: (1) a laser gaging head, (2) a tire handling device, and (3) a computer that controls the movement of the tire handling machine, processes the data, and computes the least-squares straight line from which a wear rate may be estimated. Experimental tests show that the machine has good repeatability. In comparisons with measurements obtained by a hand gage, the automatic machine gives smaller average groove depths. The difference before and after a period of wear for both methods of measurement are the same. Wear rates estimated from the slopes of straight lines fitted to both sets of data are not significantly different.

scholarly journals An Improved Path-Generating Regulator for Two-Wheeled Robots to Track the Circle/Arc Passage

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jun Dai ◽  
Naohiko Hanajima ◽  
Toshiharu Kazama ◽  
Akihiko Takashima
Keyword(s):  
Control Method ◽  
Convergence Property ◽  
Tangential Direction ◽  
Navigation Problem ◽  
Wheeled Robots ◽  
Robot Trajectory ◽  
Look Ahead ◽  
Straight Line ◽  
The Family ◽  
Straight Lines

The improved path-generating regulator (PGR) is proposed to path track the circle/arc passage for two-wheeled robots. The PGR, which is a control method for robots so as to orient its heading toward the tangential direction of one of the curves belonging to the family of path functions, is applied to navigation problem originally. Driving environments for robots are usually roads, streets, paths, passages, and ridges. These tracks can be seen as they consist of straight lines and arcs. In the case of small interval, arc can be regarded as straight line approximately; therefore we extended the PGR to drive the robot move along circle/arc passage based on the theory that PGR to track the straight passage. In addition, the adjustable look-ahead method is proposed to improve the robot trajectory convergence property to the target circle/arc. The effectiveness is proved through MATLAB simulations on both the comparisons with the PGR and the improved PGR with adjustable look-ahead method. The results of numerical simulations show that the adjustable look-ahead method has better convergence property and stronger capacity of resisting disturbance.

A series exact solution for one-dimensional non-linear particle equation of motion

2011 ◽  
Vol 207 (1-3) ◽  
pp. 461-464 ◽  
Author(s):  
M. Jalaal ◽  
H. Bararnia ◽  
G. Domairry
Keyword(s):  
Exact Solution ◽  
Equation Of Motion ◽  
One Dimensional ◽  
Non Linear

Optimal Design of Computerized Flat Knitting Machine Cam Curves Based on UG and ANSYS/LS-DYNA

2014 ◽  
Vol 529 ◽  
pp. 410-414
Author(s):  
Cang Zhao ◽  
Guang Li Song ◽  
Lei Xu
Keyword(s):  
Finite Element ◽  
Optimal Design ◽  
Dynamic Analysis ◽  
Maximum Stress ◽  
Analysis Software ◽  
Forming Process ◽  
Polynomial Curve ◽  
Circular Arcs ◽  
Design Software ◽  
Straight Lines

By combining the industrial design software UG and finite element dynamic analysis software ANSYS/LS-DYNA, the paper respectively designs the non-linear knitting cams with polynomial curves, and simulates the loop-forming process in the interaction between the cams and needles. Based on comparative analyses, it’s thereby concluded that the polynomial curve has the best performance and is significantly superior to the cam curve composed of straight-lines and circular-arcs; the elements with higher stresses are located above the butt of needle jack and the joint of the jack and latch needle; and the polynomial curve is effective in lowering the maximum stress of the needle.

On the asymptotic solution of the Orr–Sommerfeld equation by the method of multiple-scales

1968 ◽  
Vol 34 (1) ◽  
pp. 145-158 ◽  
Author(s):  
K. Kuen Tam
Keyword(s):  
Exact Solution ◽  
Velocity Profile ◽  
Asymptotic Solution ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Order Equation ◽  
Zeroth Order ◽  
Independent Variables ◽  
Sommerfeld Equation ◽  
Special Case

The method of multiple-scales is used to obtain the asymptotic solution of the Orr–Sommerfeld equation. For the special case of a linear velocity profile, the solution so obtained agrees well with an approximation of the exact solution which is known. For the general case, transformations on both the dependent and independent variables are introduced to obtain a zeroth-order equation which differs from the inner equation studied so far. On the ground of the favourable comparison for the special case, the asymptotic solution constructed is expected to be uniformly valid.

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