scholarly journals Degeneracy Study of the Forward Kinematics of Planar 3-RP̱R Parallel Manipulators

2006 ◽  
Vol 129 (12) ◽  
pp. 1265-1268 ◽  
Author(s):  
P. Wenger ◽  
D. Chablat ◽  
M. Zein
Keyword(s):  
Characteristic Polynomial ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Industrial Applications ◽  
Forward Kinematics ◽  
Double Root ◽  
Degree Polynomial ◽  
New Family ◽  
Planar Manipulators ◽  
First Time

This paper investigates two situations in which the forward kinematics of planar 3-RP̱R parallel manipulators degenerates. These situations have not been addressed before. The first degeneracy arises when the three input joint variables ρ1, ρ2, and ρ3 satisfy a certain relationship. This degeneracy yields a double root of the characteristic polynomial in t=tan(φ∕2), which could be erroneously interpreted as two coalesce assembly modes. However, unlike what arises in nondegenerate cases, this double root yields two sets of solutions for the position coordinates (x,y) of the platform. In the second situation, we show that the forward kinematics degenerates over the whole joint space if the base and platform triangles are congruent and the platform triangle is rotated by 180deg about one of its sides. For these “degenerate” manipulators, which are defined here for the first time, the forward kinematics is reduced to the solution of a third-degree polynomial and a quadratic in sequence. Such manipulators constitute, in turn, a new family of analytic planar manipulators that would be more suitable for industrial applications.

Performing Nonsingular Transitions Between Assembly Modes in Analytic Parallel Manipulators by Enclosing Quadruple Solutions

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Adrián Peidró ◽  
José María Marín ◽  
Arturo Gil ◽  
Óscar Reinoso
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Parallel Robots ◽  
Forward Kinematics ◽  
Characteristic Polynomials ◽  
Forward Kinematic ◽  
Three Degrees Of Freedom

This paper analyzes the multiplicity of the solutions to forward kinematics of two classes of analytic robots: 2RPR-PR robots with a passive leg and 3-RPR robots with nonsimilar flat platform and base. Since their characteristic polynomials cannot have more than two valid roots, one may think that triple solutions, and hence nonsingular transitions between different assembly modes, are impossible for them. However, the authors show that the forward kinematic problems of these robots always admit quadruple solutions and obtain analytically the loci of points of the joint space where these solutions occur. Then, it is shown that performing trajectories in the joint space that enclose these points can produce nonsingular transitions, demonstrating that it is possible to design simple analytic parallel robots with two and three degrees-of-freedom (DOF) and the ability to execute these transitions.

Maximally Regular T2R1-Type Parallel Manipulators With Bifurcated Spatial Motion

2011 ◽  
Vol 3 (1) ◽  
Author(s):  
Grigore Gogu
Keyword(s):  
Jacobian Matrix ◽  
Rotation Axis ◽  
Parallel Manipulators ◽  
Identity Matrix ◽  
Spatial Motion ◽  
Regular Solutions ◽  
New Family ◽  
Fixed Base ◽  
Moving Platform ◽  
First Time

This paper presents a new family of maximally regular T2R1-type parallel manipulators with bifurcated spatial motion. In each branch, the moving platform has two independent translations (T2) and one rotation (R1) driven by three actuators mounted on the fixed base. The rotation axis is situated in the plane of translation and can bifurcate in two orthogonal directions. This bifurcation occurs in a constraint singularity in which the connectivity between the moving and fixed platforms increases instantaneously, incurring no change in limb connectivity. The Jacobian matrix of the maximally regular solutions presented in this paper is a 3×3 identity matrix in the entire workspace of each branch. This paper presents for the first time a family of maximally regular T2R1-type parallel manipulators with bifurcated spatial motion of the moving platform along with solutions using uncoupled motions.

Analysis of kinematics and solution of active/constrained forces of asymmetric 2UPU+X parallel manipulators

2006 ◽  
Vol 220 (12) ◽  
pp. 1819-1830 ◽  
Author(s):  
Y Lu ◽  
B Hu
Keyword(s):  
Parallel Manipulators ◽  
Transformation Matrix ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
New Family ◽  
Kinematic Characteristics ◽  
Force Transformation

A new family of asymmetric 2UPU+X parallel manipulators is proposed. It includes two identical UPU-type active legs and one X-type active leg which may be various five-degree-of-freedom serial mechanisms. First, their common kinematic characteristics and singularity are analysed, and some common formulae for analysing inverse-forward kinematics, solving active/constrained force transformation matrix and active/constrained forces, are derived. Second, three asymmetric 3-UPU, 2UPU + SPR, and 2UPU + RPRU parallel manipulators are created, their kinematics and singularity are analysed, and their active/constrained forces are solved.

scholarly journals Interactions between an Associative Amphiphilic Block Polyelectrolyte and Surfactants in Water: Effect of Charge Type on Solution Properties and Aggregation

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1729
Author(s):  
Patrizio Raffa
Keyword(s):  
Surface Tension ◽  
Self Assembly ◽  
Interaction Model ◽  
Industrial Applications ◽  
Molecular Organization ◽  
Different Types ◽  
Solution Rheology ◽  
Interesting Class ◽  
First Time

The study of interactions between polyelectrolytes (PE) and surfactants is of great interest for both fundamental and applied research. These mixtures can represent, for example, models of self-assembly and molecular organization in biological systems, but they are also relevant in industrial applications. Amphiphilic block polyelectrolytes represent an interesting class of PE, but their interactions with surfactants have not been extensively explored so far, most studies being restricted to non-associating PE. In this work, interactions between an anionic amphiphilic triblock polyelectrolyte and different types of surfactants bearing respectively negative, positive and no charge, are investigated via surface tension and solution rheology measurements for the first time. It is evidenced that the surfactants have different effects on viscosity and surface tension, depending on their charge type. Micellization of the surfactant is affected by the presence of the polymer in all cases; shear viscosity of polymer solutions decreases in presence of the same charge or nonionic surfactants, while the opposite charge surfactant causes precipitation. This study highlights the importance of the charge type, and the role of the associating hydrophobic block in the PE structure, on the solution behavior of the mixtures. Moreover, a possible interaction model is proposed, based on the obtained data.

scholarly journals Phylogeny and character evolution in the Dacrymycetes, and systematics of Unilacrymaceae and Dacryonaemataceae fam. nov.

2020 ◽  
Vol 44 (1) ◽  
pp. 161-205
Author(s):  
J.C. Zamora ◽  
S. Ekman
Keyword(s):  
Species Level ◽  
Single Locus ◽  
Phenotypic Characters ◽  
New Family ◽  
Multispecies Coalescent ◽  
Morphometric Analyses ◽  
Methodological Approaches ◽  
First Time ◽  
A New Species ◽  
Multilocus Phylogeny

We present a multilocus phylogeny of the class Dacrymycetes, based on data from the 18S, ITS, 28S, RPB1, RPB2, TEF-1α, 12S, and ATP6 DNA regions, with c. 90 species including the types of most currently accepted genera. A variety of methodological approaches was used to infer phylogenetic relationships among the Dacrymycetes, from a supermatrix strategy using maximum likelihood and Bayesian inference on a concatenated dataset, to coalescence-based calculations, such as quartet-based summary methods of independent single-locus trees, and Bayesian integration of single-locus trees into a species tree under the multispecies coalescent. We evaluate for the first time the taxonomic usefulness of some cytological phenotypic characters, i.e., vacuolar contents (vacuolar bodies and lipid bodies), number of nuclei of recently discharged basidiospores, and pigments, with especial emphasis on carotenoids. These characters, along with several others traditionally used for the taxonomy of this group (basidium shape, presence and morphology of clamp connections, morphology of the terminal cells of cortical/marginal hyphae, presence and degree of ramification of the hyphidia), are mapped on the resulting phylogenies and their evolution through the class Dacrymycetes discussed. Our analyses reveal five lineages that putatively represent five different families, four of which are accepted and named. Three out of these four lineages correspond to previously circumscribed and published families (Cerinomycetaceae, Dacrymycetaceae, and Unilacrymaceae), and one is proposed as the new family Dacryonaemataceae. Provisionally, only a single order, Dacrymycetales, is accepted with in the class. Furthermore, the systematics of the two smallest families, Dacryonaemataceae and Unilacrymaceae, are investigated to the species level, using coalescence-based species delimitation on multilocus DNA data, and a detailed morphological study including morphometric analyses of the basidiospores. Three species are accepted in Dacryonaema, the type, Da. rufum, the newly combined Da. macnabbii (basionym Dacrymyces macnabbii), and a new species named Da. macrosporum. Two species are accepted in Unilacryma, the new U. bispora, and the type, U. unispora, the latter treated in a broad sense pending improved sampling across the Holarctic.

scholarly journals Regions of Feasible Point-to-Point Trajectories in the Cartesian Workspace of Fully-Parallel Manipulators

1999 ◽  
Author(s):  
Damien Chablat ◽  
Philippe Wenger
Keyword(s):  
Parallel Manipulator ◽  
Cartesian Product ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Inverse Kinematic ◽  
Connected Components ◽  
Feasible Point ◽  
Cartesian Space ◽  
Point Trajectories ◽  
Point To Point

Abstract The goal of this paper is to define the n-connected regions in the Cartesian workspace of fully-parallel manipulators, i.e. the maximal regions where it is possible to execute point-to-point motions. The manipulators considered in this study may have multiple direct and inverse kinematic solutions. The N-connected regions are characterized by projection, onto the Cartesian workspace, of the connected components of the reachable configuration space defined in the Cartesian product of the Cartesian space by the joint space. Generalized octree models are used for the construction of all spaces. This study is illustrated with a simple planar fully-parallel manipulator.

Wrench capabilities of planar parallel manipulators. Part I: Wrench polytopes and performance indices

Robotica ◽  
2008 ◽  
Vol 26 (6) ◽  
pp. 791-802 ◽  
Author(s):  
Flavio Firmani ◽  
Alp Zibil ◽  
Scott B. Nokleby ◽  
Ron P. Podhorodeski
Keyword(s):  
Parallel Manipulators ◽  
Joint Space ◽  
Linear Mapping ◽  
Redundant Manipulators ◽  
Task Space ◽  
Performance Indices ◽  
Study Case ◽  
And Performance ◽  
Planar Parallel Manipulators

SUMMARYThis paper is organized in two parts. In Part I, the wrench polytope concept is presented and wrench performance indices are introduced for planar parallel manipulators (PPMs). In Part II, the concept of wrench capabilities is extended to redundant manipulators and the wrench workspace of different PPMs is analyzed. The end-effector of a PPM is subject to the interaction of forces and moments. Wrench capabilities represent the maximum forces and moments that can be applied or sustained by the manipulator. The wrench capabilities of PPMs are determined by a linear mapping of the actuator output capabilities from the joint space to the task space. The analysis is based upon properly adjusting the actuator outputs to their extreme capabilities. The linear mapping results in a wrench polytope. It is shown that for non-redundant PPMs, one actuator output capability constrains the maximum wrench that can be applied (or sustained) with a plane in the wrench space yielding a facet of the polytope. Herein, the determination of wrench performance indices is presented without the expensive task of generating polytopes. Six study cases are presented and performance indices are derived for each study case.

LM9000 Passive Clearance Control (PCC)

2020 ◽  
Author(s):  
Simone Marchetti ◽  
Duccio Nappini ◽  
Roberto De Prosperis ◽  
Paolo Di Sisto
Keyword(s):  
Control System ◽  
Low Pressure ◽  
Industrial Applications ◽  
Flow Path ◽  
Operating Conditions ◽  
Low Pressure Turbine ◽  
Power Turbine ◽  
Extensive Test ◽  
First Time ◽  
Clearance Control

Abstract This paper describes the design of the Free Power Turbine (FPT) of the LM9000, in particularly the design of its Passive Clearance Control (PCC) system. The LM9000 is the aero-derivative version of the GE90-115B jet engine. Its core engine has many common parts with the GE90; what differs is the booster (low pressure compressor) and the lower pressure turbine (LPT). The booster of the LM9000 is without fan because the engine is not used to provide thrust but torque only, subsequently it has a new flow path [5]. The LPT has instead been replaced by an intermediate pressure turbine (IPT) and by the FPT. The IPT drives the booster, while the FPT is a free low-pressure turbine designed for both power generation and mechanical drive industrial applications, including LNG production plants. Due to its different application, the LM9000 FPT flow path differs sensibly from the GE90 LPT, however as the GE90 it is provided of a clearance control system that cools the casing in order to reduce its radial deflection. It is not the first time that a clearance control system has been used in industrial applications; in GE aero-derivative power turbines is already present in the LM6000 and LMS100. Design constraints, system complexity, high environment variability because the PCC is located outside the GT, harsh environments and long periods of usage still make the design of this component challenging. The design of the PCC has been supported by extensive heat transfer and mechanical simulations. Each PCC component has been addressed with a dedicated life calculation and all the blade and seal clearances have been estimated for all the operating conditions of the engine. Simulations have been validated by an extensive test campaign performed on the first engine.

Forward Displacement Analysis of Three New Classes of Analytic Spherical Parallel Manipulators

1998 ◽  
Author(s):  
Xian-Wen Kong
Keyword(s):  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Dual Solutions ◽  
Fourth Degree ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
The Third ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

Abstract The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

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