Optimum Design of Curve-Generating Linkages With Inequality Constraints

1967 ◽  
Vol 89 (1) ◽  
pp. 144-151 ◽  
Author(s):  
R. L. Fox ◽  
K. D. Willmert
Keyword(s):  
Mathematical Programming ◽  
Inequality Constraints ◽  
Problem Area ◽  
Mathematical Programming Problem ◽  
Iterative Technique ◽  
Circular Arc ◽  
Open Questions ◽  
Design Variables ◽  
Straight Line ◽  
Four Bar Linkage

The problem of synthesizing a four-bar linkage is presented as a mathematical programming problem. The objective is to synthesize a four-bar linkage whose coupler point will generate, as closely as possible, a given curve, and whose crank rotations will be as close as possible to desired values. Constraints are imposed on the design variables which force the result to be a four-bar linkage, limit the forces and torques within the linkage, restrict the location of the pivot points, limit the lengths of the links, and so on. The solution is found using an iterative technique with the aid of a digital computer. Several examples are presented which demonstrate the effectiveness of this approach. They include generation of a straight line, a figure eight, and a portion of a circular arc (previously investigated using a method developed by Freudenstein and Sandor). The work on this problem area is still in progress and there remain a number of open questions and unexplored alternatives.

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.

scholarly journals Lagrange duality and saddle point optimality conditions for semi-infinite mathematical programming problems with equilibrium constraints

2019 ◽  
Vol 29 (4) ◽  
pp. 433-448
Author(s):  
Kunwar Singh ◽  
J.K. Maurya ◽  
S.K. Mishra
Keyword(s):  
Mathematical Programming ◽  
Saddle Point ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Mathematical Programming Problem ◽  
Dual Model ◽  
Equilibrium Constraints ◽  
Convexity Assumptions ◽  
Mathematical Programming Problems

In this paper, we consider a special class of optimization problems which contains infinitely many inequality constraints and finitely many complementarity constraints known as the semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC). We propose Lagrange type dual model for the SIMPEC and obtain their duality results using convexity assumptions. Further, we discuss the saddle point optimality conditions for the SIMPEC. Some examples are given to illustrate the obtained results.

Computer-Aided Synthesis of Mechanisms Using Nonlinear Programming

1973 ◽  
Vol 95 (1) ◽  
pp. 339-344 ◽  
Author(s):  
V. K. Gupta
Keyword(s):  
Nonlinear Programming ◽  
Mathematical Programming ◽  
Penalty Function ◽  
Inequality Constraints ◽  
Mathematical Programming Problem ◽  
Spatial Mechanisms ◽  
Synthesis Of Mechanisms ◽  
Computer Aided ◽  
Equality And Inequality Constraints ◽  
Penalty Function Approach

The synthesis of spatial mechanisms is formulated as a mathematical programming problem and solved using a penalty function approach. The objective function as well as the equality and inequality constraints are determined explicitly from conditions such as those required for linkage closure, mobility, and transmissibility.

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]).

Duplex Spread Blade Method for Cutting Hypoid Gears with Modified Tooth Surface

1998 ◽  
Vol 120 (3) ◽  
pp. 441-447 ◽  
Author(s):  
K. Kawasaki ◽  
H. Tamura
Keyword(s):  
Cutting Edge ◽  
Tooth Surface ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Ring Gear ◽  
Circular Arc ◽  
Hypoid Gears ◽  
Manufacturing Method ◽  
Straight Line

In this paper, a duplex spread blade method for cutting hypoid gears with modified tooth surface is proposed. The duplex spread blade method provides a rapid and economical manufacturing method because both the ring gear and pinion are cut by a spread blade method. In the proposed method, the nongenerated ring gear is manufactured with cutting edge that is altered from the usual straight line to a circular arc with a large radius of curvature and the circular arc cutting edge produces a modified tooth surface. The pinion is generated by a cutter with straight cutting edges as usual. The main procedure of this method is the determination of the cutter specifications and machine settings. The proposed method was validated by gear manufacture.

Design of backlash-free straight-curved guide devices

2014 ◽  
Vol 228 (15) ◽  
pp. 2833-2843
Author(s):  
Long-Iong Wu ◽  
Kuan-Lwun Shu
Keyword(s):  
Common Point ◽  
Transition Curve ◽  
Circular Arc ◽  
Contact Points ◽  
Straight Line ◽  
Pitch Curve ◽  
Slider Motion ◽  
Guide Device

This article presents a method for designing a planar guide device that can guide sliders to move along a straight-curved rail and can eliminate the backlash between the slider and the rail throughout the whole range of the slider travel. The guide device has many sliders and each slider has three rollers that can separately roll on both sides of the rail. The straight-curved rail is composed of straight sections, connection sections, and circular-arc sections. For each slider, the three normal lines through the contact points between the rollers and the rail must always intersect at a common point, which is an instant center. Using this as a basis, the side profiles of the straight-curved rail can be determined. To avoid infinite jerk of the slider motion, the pitch curve of the connection section should consist of a transition curve, which is interposed between the straight line and the circular arc.

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