Synthesis of Planar Mechanisms for Coupler Tangent-Line Envelope Generation: An Alternative to Coupler Point-Path Generation

1988 ◽  
Vol 110 (2) ◽  
pp. 122-129 ◽  
Author(s):  
Dev P. Sathyadev ◽  
A. H. Soni
Keyword(s):  
Plane Curve ◽  
Tangent Line ◽  
Path Generation ◽  
Planar Mechanisms ◽  
Novel Approach ◽  
Rigid Body Displacement ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
The Given

A synthesis procedure is developed to envelope a given plane curve by a tangent line carried by the coupler plane of a planar four-bar linkage. The synthesis procedure is based on a modification of the planar rigid-body displacement matrix developed by Suh [1]. The approach is based on considering a given curve as the envelope of a moving tangent line and synthesizing mechanisms to envelope the given curve. This is a novel approach in mechanism design and adds a new dimension to the path-generation problem of mechanism synthesis. The foregoing procedure is also extended to synthesize eight-link mechanisms to simultaneously coordinate the motion of two tangent lines. In addition to finite position synthesis, both infinitesimal and mixed position synthesis are considered.

Synthesis of Compliant Mechanisms With Specified Equilibrium Positions

2005 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Compliant Mechanisms ◽  
Equilibrium Constraints ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Form Design ◽  
Design Requirements ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Sine And Cosine Functions

This paper presents a synthesis procedure for a compliant four-bar linkage with three specified equilibrium configurations. The finite position synthesis equations are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Solutions to these design equations were computed using a polynomial homotopy solver. In order to provide a design specification, we first compute the six equilibrium configurations of a known compliant four-bar mechanism. We use these results as design requirements to synthesize a compliant four-bar. The solver obtained eight real solutions which we refined using a Newton-Raphson technique. A numerical example is provided to verify the design methodology.

scholarly journals The Synthesis of Planar Four-Bar Linkage for Mixed Motion and Function Generation

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3504
Author(s):  
Bin Wang ◽  
Xianchen Du ◽  
Jianzhong Ding ◽  
Yang Dong ◽  
Chunjie Wang ◽  
...  
Keyword(s):  
Complex Plane ◽  
Path Generation ◽  
Motion Generation ◽  
Numerical Examples ◽  
Function Generation ◽  
Long Time ◽  
Synthesis Procedure ◽  
And Function ◽  
Four Bar Linkage ◽  
Numerical Synthesis

The synthesis of four-bar linkage has been extensively researched, but for a long time, the problem of motion generation, path generation, and function generation have been studied separately, and their integration has not drawn much attention. This paper presents a numerical synthesis procedure for four-bar linkage that combines motion generation and function generation. The procedure is divided into two categories which are named as dependent combination and independent combination. Five feasible cases for dependent combination and two feasible cases for independent combination are analyzed. For each of feasible combinations, fully constrained vector loop equations of four-bar linkage are formulated in a complex plane. We present numerical examples to illustrate the synthesis procedure and determine the defect-free four-bar linkages.

Synthesis and Balancing of Cam-Modulated Linkages

1987 ◽  
Author(s):  
P. Pracht ◽  
P. Minotti ◽  
M. Dahan
Keyword(s):  
Systematic Approach ◽  
Kinematic Chain ◽  
Path Generation ◽  
Industrial Manipulator ◽  
High Speeds ◽  
Structural Error ◽  
Mass Balancing ◽  
Four Bar Linkage ◽  
Robotic Applications ◽  
Class Of Functions

Abstract Linkages are inherently light, inexpensive, strong, adaptable to high speeds and have little friction. Moreover the class of functions suitable for linkage representation is large. For all these reasons numerous recent works deal with the problem of design mechanisms for robotic applications, but very often in terms of components such as gripper, transmission, balancing. We investigate a new application for linkages, using them to design industrial manipulator. The selected mechanism for this application is a four bar linkage with an adjustable lengh for exact path generation. This adjustment is performed by a track or cam which is substituted to a bar. By this mean, we define a cam-modulated linkage which possess superior accuracy potential and is capable of accomodating of industrial design restrictions. Such a kinematic chain is free from structural error for path generation and the presence of the track introduces the flexibility and versality in the usefull four bar chain. The synthesis technique of cam modulated linkage utilizes loop closure equations, envelop theory to find the centerline and the profile of the track. These techniques provide a systematic approach to the design of mechanism for path generation when extreme accuracy is required. In order to complete an contribution, we take in consideration the static balancing of the synthesized manipulator. To achieve static mass balancing we use the potential energy storage capabilities of linear springs, and integrated it with the non-linear motion of mechanism to provide an exact value of the desired counter loading functions. Examples are worked to demonstrate applications of these procedures and to illustrate the industrial potential of spring balancing and cam-modulated linkage.

Five Position Synthesis of a Slider-Crank Function Generator

2011 ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Full Range ◽  
Linear Actuator ◽  
Tolerance Zone ◽  
Function Generator ◽  
Front End ◽  
Input And Output ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Branching Solutions

In this paper, we present a synthesis procedure for the coupler link of a planar slider-crank linkage in order to coordinate input by a linear actuator with the rotation of an output crank. This problem can be formulated in a manner similar to the synthesis of a five position RR coupler link. It is well-known that the resulting equations can produce branching solutions that are not useful. This is addressed by introducing tolerances for the input and output values of the specified task function. The proposed synthesis procedure is then executed on two examples. In the first example, a survey of solutions for tolerance zones of increasing size is conducted. In this example we find that a tolerance zone of 5% of the desired full range results in a number of useful task functions and usable slider-crank function generators. To demonstrate the use of these results, we present an example design for the actuator of the shovel of a front-end loader.

Eliminating Structural Error in Real-Time Adjustable Four-Bar Path Generators Using Iterative Learning Control

2004 ◽  
Author(s):  
Hong-Jen Chen ◽  
Richard W. Longman ◽  
Meng-Sang Chew
Keyword(s):  
Control Systems ◽  
Real Time ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Path Generation ◽  
Structural Error ◽  
Four Bar Linkage

Fundamental concepts of Iterative Learning Control (ILC) are applied to path generating problems in mechanisms. As an illustration to such class of problems, an adjustable four-bar linkage is used. The coupler point of a four-bar traces a coupler curve that will in general deviate from the desired coupler path. Except at the precision points, the coupler curve will exhibit some structural error, which is the deviation from the specified curve. The structural error will repeat itself every cycle at exactly the same points over the range of interest. Since ILC is a methodology that was developed to handle similar repetitive errors in control systems, it is believed that it will be well served to apply it to this class of problems. Results show that ILC can be simple to implement, and it is found to be very well suited for such path generation problems.

scholarly journals Dynamic approach to minimize overhead and response time in scheduling periodic real-time tasks

2021 ◽  
Vol 8 (4) ◽  
pp. 75-81
Author(s):  
Ahmed A. Alsheikhy ◽  
Keyword(s):  
Response Time ◽  
Real Time ◽  
Periodic Tasks ◽  
Dynamic Priority ◽  
New Novel ◽  
Context Switching ◽  
Novel Approach ◽  
Efficiency And Effectiveness ◽  
Time Systems ◽  
The Given

In real-time systems, a task or a set of tasks needs to be executed and completed successfully within a predefined time. Those systems require a scheduling technique or a set of scheduling methods to distribute the given task or the set of tasks among different processors or on a processor. In this paper, a new novel scheduling approach to minimize the overhead from context switching between several periodic tasks is presented. This method speeds up a required response time while ensuring that all tasks meet their deadline times and there is no deadline miss occurred. It is a dynamic-priority technique that works either on a uniprocessor or several processors. In particular, it is proposed to be applied on multiprocessor environments since many applications run on several processors. Various examples are presented within this paper to demonstrate its optimality and efficiency. In addition, several comparison experiments with an earlier version of this approach were performed to demonstrate its efficiency and effectiveness too. Those experiments showed that this novel approach sped up the execution time from 15% to nearly around 46%. In addition, it proved that it reduced the number of a context switch between tasks from 12% to around 50% as shown from simulation tests. Furthermore, this approach delivered all tasks/jobs successfully and ensured there was no deadline miss happened.

scholarly journals Optimal synthesis of a four-bar linkage by method of controlled deviation

2004 ◽  
Vol 31 (3-4) ◽  
pp. 265-280 ◽  
Author(s):  
Radovan Bulatovic ◽  
Stevan Djordjevic
Keyword(s):  
Objective Function ◽  
Optimal Synthesis ◽  
Straight Line ◽  
Individual Comparison ◽  
Four Bar Linkage ◽  
The Given ◽  
Initial Selection ◽  
Selection Of ◽  
Process Calculation ◽  
Made In

This paper considers optimal synthesis of a four-bar linkage by method of controlled deviations. The advantage of this approximate method is that it allows control of motion of the coupler in the four-bar linkage so that the path of the coupler is in the prescribed environment around the given path on the segment observed. The Hooke-Jeeves?s optimization algorithm has been used in the optimization process. Calculation expressions are not used as the method of direct searching, i.e. individual comparison of the calculated value of the objective function is made in each iteration and the moving is done in the direction of decreasing the value of the objective function. This algorithm does not depend on the initial selection of the projected variables. All this is illustrated on an example of synthesis of a four-bar linkage whose coupler point traces a straight line, i.e. passes through sixteen prescribed points lying on one straight line. .

Designing Planar Mechanisms Using a Bi-Invariant Metric in the Image Space of SO (3)

1994 ◽  
Author(s):  
Pierre Larochelle ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Numerical Results ◽  
Image Space ◽  
Dimensional Synthesis ◽  
Invariant Metric ◽  
Planar Mechanisms ◽  
Position And Orientation ◽  
Position Synthesis

Abstract In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of SO(3). The optimal linkage is obtained by minimizing this distance over all of the n goal positions. The paper proceeds as follows. First, we approximate planar rigid body displacements with spherical displacements and show that the error induced by such an approximation is of order 1/R2, where R is the radius of the approximating sphere. Second, we use a bi-invariant metric in the image space of spherical displacements to synthesize an optimal spherical 4R mechanism. Finally, we identify the planar 4R mechanism associated with the optimal spherical solution. The result is a planar 4R mechanism that has been optimized for n position rigid body guidance using an approximate bi-invariant metric with an error dependent only upon the radius of the approximating sphere. Numerical results for ten position synthesis of a planar 4R mechanism are presented.

Mechanisms of the Ancient Greek Theater

1992 ◽  
Author(s):  
Andrew D. Dimarogonas
Keyword(s):  
The Political ◽  
Path Generation ◽  
Space Travel ◽  
Ancient Greek ◽  
Machine Element ◽  
Four Bar Linkage ◽  
Indirect Information ◽  
First Time ◽  
Latin Term

Abstract The word Mechanism is a derivative of the Greek word mechane (which meant machine, more precisely, machine element) meaning an assemblage of machines. While it was used for the first time by Homer in the Iliad to describe the political manipulation, it was used with its modern meaning first in Aeschylos times to describe the stage machine used to bring the gods or the heroes of the tragedy on stage, known with the Latin term Deus ex machina. At the same time, the word mechanopoios, meaning the machine maker or engineer, was introduced for the man who designed, built and operated the mechane. None of these machines, made of perishable materials, is extant. However, there are numerous references to such machines in extant tragedies or comedies and vase paintings from which they can be reconstructed: They were large mechanisms consisting of beams, wheels and ropes which could raise weights up-to one ton and, in some cases, move them back-and-forth violently to depict space travel, when the play demanded it. The vertical dimensions were over 4 m while the horizontal travel could be more than 8 m. They were well-balanced and they could be operated, with some exaggeration perhaps, by the finger of the engineer. There is indirect information about the timing of these mechanisms. During the loading and the motion there were specific lines of the chorus, from which we can infer the duration of the respective operation. The reconstructed mechane is a spatial three- or four-bar linkage designed for path generation.

Implementing Background Net with Knowware System for Personalized Keyword Support

2011 ◽  
Vol 2 (1) ◽  
pp. 77-90
Author(s):  
Yuan Chen ◽  
Liya Ding ◽  
Sio-Long Lo ◽  
Dickson K.W. Chiu
Keyword(s):  
Search Engine ◽  
Undirected Graph ◽  
Target System ◽  
Component Reuse ◽  
Personal Preference ◽  
Development Tool ◽  
Novel Approach ◽  
The Given ◽  
Contextual Association

This article proposes a novel approach that combines user’s instant requirement described in keywords with her or his long-term knowledge background to better serve article selection based on personal preference. The knowledge background is represented as a weighted undirected graph called background net that captures the contextual association of words that appear in the articles recommended by the user through incremental learning. With a background net of user constructed, a keyword from the user is personalized to a fuzzy set that represents contextual association of the given keyword to other words involved in the user’s background net. An article evaluation with personal preference can be achieved by evaluating similarity between personalized keyword set based on user’s background net and a candidate article. The proposed approach makes it possible to construct a search engine optimizer running on the top of search engines to adjust search results, and offer the potential to be integrated with existing search engine techniques to achieve better performance. The target system of personalized article selection can be automatically constructed using Knowware System which is a development tool of KBS for convenient modeling and component reuse.

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