The Dimensional Synthesis of Planar Parallel Cable-Driven Mechanisms Through Convex Relaxations

2012 ◽  
Vol 4 (3) ◽  
Author(s):  
K. Azizian ◽  
P. Cardou
Keyword(s):  
Interval Analysis ◽  
Scaling Factor ◽  
Linear Program ◽  
Synthesis Problem ◽  
Feasibility Problem ◽  
Nonlinear Program ◽  
Convex Relaxations ◽  
Dimensional Synthesis ◽  
End Effector

The wrench-closure workspace (WCW) of parallel cable-driven mechanisms is the set of poses for which any wrench can be produced at the end-effector by a set of positive cable tensions. In this paper, we tackle the dimensional synthesis problem, namely, that of finding a geometry for a planar parallel cable-driven mechanism (PPCDM) whose WCW contains a prescribed workspace. To this end, we first recall a linear program to determine whether a given pose is inside or outside the WCW of a given PPCDM. The relaxation of this linear program over a box leads to a nonlinear feasibility problem that can only be satisfied when this box is completely inside the WCW. We extend this feasibility problem to find a PPCDM geometry whose WCW includes a given set of boxes. These boxes represent the prescribed workspace or an estimate thereof, which may be obtained through interval analysis. Finally, we introduce a nonlinear program through which the PPCDM geometry is changed while maximizing the scaling factor of the prescribed set of boxes. When the optimum scaling factor is greater or equal to one, the WCW of the resulting PPCDM contains the set of boxes.

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.

The Dimensional Synthesis of Spatial Cable-Driven Parallel Mechanisms

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
K. Azizian ◽  
P. Cardou
Keyword(s):  
Synthesis Method ◽  
Sufficient Condition ◽  
Nonlinear Program ◽  
Parallel Mechanisms ◽  
Dimensional Synthesis ◽  
End Effector ◽  
A Value ◽  
Null Value ◽  
Objective Value

This paper presents a method for the dimensional synthesis of fully constrained spatial cable-driven parallel mechanisms (CDPMs), namely, the problem of finding a geometry whose wrench-closure workspace (WCW) contains a prescribed workspace. The proposed method is an extension to spatial CDPMs of a synthesis method previously published by the authors for planar CDPMs. The WCW of CDPMs is the set of poses for which any wrench can be produced at the end-effector by non-negative cable tensions. A sufficient condition is introduced in order to verify whether a given six-dimensional box, i.e., a box covering point-positions and orientations, is fully inside the WCW of a given spatial CDPM. Then, a nonlinear program is formulated, whose optima represent CDPMs that can reach any point in a set of boxes prescribed by the designer. The objective value of this nonlinear program indicates how well the WCW of the resulting CDPM covers the prescribed box, a null value indicating that none of the WCW is covered and a value greater or equal to one indicating that the full prescribed workspace is covered.

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.

Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator

2003 ◽  
Vol 125 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Han Sung Kim ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Solution Methods ◽  
Moving Platform ◽  
At Will

This paper presents the design of spatial 3-RPS parallel manipulators from dimensional synthesis point of view. Since a spatial 3-RPS manipulator has only 3 degrees of freedom, its end effector cannot be positioned arbitrarily in space. It is shown that at most six positions and orientations of the moving platform can be prescribed at will and, given six prescribed positions, there are at most ten RPS chains that can be used to construct up to 120 manipulators. Further, solution methods for fewer than six prescribed positions are also described.

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.

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.

scholarly journals Collision-free workspace of parallel mechanisms based on an interval analysis approach

Robotica ◽  
2016 ◽  
Vol 35 (8) ◽  
pp. 1747-1760 ◽  
Author(s):  
MohammadHadi FarzanehKaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro
Keyword(s):  
Interval Analysis ◽  
Parallel Mechanism ◽  
Spherical Shape ◽  
Stewart Platform ◽  
Analysis Approach ◽  
Parallel Mechanisms ◽  
Planar Case ◽  
End Effector ◽  
Mechanical Interference

SUMMARYThis paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

Dimensional Synthesis of Planar Eight-Bar Linkages Based on a Parallel Robot With a Prismatic Base Joint

2013 ◽  
Author(s):  
Gim Song Soh ◽  
Fangtian Ying
Keyword(s):  
Rigid Body ◽  
Design Process ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Prismatic Joint ◽  
Serial Chain ◽  
Different Types

This paper details the dimensional synthesis for the rigid body guidance of planar eight-bar linkages that could be driven by a prismatic joint at its base. We show how two RR cranks can be added to a planar parallel robot formed by a PRR and 3R serial chain to guide its end-effector through a set of five task poses. This procedure is useful for designers who require the choice of ground pivot locations. The results are eight different types of one-degree of freedom planar eight-bar linkages. We demonstrate the design process with the design of a multifunctional wheelchair that could transform its structure between a self-propelled wheelchair and a walking guide.

A Fourier Descriptor Approach to Integrated Type and Dimensional Synthesis of Coupled Serial Mechanism for Motion Generation

2019 ◽  
Author(s):  
Hao Lv ◽  
Yuanfei Han ◽  
Xiangyun Li ◽  
Liuxian Zhu
Keyword(s):  
Fourier Descriptor ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Motion Generation ◽  
End Effector ◽  
Novel Approach ◽  
Descriptor Approach ◽  
Harmonic Components ◽  
The Given ◽  
Serial Mechanism

Abstract Coupled serial mechanism is a class of mechanisms that couple the relative rotation of successive links utilizing gears or cable-pulley systems. They can be used to generate complex end-effector trajectories or motions with a single actuator. With the employment of Fourier descriptors, a novel approach to integrate type synthesis and dimensional synthesis of such mechanisms is proposed in this paper. Through the Fourier analysis of two arbitrary trajectories from the given motion, the simplest trajectory that contains the least number of harmonic components is identified. Then, characteristic information of those harmonics such as their numbers, amplitudes and initial phases are used to determine the topology and dimensions of the corresponding coupled serial mechanism, thus effectively solving the motion synthesis problem of this type of mechanisms. Finally, three examples are given to demonstrate the validity of the proposed method.

scholarly journals Spatial Sharpening of KOMPSAT-3A MIR Images Using Optimal Scaling Factor

2020 ◽  
Vol 12 (22) ◽  
pp. 3772
Author(s):  
Kwan-Young Oh ◽  
Hyung-Sup Jung ◽  
Sung-Hwan Park ◽  
Kwang-Jae Lee
Keyword(s):  
Spectral Resolution ◽  
Visual Analysis ◽  
Spatial Information ◽  
Optimal Scaling ◽  
Scaling Factor ◽  
High Spectral Resolution ◽  
Qualitative Assessment ◽  
Dimensional Synthesis ◽  
The One ◽  
Comparison Of The Results

This paper present efficient methods for merging KOMPSAT-3A (Korea Multi-Purpose Satellite) medium wave Infrared (MIR) and panchromatic (PAN) images. Spatial sharpening techniques have been developed to create an image with both high spatial and high spectral resolution by combining the desired qualities of a PAN image with high spatial and low spectral resolution and an MS/MIR image with low spatial and high spectral resolution. The proposed methods can extract an optimal scaling factor, and uses the tactics of appropriately controlling the balance between the spatial and spectral resolutions. KOMPSAT-3A PAN and MIR images were used to test and evaluate the performance of the proposed methods. A qualitative assessment were performed using the image quality index (Q4), the cross correlation index (CC) and the relative global dimensional synthesis error (Spectral/Spatial ERGAS). These tests indicate that the proposed methods preserve the spectral and spatial characteristics of the original MIR and PAN images. Visual analysis reveals that the spectral and spatial information derived from the proposed methods were well retained in the test images. A comparison of the results of the proposed methods with those obtained from applying existing ones such as the Multi Sensor Fusion (MSF) technique or the Guide Filter Based Fusion (GF) show the efficiency of the new fusion process to be superior to the one of the others. The results showed a significant improvement in fusion capability for KOMPSAT-3A MIR imagery.

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