Solution Region Synthesis Methodology of Spatial 5-SS Linkages for Six Given Positions

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Jianyou Han ◽  
Guangzhen Cui
Keyword(s):  
Feasible Solution ◽  
Limited Range ◽  
The Other ◽  
Dimensional Synthesis ◽  
Link Length ◽  
End Effector ◽  
Solution Region ◽  
Fixed Solution ◽  
Synthesis Methodology

This paper presents a solution region synthesis methodology to perform the dimensional synthesis of spatial 5-spherical–spherical (SS) linkages for six specified positions of the end-effector. Dimensional synthesis equations for an SS link are formulated. After solving the synthesis equations, the curves of moving and fixed joints can be obtained, and they are called moving and fixed solution curves, respectively. Each point on the curves represents an SS link. Considering the limited range of joints at the first position, we can obtain the feasible solution curves. The link length curves can be obtained based on the feasible solution curves. We determine three SS links by selecting three points meeting the requirements on link length curves. Then, the solution region is built by sorting and adding feasible solution curves and projecting the feasible solution curves on the line. The feasible solution region can be obtained by eliminating defective linkages and linkages that fail to meet the other requirements from the solution region. The validity of the formulas and applicability of the proposed approach is illustrated by example.

Solution Region Synthesis Method for Six Positions Synthesis of 5-SS Spatial Linkage

2016 ◽  
Author(s):  
Jianyou Han ◽  
Guangzhen Cui ◽  
Junjie Hu
Keyword(s):  
Systematic Approach ◽  
Synthesis Method ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Region Method ◽  
Solution Region ◽  
The One

This paper presents a systematic approach to perform the dimensional synthesis of spatial 5-SS (spherical-spherical) link-ages for six specified positions of the end-effector. The dimensional synthesis equations for a SS link are formulated and solved. We synthesize five SS links to connect the base and end-effector, and then obtain the one-degree-of-freedom spatial 5-SS linkage, which can move through six specified positions. We use the solution region method to build the planar solution region expressing the linkages, due to there are infinite linkages for six positions synthesis. It is convenient to select the linkages from the solution region for designers. The applicability of the proposed approach is illustrated by the example.

On the Solution of Eight-Precision-Point Path Synthesis of Planar Four-Bar Mechanisms Based on the Solution Region Methodology

2019 ◽  
Vol 11 (6) ◽  
Author(s):  
Jianyou Han ◽  
Wupeng Liu
Keyword(s):  
Computer Program ◽  
Infinite Number ◽  
Feasible Solution ◽  
Path Generation ◽  
Characteristic Curves ◽  
Different Types ◽  
Design Requirements ◽  
Solution Region ◽  
Synthesis Methodology ◽  
Path Synthesis

Abstract In this paper, the solution region synthesis methodology (abbreviated as SRSM below) for the eight-precision-point path synthesis of planar four-bar mechanisms is presented. The so-called solution region synthesis methodology represents an infinite number of mechanism solutions in a plane, and the solution region is the area where the mechanism solutions are distributed in the plane. The x-coordinate and the y-coordinate of the plane are both taken as the concerned parameters of mechanisms. Furthermore, characteristic curves of mechanisms can be expressed in the plane. In addition, a defect judgment method is proposed, which can be realized in the computer program. The defective solutions can be eliminated efficiently, and the solutions without defects are obtained using the proposed method. After considering and imposing additional design requirements, the linkages of different types and different curve shapes are classified in the solution region. Finally, taking the path generation for eight points as the example, the methodology of establishing the solution region and the feasible solution region are presented, and the synthesis results are illustrated.

scholarly journals Solution Region Synthesis Methodology of RCCC Linkages for Four Poses

2018 ◽  
Vol 9 (2) ◽  
pp. 297-305 ◽  
Author(s):  
Jianyou Han ◽  
Yang Cao
Keyword(s):  
Exact Solutions ◽  
Feasible Solution ◽  
Optimization Method ◽  
Step Length ◽  
Coupling Condition ◽  
Revolute Joint ◽  
A Value ◽  
Cylindrical Joint ◽  
Solution Region ◽  
Synthesis Methodology

Abstract. This paper presents a synthesis methodology of RCCC linkages based on the solution region methodology, R denoting a revolute joint and C denoting a cylindrical joint. The RCCC linkage is usually synthesized via its two defining dyads, RC and CC. For the four poses problem, there are double infinite solutions of the CC dyad, but there is no solution for the RC dyad. However, if a condition is imposed that leads to a coupling of the two dyads, a maximum of four poses can be visited with the RCCC linkage. Unfortunately, until now, there is no methodology to synthesize the RCCC linkage for four given poses besides optimization method. According to the coupling condition above, infinite exact solutions of RCCC linkages can be obtained. For displaying these RCCC linkages, we first build a spherical 4R linkage solution region. Then solutions with circuit and branch defects can be eliminated on this solution region, so that the feasible solution region is obtained. An RCCC linkage can be obtained by using the prescribed spatial positions and selected a value on the feasible solution region. We take values on the feasible solution region by a certain step length and many exact solutions for RCCC linkages can be obtained. Finally we display these solutions on a map, this map is the solution region for RCCC linkages.

Solution region synthesis methodology of planar eight-bar linkage for four specified positions of a 4R chain

2020 ◽  
Vol 234 (24) ◽  
pp. 4813-4826
Author(s):  
Guangzhen Cui ◽  
Jianyou Han ◽  
Yanqiu Xiao ◽  
Caidong Wang
Keyword(s):  
Feasible Solution ◽  
Solution Curve ◽  
Defect Identification ◽  
Different Types ◽  
Practical Engineering ◽  
Solution Region ◽  
Synthesis Methodology ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

The solution region methodology for solving the problem of four-bar linkage synthesis with four specified positions was extended to solve the problem of eight-bar linkage synthesis. The processes to build solution regions for synthesizing different types of eight-bar linkages are described, and the methods of building solution regions are divided into five types. First, the synthesis equation is derived, and the curve expressed by the synthesis equation is called the solution curve. Second, the process to build the spatial solution regions from the solution curves is detailed, and a new defect identification method is developed for building the spatial feasible solution region, which is a set of linkage solutions meeting four positions and excluding defects. Finally, linkage solutions that do not meet practical engineering requirements are eliminated from the spatial feasible solution region to obtain the useful spatial solution region. The examples demonstrate the feasibility of the proposed method. The proposed synthesis methodology is simple and easy to program, and provides reference for four specified position synthesis of other multi-bar linkages.

A Generalized Performance Sensitivity Synthesis Methodology for Four-Bar Mechanisms

1992 ◽  
Author(s):  
Ming-Yih Lee ◽  
Arthur G. Erdman ◽  
Salaheddine Faik
Keyword(s):  
Solution Space ◽  
Design Solution ◽  
Link Length ◽  
Performance Sensitivity ◽  
Closed Chain ◽  
Synthesis Methodology ◽  
Position Synthesis ◽  
The Relationship ◽  
Accuracy Performance ◽  
Sensitivity Maps

Abstract A generalized accuracy performance synthesis methodology for planar closed chain mechanisms is proposed. The relationship between the sensitivity to variations of link lengths and the location of the moving pivots of four-link mechanisms is investigated for the particular objective of three and four position synthesis. In the three design positions case, sensitivity maps with isosensitivity curves plotted in the design solution space allow the designer to synthesize a planar mechanism with desired sensitivity value or to optimize sensitivity from a set of acceptable design solutions. In the case of four design positions, segments of the Burmester design curves that exhibit specified sensitivity to link length tolerance are identified. A performance sensitivity criterion is used as a convenient and a useful way of discriminating between many possible solutions to a given synthesis problem.

scholarly journals Special Issue on Reconfiguration Problems

Algorithms ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 187
Author(s):  
Faisal Abu-Khzam ◽  
Henning Fernau ◽  
Ryuhei Uehara
Keyword(s):  
Feasible Solution ◽  
Solution Space ◽  
The Other ◽  
Special Issue ◽  
Typical Application ◽  
Repair Work ◽  
One Step

The study of reconfiguration problems has grown into a field of its own. The basic idea is to consider the scenario of moving from one given (feasible) solution to another, maintaining feasibility for all intermediate solutions. The solution space is often represented by a “reconfiguration graph”, where vertices represent solutions to the problem in hand and an edge between two vertices means that one can be obtained from the other in one step. A typical application background would be for a reorganization or repair work that has to be done without interruption to the service that is provided.

scholarly journals Synthesis of Spatial RPRP Closed Linkages for a Given Screw System

2011 ◽  
Vol 3 (2) ◽  
Author(s):  
Alba Perez-Gracia
Keyword(s):  
Design Method ◽  
Parallel Robots ◽  
Synthesis Problem ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Serial Chain

The dimensional synthesis of spatial chains for a prescribed set of positions can be applied to the design of parallel robots by joining the solutions of each serial chain at the end-effector. This design method does not provide with the knowledge about the trajectory between task positions and, in some cases, may yield a system with negative mobility. These problems can be avoided for some overconstrained but movable linkages if the finite-screw system associated with the motion of the linkage is known. The finite-screw system defining the motion of the robot is generated by a set of screws, which can be related to the set of finite task positions traditionally used in the synthesis theory. The interest of this paper lies in presenting a method to define the whole workspace of the linkage as the input task for the exact dimensional synthesis problem. This method is applied to the spatial RPRP closed linkage, for which one solution exists.

Kinematic Synthesis of Spatial R-R Dyads for Path Following Revisited Using the Rotation Matrix Approach

1999 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Linear System ◽  
Path Following ◽  
Rotation Matrix ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Serial Chain ◽  
Systematic Development ◽  
Matrix Vector ◽  
Selection Of

Abstract We revisit the dimensional synthesis of a spatial two-link, two revolute-jointed serial chain for path following applications, focussing on the systematic development of the design equations and their analytic solution for the three precision point synthesis problem. The kinematic design equations are obtained from the equations of loop-closure for end-effector position in rotation-matrix/vector form at the three precision points. These design equations form a rank-deficient linear system in the link-vector components. The nullspace of the rank deficient linear system is then deduced analytically and interpreted geometrically. Tools from linear algebra are applied to systematically create the auxiliary conditions required for synthesis and to verify consistency. An analytic procedure for obtaining the link-vector components is then developed after a suitable selection of free choices. Optimization over the free choices is possible to permit the matching of additional criteria and explored further. Examples of the design of optimal two-link coupled spatial R-R dyads are presented where the end-effector interpolates three positions exactly and closely approximates an entire desired path.

The diffusion of load from a stiffener into an infinite elastic sheet

1957 ◽  
Vol 239 (1218) ◽  
pp. 296-310 ◽  
Keyword(s):  
Mixed Boundary ◽  
Functional Differential Equations ◽  
Mixed Boundary Conditions ◽  
Limited Range ◽  
The Other ◽  
Shear Stresses ◽  
Variable Theory ◽  
Elastic Sheet ◽  
Complex Variable Theory ◽  
In Series

The use of complex variable theory to express problems in generalized plane stress is well known, but methods of finding particular solutions are available for only a limited range of problems. This paper and its sequel will develop a new technique, reducing certain problems with mixed boundary conditions to second order functional differential equations, whose solutions can be found in series form. Exact solutions are given to three fundamental problems of the diffusion of load in an infinite two-dimensional elastic sheet to which a semi-infinite elastic stiffener is continuously attached throughout its length. The first problem has a load applied to the end of the stiffener, with its line of action along the stiffener and its reactions at infinity. In the other two problems the stiffener end is unloaded but a uniform tension is applied to the sheet at infinity, in one case parallel to the stiffener, in the other perpendicular to it. Expressions for the load in the stiffener and for the direct and shear stresses in the sheet are found and plotted in non-dimensional form.

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