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.

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.

Generic Models for Designing Dwell Mechanisms: A Novel Kinematic Design of Stirling Engines as an Example

1991 ◽  
Vol 113 (4) ◽  
pp. 446-450 ◽  
Author(s):  
S. Kota
Keyword(s):  
Design Models ◽  
Circular Arc ◽  
Generic Models ◽  
Straight Line ◽  
Stirling Engines ◽  
Finite Set ◽  
Single Input ◽  
Motion Characteristics ◽  
Generic Design ◽  
Four Bar Linkage

The desirable motion characteristics of mechanisms are so implicit that they are difficult to express analytically. Our design methodology involves development of generic design models through abstractions of entire emotion characteristics. We have developed a finite set of generic models (for straight-line, circular-arc, and dwell mechanisms) that represents the entire design space in the sense that a given design specification falls under at least one of the generic design models. This paper presents the generic design models for four-bar straight-line, circular arc, and six-bar dwell linkage mechanisms. The models presented here provide ready-made designs for many dwell applications. We have also presented a new concept in mechanisms design in which multiple coupler points on a four-bar linkage are used to drive different output dyads resulting in multiple dwell outputs. Finally, a new mechanism for the opposed piston stirling engine is presented to illustrate the use of generic design models and the application of a single-input controlling dual output motions with dwells.

Development of Knowledge Base for Designing Linkage-Type Dwell Mechanisms: Part 2—Application

1987 ◽  
Vol 109 (3) ◽  
pp. 316-321 ◽  
Author(s):  
Sridhar Kota ◽  
Arthur G. Erdman ◽  
Donald R. Riley
Keyword(s):  
Expert System ◽  
Design Process ◽  
System Development ◽  
Dimensional Synthesis ◽  
Structural Representation ◽  
Domain Specific ◽  
Straight Line ◽  
Rules Of Thumb ◽  
Domain Specific Knowledge ◽  
Path Curvature

Knowledge acquisition is a big bottleneck in any expert system development. Several “rules-of-thumb” are developed for designing linkage-type dwell mechanisms. These rules of thumb are based on path curvature theory (Part 1 of this paper) and systematic synthesis, analysis and classification of straight-line, circular-arc and symmetrical coupler-curve generating linkages. The methods of representing the domain-specific knowledge in an expert system are discussed here. “Frames” for structural representation of knowledge and “production rules” to control the reasoning during the design process are proposed here. Frames and rules, in the light of dwell-mechanism synthesis are presented. Finally, a conceptual design example illustrates the various stages that the actual expert system goes through in the design process when these concepts are fully developed and programs are written out in LISP. These concepts are developed with an eye toward future development of a general expert system for type and dimensional synthesis of mechanisms.

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.

Circular-Arc Radial Cams with One Connection Arc

2020 ◽  
Vol 896 ◽  
pp. 83-94
Author(s):  
Simona Mariana Cretu ◽  
Ionuţ Daniel Geonea
Keyword(s):  
Line Profile ◽  
Kinematic Analysis ◽  
Geometric Analysis ◽  
Circular Arc ◽  
Circular Arcs ◽  
Straight Line ◽  
Cam Profile

This paper deals with the geometric and kinematic analysis of the circular-arc profile cams with one connection arc. If the maximum lift of the follower is required, it is shown that it is possible to connect two circular-arcs – that are defined by center of curvature and radius – through a single circular-arc, and the connection points result. But, if the connection points of two given circular-arcs of the cam profile are required, at least two circular-arcs are needed to connect them. The specific equations for the geometric analysis for one circular-arc profile are described. Also, for two mechanisms, one with straight-line profile and another with one circular-arc connection profile, the geometric and kinematic analysis and simulations of the movements using SolidWorks and ADAMS programs are presented

Novel Methodology for Inflection Circle based synthesis of Straight Line Crank Rocker Mechanism

2021 ◽  
pp. 1-13
Author(s):  
Prashant Shiwalkar ◽  
S. D. Moghe ◽  
J. P. Modak
Keyword(s):  
Compliant Mechanisms ◽  
Relative Length ◽  
Dimensional Synthesis ◽  
Straight Line ◽  
Synthesis Of Mechanisms ◽  
Acceptable Deviation ◽  
Curvature Theory ◽  
Path Curvature ◽  
Artificial Neural Network Ann ◽  
Line Path

Abstract Emerging fields like Compact Compliant Mechanisms have created newer/novel situations for application of straight line mechanisms. Many of these situations in Automation and Robotics are multidisciplinary in nature. Application Engineers from these domains are many times uninitiated in involved procedures of synthesis of mechanisms and related concepts of Path Curvature Theory. This paper proposes a predominantly graphical approach using properties of Inflection Circle to synthesize a crank rocker mechanism for tracing a coupler curve which includes the targeted straight line path. The generated approximate straight line path has acceptable deviation in length, orientation and extent of approximate nature well within the permissible ranges. Generation of multiple choices for the link geometry is unique to this method. To ease the selection, a trained Artificial Neural Network (ANN) is developed to indicate relative length of various options generated. Using studied unique properties of Inflection Circles a methodology for anticipating the orientation of the straight path vis-à-vis the targeted path is also included. Two straight line paths are targeted for two different crank rockers. Compared to the existing practice of selecting the mechanism with some compromise due to inherent granularity of the data in Atlases, proposed methodology helps in indicating the possibility of completing the dimensional synthesis. The case in which the solution is possible, the developed solution is well within the design specifications and is without a compromise.

scholarly journals Open questions on Tantrix graphs

2017 ◽  
Vol 101 (550) ◽  
pp. 83-89
Author(s):  
Heidi Burgiel ◽  
Mahmoud El-Hashash
Keyword(s):  
Opposite Edge ◽  
Circular Arc ◽  
Open Questions ◽  
Straight Line ◽  
Single Colour ◽  
Straight Lines ◽  
Long Paths

TantrixTM tiles are black hexagons imprinted with three coloured paths [1] joining pairs of edges. There are three different kinds of path. One is a straight line going from an edge to the opposite edge, one a circular arc joining adjacent edges and one an arc of larger radius joining alternate edges (or two apart). Tiles can be rotated but, since they are opaque, they cannot be turned over. A careful enumeration would indicate that, identifying tiles under rotation but not under reflection, there are 16 such tiles. However, the two tiles consisting of three straight lines (meeting at the centre of the hexagon) are not part of the set, so actually there are only 14 different tiles. The game is played by matching tiles to connect paths of the same colour; the goal is to create loops or long paths of a single colour This easy to learn yet hard to master game has inspired research on strategy (e.g. [2]) and complexity (e.g. [3]).

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.

Computer-Aided Synthesis of Linkage-Type Straight-Line and Dwell Mechanisms

1996 ◽  
Author(s):  
Pei-Lum Tso ◽  
Shan-Shun Yan
Keyword(s):  
Optimal Solution ◽  
Primary Methods ◽  
Programming Technique ◽  
The Third ◽  
The Past ◽  
Design Charts ◽  
Straight Line ◽  
Curvature Theory ◽  
Set Up ◽  
Position Synthesis

Abstract The synthesis of the four-bar mechanism has received a substantial amount of attention in the area of straight-line mechanisms. Various geometrical and analytical methods have been developed with numerous papers published in this area over the past few decades. Three primary methods are generally available for synthesis of the linkages. The first approach is the classical Burmester finite separated position synthesis technique. The precision points are assigned for describing the desired straight-line motion (Mahyuddin etc. 1986;Shagan,Fallahi and Lai 1989). The second approach uses the mathematical programming technique for finding the optimal solution which mimimizes the error between the desired straight line and the real tracing points of a linkage (Hwang and Hsiao 1989;Hwang and Lee 1987). The third approach is based on the curvature theory. Any point on the inflection circle generates an approximate straight Tine motion. A series of design charts was set up by Vidosic and Tesar (Vidosic and Tesar 1967) as the basis of synthesizing the mechanisms. However, the direction of the coupler point has generally not been controlled. The constraint was taken into consideration by Hsu (Hsu and Lee 1990).

scholarly journals On Binocular Vision: The Geometric Horopter and Cyclopean Eye

2016 ◽  
Author(s):  
Jacek Turski
Keyword(s):  
Binocular Vision ◽  
Nodal Point ◽  
Infinite Family ◽  
Point Location ◽  
Circular Arc ◽  
Depth Discrimination ◽  
Circular Arcs ◽  
The Family ◽  
The Difference ◽  
Straight Lines

We study geometric properties of horopters defined by the criterion of equality of angle. Our primary goal is to derive the precise geometry for anatomically correct horopters. When eyes fixate on points along a curve in the horizontal visual plane for which the vergence remains constant, this curve is the larger arc of a circle connecting the eyes'rotation centers. This isovergence circle is known as the Vieth-M&uumlller circle. We show that, along the isovergence circular arc, there is an infinite family of horizontal horopters formed by circular arcs connecting the nodal points. These horopters intersect at the point of symmetric convergence. We prove that the family of 3D geometric horopters consists of two perpendicular components. The first component consists of the horizontal horopters parametrized by vergence, the point of the isovergence circle, and the choice of the nodal point location. The second component is formed by straight lines parametrized by vergence. Each of these straight lines is perpendicular to the visual plane and passes through the point of symmetric convergence. Finally, we evaluate the difference between the geometric horopter and the Vieth-M&uumlller circle for typical near fixation distances and discuss its possible significance for depth discrimination and other related functions of vision that make use of disparity processing.

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