The Spring-Connected Rigid Block Model Based Automatic Synthesis of Planar Linkage Mechanisms: Numerical Issues and Remedies

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Sang Jun Nam ◽  
Gang-Won Jang ◽  
Yoon Young Kim
Keyword(s):  
Closed Loop ◽  
Synthesis Method ◽  
Direct Application ◽  
Rigid Block ◽  
Block Model ◽  
Automatic Synthesis ◽  
Open Path ◽  
Synthesis Of Mechanisms ◽  
Input Motion ◽  
Linkage Synthesis

Because it is difficult to select in advance an appropriate linkage for converting an input motion to a desired output motion, a linkage synthesis method that does not require any baseline linkage would be preferred. To this end, an optimization-based linkage synthesis method that employs a spring-connected rigid block model has recently been suggested and applied for open-path problems. The objective of this study is to expand the method for the synthesis of more complex linkage mechanisms such as closed-loop linkages. Because the direct application of the method originally developed for open-path problems causes several numerical difficulties for closed-loop problems, an alternative optimization-based synthesis formulation is proposed in this investigation. The effectiveness of the suggested formulation is verified through several case studies including the synthesis of mechanisms generating closed paths.

Automatic Synthesis of a Planar Linkage With a Stiffness-Varying Spring Connected Rigid Block Model

2007 ◽  
Author(s):  
Sang Jun Nam ◽  
Gang-Won Jang ◽  
Jung Hun Park ◽  
Jin Sub Hun ◽  
Yong Sub Yi ◽  
...  
Keyword(s):  
Minimization Problem ◽  
Variable Stiffness ◽  
Synthesis Process ◽  
Rigid Block ◽  
Linkage Mechanism ◽  
Block Model ◽  
Revolute Joints ◽  
Gradient Based ◽  
Input Motion ◽  
Linkage Model

A linkage mechanism is a device to convert an input motion into a desired motion in a machine or a robot. The traditional linkage synthesis practice is depended on the experience and intuition of the skilled designer. This practice based on trial and error approach or only size/shape changes of already-available mechanism often results in improper design. This observation has motivated us to develop a so-called “automatic” design methodology that determines the linkage type and dimensions during synthesis process. The synthesis process can be formulated as a minimization problem. However, the process can be extremely difficult and time-consuming unless there is a single unified linkage model that represents any linkage mechanism without complicating kinematic analysis and allows the use of an efficient gradient-based optimizer. The main contribution of this research is to propose a unified planar linkage model consisting of rigid blocks connected by zero-length springs having real-valued variable stiffness. Stiffness controlling variables are the design variable of the minimization problem and a general planar linkage can be simulated by the spring-connected rigid block model if the stiffness value is chosen appropriately. This work shows how new idea works and verifies this new approach on the synthesis of the planar linkages consisting of links and revolute joints.

Automatic Structural Synthesis of the Whole Family of Planar 3-Degrees of Freedom Closed Loop Mechanisms

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
Huafeng Ding ◽  
Peng Huang ◽  
Jingfang Liu ◽  
Andrés Kecskeméthy
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Synthesis Method ◽  
Synthesis Process ◽  
Structural Synthesis ◽  
Planar Mechanisms ◽  
Systematic Method ◽  
Automatic Synthesis ◽  
Heavy Load ◽  
Structure Representation

Conception of the kinematic structures with better performance has been a challenging, yet pivotal issue, since the beginning of the design of mechanisms or robots. This paper proposes a systematic method to synthesize and classify automatically all the valid kinematic structures of planar 3-DOF closed loop mechanisms or robots. First, after the structure representation graphs of planar mechanisms or robots are addressed, the unique representation of both contracted graphs and topological graphs is proposed and used to detect isomorphism in the synthesis process. Then the valid atlas database of the contracted graphs for planar 3-DOF closed loop mechanisms or robots up to 16-link is built. Based on the atlas database, an automatic synthesis method is proposed to synthesize all the kinematic structures of planar 3-DOF closed loop mechanisms or robots, and the complete atlas database with all the valid kinematic structures classified for planar 3-DOF closed loop mechanisms or robots up to 16-link is established. The creative design of 3-DOF heavy-load hydraulic robots is conducted to show the usefulness of the established atlas database.

Automatic Synthesis of a Planar Linkage Mechanism With Revolute Joints by Using Spring-Connected Rigid Block Models

2006 ◽  
Vol 129 (9) ◽  
pp. 930-940 ◽  
Author(s):  
Yoon Young Kim ◽  
Gang-Won Jang ◽  
Jung Hun Park ◽  
Jin Sub Hyun ◽  
Sang Jun Nam
Keyword(s):  
Minimization Problem ◽  
Synthesis Method ◽  
Synthesis Process ◽  
Rigid Block ◽  
Linkage Mechanism ◽  
Block Model ◽  
Mechanism Synthesis ◽  
Revolute Joints ◽  
Planar Linkage Mechanism ◽  
Linkage Model

In traditional linkage design practice, a designer first decides the specific linkage type, such as a four- or six-bar linkage, and then varies the joint locations and link lengths until the designer finds the desired linkage. The objective of this research is to establish an automatic mechanism synthesis method that determines the linkage type and dimensions during the synthesis process. The synthesis process can be formulated as a minimization problem. However, the process can be extremely difficult and time-consuming unless there is a single unified linkage model that represents any linkage mechanism without complicating kinematic analysis and allows the use of an efficient gradient-based optimizer. The main contribution of this investigation is to propose a unified planar linkage model consisting of rigid blocks connected by zero-length springs having real-valued variable stiffness. Stiffness controlling variables are the design variable of the minimization problem and a general planar linkage can be simulated by the spring-connected rigid block model if the stiffness value is chosen appropriately. Though mechanisms involving only revolute joints are investigated and the solved problems are relatively simple, the notion of the block model and the synthesis formulation in real variables are expected to give a different perspective on mechanism synthesis.

A Simple Synthesis Method for Spherical 4R Linkages Reaching Four Positions

2011 ◽  
Vol 199-200 ◽  
pp. 1236-1239 ◽  
Author(s):  
Tong Yang ◽  
Jian You Han ◽  
Lai Rong Yin
Keyword(s):  
Matrix Method ◽  
Synthesis Method ◽  
Simple Synthesis ◽  
Simple Derivation ◽  
Derivation Method ◽  
Curve Equation ◽  
Linkage Synthesis

For spherical 4R linkage synthesis reaching four specified task positions, we introduce a simple derivation method of spherical Burmester curve equation by employing a displacement matrix method. Then we presented a method to calculate the coordinates of circle and center points, so the spherical Burmester curves can be drawn by the software developed.

Simultaneous Shape and Topology Optimization of Planar Linkage Mechanisms Based on the Spring-Connected Rigid Block Model

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Jeonghan Yu ◽  
Sang Min Han ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Simultaneous Optimization ◽  
Optimization Process ◽  
Rigid Block ◽  
Low Resolution ◽  
Block Model ◽  
Shape And Topology Optimization ◽  
Fixed Grid ◽  
Computation Efficiency ◽  
And Topology

Abstract Using the topology optimization can be an effective means of synthesizing planar rigid-body linkage mechanisms to generate desired motion, as it does not require a baseline mechanism for a specific topology. While most earlier studies were mainly concerned with the formulation and implementation of topology optimization-based synthesis in a fixed grid, this study aims to realize the simultaneous shape and topology optimization of planar linkage mechanisms using a low-resolution spring-connected rigid block model. Here, we demonstrate the effectiveness of simultaneous optimization over a higher-resolution fixed-grid rigid block-based topology optimization process. When shape optimization to change the block shapes is combined with topology optimization to synthesize the mechanism, the use of low-resolution discretized models improves the computation efficiency considerably and helps to yield compact mechanisms with less complexity, making them more amenable to fabrication. After verifying the effectiveness of the simultaneous shape and topology optimization process with several benchmark problems, we apply the method to synthesize a mechanism which guides a planar version of a human's gait trajectory.

Method for the Creation of a Six Bar Linkage to Simultaneously Carry Two Rigid Bodies Through Four Coordinated Positions

2012 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Synthesis Method ◽  
Rigid Bodies ◽  
Type Synthesis ◽  
Linkage Mechanism ◽  
Center Point ◽  
Seat Cushion ◽  
The Creation ◽  
Linkage Synthesis

A method for the creation of a six bar linkage with two ground pivots to simultaneously carry two rigid bodies through four coordinated positions was invented and is described and illustrated herein. Type synthesis was used to identify possible linkage classes and specific types of possible six bar linkages. A linkage synthesis method which superimposes three Burmester center point curves to create a six bar linkage mechanism with two ground pivots, to carry two coupled rigid bodies simultaneously through four specified, coordinated positions was developed and is demonstrated. An extension of the method to carry two non-coupled rigid bodies through four positions is indicated. This method was invented in the process of developing a 2nd row automotive truck seat, which is used as an example to illustrate the procedure. A six bar linkage which carries an automotive truck seat back and seat cushion through four coordinated positions is shown.

scholarly journals Tolerance Synthesis of Mechanisms: A Robust Design Approach

2003 ◽  
Author(s):  
Ste´phane Caro ◽  
Fouad Bennis ◽  
Philippe Wenger
Keyword(s):  
Robust Design ◽  
Optimization Problem ◽  
Synthesis Method ◽  
Upper And Lower Bounds ◽  
Design Parameters ◽  
Design Problems ◽  
Tolerance Synthesis ◽  
Design Variables ◽  
Synthesis Of Mechanisms ◽  
Serial Positioning

The paper aims at dimensioning a mechanism in order to make it robust, and synthesizing its dimensional tolerances. The design of a mechanism is supposed to be robust when its performance is as little as sensitive as possible to variations. First, a distinction is made between three sets to formulate a robust design problem; (i) the set of Design Variables (DV) whose nominal values can be selected between a range of upper and lower bounds, they are controllable; (ii) the set of Design Parameters (DP) that cannot be adjusted by the designer, they are uncontrollable; (iii) the set of performance functions. DV are however under uncontrollable variations although their nominal value can be adjusted. Moreover, two methods are described to solve robust design problems. The first method is explicit and solves problems that aim at minimizing variations in performance. The second method, an optimization problem, aims at optimizing the performance and minimizing its variations, but only when the ranges of variations in DV and DP are known. Besides, we define and compare some robustness indices. From the explicit method, we develop a new tolerance synthesis method. Finally, three examples are included to illustrate these methods: a damper, a two-dof and a three-dof serial positioning manipulator.

Dimensional Synthesis of Open Path Generator of Four-Bar Mechanisms Using the Haar Wavelet

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Jianwei Sun ◽  
Wenrui Liu ◽  
Jinkui Chu
Keyword(s):  
Synthesis Method ◽  
Haar Wavelet ◽  
Characteristic Dimension ◽  
Dimensional Synthesis ◽  
Open Path ◽  
Actual Mechanism ◽  
Mechanism Parameter ◽  
Relationship Of ◽  
Parameter Values ◽  
Internal Relationship

This paper presents a synthesis method for the open path generation of a four-bar mechanism using the Haar wavelet. The synthesis method utilizes the wavelet transform and normalization to extract the wavelet output feature parameters (WOFP) of the open path. Analysis of the WOFP reveals a particular characteristic: for the same four-bar mechanism, not only do variations of the mechanism origin and angles and the proportional scaling of the linkage lengths have no influence on the details of the WOFP but the same holds true for the position of the point that generates the coupler curve. Based on this finding, a numerical atlas database comprises 192,596 groups of basic dimensional types was established and a method of matching recognition was proposed as well. According to the internal relationship of the wavelet characteristic dimension parameters (WCDP), the actual mechanism parameter values and position parameters of an objective four-bar mechanism can be calculated. Four examples are presented to verify the accuracy and practicality of the proposed theory.

scholarly journals Tolerance Synthesis of Mechanisms: A Robust Design Approach

2005 ◽  
Vol 127 (1) ◽  
pp. 86-94 ◽  
Author(s):  
Ste´phane Caro ◽  
Fouad Bennis ◽  
Philippe Wenger
Keyword(s):  
Robust Design ◽  
Design Method ◽  
Synthesis Method ◽  
Second Step ◽  
Serial Manipulators ◽  
Tolerance Synthesis ◽  
General Issue ◽  
Synthesis Of Mechanisms ◽  
Performance Error ◽  
Robust Design Method

This paper provides a new robust design method to dimension a mechanism and to synthesize its dimensional tolerances. The general issue is to find a robust mechanism for a given task, and to compute its optimal dimensional tolerances. For that purpose, the developed approach follows two consecutive steps, which are independent and complementary. First, the dimensions of the mechanism are computed by means of an appropriate robustness index, which is used to minimize the sensitivity of its performances to variations. These robust dimensions are obtained independently of the amount of variations, and tolerate globally the largest variations. Thus, knowing the acceptable performance error of the mechanism, the second step aims at computing the optimal dimensional tolerances of the mechanism by means of the new tolerance synthesis method. This method is used to find the best distribution of the error between the dimensions of the mechanism. Two serial manipulators are studied to illustrate the theory.

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