A Note on the Waldron Construction for Transmission Angle Rectification

2005 ◽  
Vol 128 (2) ◽  
pp. 509-512 ◽  
Author(s):  
Thomas R. Chase
Keyword(s):  
High Probability ◽  
Synthesis Methods ◽  
Graphical Methods ◽  
Transmission Angle ◽  
Pass Through ◽  
Four Bar Linkage

Graphical methods for synthesizing planar four-bar linkage motion generators to pass through two or three precision positions are well known. However, the practicality of these methods is limited by a high probability that the resulting linkages will suffer from kinematic defects. These may include change of circuit, change of branch or poor transmission angle. This technical brief distills earlier work of Waldron and associates (Chaung, J. C, Strong, R. T., and Waldron, K. J., 1981, J. Mech. Des., 103(3), pp. 657–664, Sun, J. W. H., and Waldron, K. J., 1981, Mech. Mach. Theory, 16(4), pp. 385–397, and Waldron, K. J., 1976, ASME J. Eng. Ind., 98(1), pp. 176–182) to an approachable procedure for controlling the transmission angle of four-bar linkages during synthesis. The procedure simultaneously eliminates the branch defect. It eliminates the circuit defect for some Grashof types but not others. The procedure is integrated with the established graphical synthesis methods by the addition of a few easily implemented substeps. The procedure is simple enough to be performed manually by undergraduates. Nevertheless, it is powerful enough to substantially improve the likelihood that the synthesized linkages will perform well when constructed. The procedure is explained in reference to an application.

Four-Bar Linkage Synthesis Methods for Two Precision Positions Combined With N Quasi-Positions

1995 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Synthesis Method ◽  
Synthesis Methods ◽  
Bounded Motion ◽  
Transmission Angle ◽  
Pass Through ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Exact Positions ◽  
Linkage Synthesis

Abstract Mechanisms seldom need to pass through more than one or two exact positions. The method of quasi-position synthesis combines a number of approximate or “quasi” positions with two exact positions to design four-bar linkages that will produce a specified, bounded motion. Quasi-position synthesis allows for the optimization of some linkage characteristic (such as link lengths or transmission angles) by using the three variables that describe a single quasi-position. Procedures for circuit and transmission angle rectification are also easily incorporated into the quasi-position synthesis method.

Linkage Synthesis Using Algebraic Curves

1986 ◽  
Vol 108 (4) ◽  
pp. 543-548 ◽  
Author(s):  
J. L. Blechschmidt ◽  
J. J. Uicker
Keyword(s):  
Nonlinear Equations ◽  
Algebraic Polynomial ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Optimization Techniques ◽  
Synthesis Methods ◽  
Nonlinear Functions ◽  
Pass Through ◽  
Four Bar Linkage ◽  
Set Of Points

A method to snythesize four-bar linkages using the algebraic curve of the motion of the coupler point on the coupler link of the four-bar linkage is developed. This method is a departure from modern synthesis methods, most of which are based upon Burmester theory. This curve, which is a planar algebraic polynomial in two variables for the four-bar linkage, is a trinodal tricircular sextic (sixth order). These properties are used to determine the coefficients of the curve given a set of points that the coupler point of the coupler link is to pass through. The coefficients of this curve are nonlinear functions of the linkage parameters. The resulting set of nonlinear equations are solved using iterative/optimization techniques for the linkage parameters.

Synthesis of a Large Oscillation Four-Bar Mechanism

1997 ◽  
Author(s):  
Gloria K. Starns ◽  
Donald R. Flugrad
Keyword(s):  
Reduced Gradient Method ◽  
Large Oscillation ◽  
Oscillation Mechanism ◽  
Straight Line ◽  
Transmission Angle ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Angular Oscillations ◽  
Four Bar Linkage ◽  
Effective Transmission

Abstract This paper demonstrates procedures implemented for the synthesis of a four-bar mechanism that produces large angular oscillations of the output member while maintaining effective transmission angles. The mechanisms are modeled as being driven by a force applied at the coupler link. Additionally this force’s line of action is constrained to occur along an approximate straight line. This research was conducted out of the need for a device that is capable of retraction of the horizontal tool bar housed on the back of a tractor. The tool bars accommodate the implements required to accomplish the numerous tasks of the farmer, i.e. row markers, sprayer arms, planters, etc. Upon retraction of the tool bar so that it is parallel to ground, the appropriate tools are lowered to their working position. As the length of these bars increases, a savings of time and increased productivity is realized. Kurt Hain makes the following observation regarding large oscillation mechanisms in [1]: “It would be very difficult to solve this problem with one four-bar linkage, because it is difficult to design a four-bar linkage having such a large oscillation of a crank without running into problems of poor transmission angle characteristics; it might be possible to use linkages in combinations with gears, but this would make the mechanism more expensive, less efficient, and probably noisier.” In this study simulated annealing, a genetic algorithm and the generalized reduced gradient method are used to produce mechanisms with large angular oscillations of the output member and transmission angles that vary by as little as 20° from 90°. A comparative analysis of each of the optimization procedures is presented with observations regarding the efficacy of each method in the solution of the large oscillation mechanism.

Notes on Graphical Methods of Recording the Dimensions of Ammonites

1929 ◽  
Vol 66 (4) ◽  
pp. 180-186 ◽  
Author(s):  
C. H. Waddington
Keyword(s):  
The Other ◽  
One Dimension ◽  
Graphical Methods ◽  
Single Curve ◽  
Pass Through ◽  
Straight Lines

Summary(1) When the diameter of the umbilicus of an ammonite is plotted against the diameter of the whole shell, or the whorl-thickness plotted against the whorl-height, the curves obtained are very commonly straight lines for the greater part of their courses.(2) If, as is usually the case, these lines do not pass through the origin, the formula for the ammonite spiral is of the form r + c = eβθ and not r = eβθ.(3) If the straight lines do not pass through the origin, it is useless to express one dimension as a percentage of the other and compare these percentages in different shells.(4) There is no way of foreseeing, before the measurements are made, whether the dimensions of a species will plot accurately on a single curve or whether they will show a considerable amount of scatter. If, however, they do fall accurately on a single curve, this fact is an argument for the validity of the species, and the curve is a useful aid in the identification of other specimens.

Kinematic Analysis of Rectangular Path Generating Adjustable Four-Bar Linkage

2014 ◽  
Vol 592-594 ◽  
pp. 1094-1098 ◽  
Author(s):  
G. Ganesan ◽  
M. Sekar
Keyword(s):  
Angular Velocity ◽  
Kinematic Analysis ◽  
Kinematic Parameters ◽  
Transmission Angle ◽  
Adjustable Mechanism ◽  
Velocity Variations ◽  
Four Bar Linkage

This paper focuses on the kinematic analysis of rectangular path generating adjustable four-bar crank rocker linkage. One of the ground pivots of rocker side of the adjustable mechanism is subjected to continuous adjustment while the crank arm is given uniform angular velocity. Variations of coupler and rocker position, velocity and acceleration are computed for continuously changing phases of the adjustable four bar linkage. These kinematic parameters are compared with non-adjustable four-bar mechanism. Effect of the continuous adjustment on transmission angle and torque ratio are presented. The above procedures are implemented successfully in MATLAB environment and graphical results are presented.

Design of a Three-Degree-of-Freedom Robotic Worktable With Prescribed Entire-Motion Characteristics

1986 ◽  
Vol 108 (3) ◽  
pp. 373-380
Author(s):  
Jau-Jung Chen ◽  
A. DiBenedetto ◽  
E. Pennestri ◽  
Ting W. Lee
Keyword(s):  
Degrees Of Freedom ◽  
Design Parameters ◽  
Primary Interest ◽  
Analysis And Design ◽  
Flight Simulators ◽  
Transmission Angle ◽  
Rotational Degrees Of Freedom ◽  
Motion Characteristics ◽  
Three Degree Of Freedom ◽  
Four Bar Linkage

This paper presents the analysis and design of a robotic worktable with a structure based on two platforms connected by three four-bar linkages. The worktable has three rotational degrees-of-freedom and is designed for special motion generators, such as gyroscope calibration instruments and flight simulators. Of primary interest is the influence of the characteristics of a single four-bar linkage on the entire-motion characteristics of the worktable. This involves an investigation of the effects of limit positions, rotatability of cranks, transmission-angle characteristics and the variation of design parameters of the four-bar linkages on the characteristics of the compound platform mechanism. Based on the analytical results, some physical insights are interpreted and general guidelines can be drawn on the design of this robotic worktable with prescribed motion characteristics.

Planar Linkage Synthesis for Function Generation Using Poles and Rotation Angles

2015 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Analytical Solution ◽  
Graphical Solution ◽  
Function Generation ◽  
Design Time ◽  
Input And Output ◽  
Linkage Design ◽  
Pass Through ◽  
Solution Mechanism ◽  
Four Bar Linkage ◽  
Selection Of

Function Generation is a long standing linkage design problem. It is possible to design a planar four bar linkage whose input and output links will pass through seven coordinated positions. This paper discloses the first graphical solution to this problem. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. This approach enables the designer to explore the range of possible solutions when fewer than seven positions are specified by dragging a fixed or moving pivot in the plane. The selection of free choices is made at the end of the process and the complete mechanism is visible when the choices are made. The constraints only need to be made once which eliminates the repetitive construction required by previous methods to consider multiple pivot locations. Since it is so easy to consider multiple pivot locations and the solution mechanism is visible, the required design time is greatly reduced. A corresponding analytical solution is also developed and solved based on the same constraints. This is a new analytical solution and is defined by a system of 20 nonlinear equations with 20 unknowns.

The Algebraic Classification of the Image Curves of Spherical Four-Bar Motion

1991 ◽  
Vol 113 (3) ◽  
pp. 227-231 ◽  
Author(s):  
Q. Jeffrey Ge ◽  
J. M. McCarthy
Keyword(s):  
Three Dimensional ◽  
Eigenvalues And Eigenvectors ◽  
Euler Parameters ◽  
Rotational Displacement ◽  
Algebraic Classification ◽  
Generalized Eigenvalues ◽  
Pass Through ◽  
Dimensional Projective Space ◽  
Four Bar Linkage

A rotational displacement of the coupler of a spherical four-bar linkage can be mapped to a point with coordinates given by the Euler parameters of the rotation. The set of rotational movements available to the coupler defines a curve in this three-dimensional projective space (four homogeneous coordinates). In this paper, we determine the generalized eigenvalues and eigenvectors of the pencil of quadrics that pass through this curve and examine their properties. The result is an algebraic classification of the image curves that parallels the well-known classification of spherical four-linkages. In addition, we find that the characteristic polynomial of the system yields Grashof’s criterion for the rotatability of cranks.

scholarly journals Four-Bar Linkage Synthesis for a Combination of Motion and Path-Point Generation

2013 ◽  
Author(s):  
Yuxuan Tong ◽  
David H. Myszka ◽  
Andrew P. Murray
Keyword(s):  
Numerical Solutions ◽  
Kinematic Chain ◽  
Object Motion ◽  
Synthesis Methods ◽  
Motion Generation ◽  
Range Of Movement ◽  
Pick And Place ◽  
Four Bar Linkage ◽  
Path Point ◽  
Linkage Synthesis

This paper develops techniques that address the design of planar four-bar linkages for tasks common to pick-and-place devices, used in assembly and manufacturing operations. Pick-and-place tasks often require the exact position and orientation of an object (motion generation) at the end points of the task. Within the range of movement, the motion restrictions are less rigorous with only the position of the object (path-point generation) being specified to avoid obstacles. Established synthesis theory has been developed for either motion generation or path-point generation tasks. This paper presents four-bar linkage synthesis methods for tasks that include a combination of motion and path requirements. This synthesis challenge is addressed via two approaches: Geometric Constraint Programming (GCP) and numerical solutions to synthesis equations. Using GCP, a step-by-step methodology has been established to find solutions to these synthesis challenges. Using numerical methods, techniques are presented to formulate kinematic chain constraint equations and solve for appropriate link lengths and pivot locations. Examples of various combinations of motion and path-point generation are presented.

Design of Drag-Link Mechanisms With Optimum Transmission Angle

1983 ◽  
Vol 105 (2) ◽  
pp. 254-258 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Extreme Values ◽  
Angular Displacement ◽  
Output Link ◽  
Link Length ◽  
Design Charts ◽  
Link Mechanism ◽  
Transmission Angle ◽  
New Criterion ◽  
Four Bar Linkage ◽  
Drag Link

In this paper, a new criterion for the design of a drag-link mechanism with optimum transmission angle is established. The transmission angle, the angle between the coupler link and output link of a four-bar linkage, is considered to be optimized when its extreme values deviate equally from 90 deg. Based on this criterion, design equations and design charts are developed. It is shown that the optimum drag-link mechanism is a turning-block linkage. It is also shown that to displace the drag-link mechanism with optimum transmission angle from its minimum lag to its maximum lag position, the input link must always rotate 180 deg and the corresponding angular displacement of the output link depends only on the link-length ratio of the output link to the fixed-link.

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