scholarly journals On Constraint Manifolds of Lorentz Sphere

2020 ◽  
Vol 28 (2) ◽  
pp. 15-34
Author(s):  
Buşra Aktaş ◽  
Olgun Durmaz ◽  
Hal˙t Gündoğan
Keyword(s):  
Lorentz Space ◽  
Structure Equation ◽  
Geometric Constructions ◽  
Open Chain ◽  
Constraint Manifold ◽  
Structure Equations ◽  
A Chain

AbstractThe expression of the structure equation of a mechanism is significant to present the last position of the mechanism. Moreover, in order to attain the constraint manifold of a chain, we need to constitute the structure equation. In this paper, we determine the structure equations and the constraint manifolds of a spherical open-chain in the Lorentz space. The structure equations of spherical open chain with reference to the causal character of the first link are obtained. Later, the constraint manifolds of the mechanism are determined by means of these equations. The geometric constructions corresponding to these manifolds are studied.

Approximate Motion Synthesis of Open and Closed Chains via Parametric Constraint Manifold Fitting: Preliminary Results

2003 ◽  
Author(s):  
Pierre M. Larochelle
Keyword(s):  
Optimization Techniques ◽  
Robotic Systems ◽  
Dimensional Synthesis ◽  
Motion Synthesis ◽  
Open Chain ◽  
Constraint Manifold ◽  
Synthesis Technique ◽  
Numerical Design ◽  
Design Case ◽  
Parametric Constraint

In this paper we present a novel dyad dimensional synthesis technique for approximate motion synthesis. The methodology utilizes an analytic representation of the dyad’s constraint manifold that is parameterized by its dimensional synthesis variables. Nonlinear optimization techniques are then employed to minimize the distance from the dyad’s constraint manifold to a finite number of desired locations of the workpiece. The result is an approximate motion dimensional synthesis technique that is applicable to planar, spherical, and spatial dyads. Here, we specifically address the planar RR, spherical RR and spatial CC dyads since these are often found in the kinematic structure of robotic systems and mechanisms. These dyads may be combined serially to form a complex open chain (e.g. a robot) or when connected back to the fixed link they may be joined so as to form one or more closed chains (e.g. a linkage, a parallel mechanism, or a platform). Finally, we present some initial numerical design case studies that demonstrate the utility of the synthesis technique.

scholarly journals Hexavalents in spermatocytes of Robertsonian heterozygotes between Mus m. domesticus 2n=26 from the Vulcano and Lipari Islands (Aeolian Archipelago, Italy)

2018 ◽  
Author(s):  
Soledad Berríos ◽  
Raúl Fernández-Donoso ◽  
Jesús Page ◽  
Eliana Ayarza ◽  
Ernesto Capanna ◽  
...  
Keyword(s):  
X Chromosome ◽  
Nuclear Architecture ◽  
Mus Musculus Domesticus ◽  
Open Chain ◽  
Telocentric Chromosome ◽  
Telocentric Chromosomes ◽  
Xy Bivalent ◽  
Chromosomal Changes ◽  
A Chain ◽  
Pachytene Spermatocytes

The size and shape of the chromosomes, as well as the chromosomal domains that compose them, are determinants in the distribution and interaction between the bivalents within the nucleus of spermatocytes in prophase I of meiosis. Thus the nuclear architecture characteristic of the karyotype of a species can be modified by chromosomal changes such as Rb chromosomes. In this study we analysed the meiotic prophase nuclear organization of the heterozygous spermatocytes from Mus musculus domesticus 2n=26, and the synaptic configuration of the hexavalent formed by the dependent Rb chromosomes Rbs 6.16, 16.10, 10.15, 15.17 and the telocentric chromosomes 6 and 17. Spreads of 88 pachytene spermatocytes from two males were studied and in all of them five metacentric bivalents, four telocentric bivalents, one hexavalent and the XY bivalent were observed. About 48% of the hexavalents formed a chain or a ring of synapsed chromosomes, the latter closed by synapsis between the short arms of telocentric chromosomes 6 and 17.  About 52% of hexavalents formed an open chain of 10 synapsed chromosomal arms belonging to 6 chromosomes.  In about half of the unsynapsed hexavalents one of the telocentric chromosome short arms appears associated with the X chromosome single axis, which was otherwise normally paired with the Y chromosome.  The cluster of pericentromeric heterochromatin mostly determines the hexavalent’s nuclear configuration, dragging the centromeric regions and all the chromosomes towards the nuclear envelope similar to an association of five telocentric bivalents. These reiterated encounters between these chromosomes restrict the interactions with other chromosomal domains and might favour eventual rearrangements within the metacentric, telocentric or hexavalent chromosome subsets. The unsynapsed short arms of telocentric chromosomes frequently bound to the single axis of the X chromosome could further complicate the already complex segregation of hexavalent chromosomes.

scholarly journals The oxidation of aromatic hydrocarbons at high pressures. I— Benzene. II— Toluene. III— Ethyl Benzene

1936 ◽  
Vol 153 (879) ◽  
pp. 448-462 ◽  
Keyword(s):  
Aromatic Hydrocarbons ◽  
High Pressures ◽  
Vapour Phase ◽  
Complete Analysis ◽  
Ethyl Benzene ◽  
Open Chain ◽  
Slow Combustion ◽  
Benzene Toluene ◽  
A Chain ◽  
Oxidation Of Benzene

It has been shown in previous papers of this series that during the slow combustion of the aliphatic hydrocarbons at high pressure conditions are particularly favourable to the isolation of the intermediate compounds involved, and that such oxidations take place by successive stages of hydroxylation. The work has now been extended to include the aromatic hydrocarbons, and the present paper embodies the results for benzene, toluene, and ethyl benzene. The homogeneous slow oxidation of benzene in the vapour phase has been studied by Fort and Hinshelwood, who concluded that at atmospheric pressure it proceeds by a chain mechanism somewhat analogous to that which they postulated for ethylene. Although a complete analysis of the products of combustion was not made, other circumstances suggested that during an "apparent period of induction" the first products were formed without pressure increase, and that, to quote their words, 'hydroxylation of the double bonds may be assumed to occur, followed by rapid further oxidation of the open chain unsaturated compound so produced to a substance like glyoxal. The remaining stages would then be analagous to the oxidation of acetylene

Controllable supramolecular polymerization via a chain-growth mechanism

2018 ◽  
Vol 54 (8) ◽  
pp. 928-931 ◽  
Author(s):  
Deep Sankar Pal ◽  
Haridas Kar ◽  
Suhrit Ghosh
Keyword(s):  
Carboxylic Acid ◽  
Sample Preparation ◽  
Growth Mechanism ◽  
Preparation Method ◽  
Chain Growth ◽  
Sample Preparation Method ◽  
Open Chain ◽  
Naphthalene Diimide ◽  
A Chain ◽  
Supramolecular Polymerization

A naphthalene-diimide appended carboxylic acid either spontaneously self-assembles (P) by an open-chain H-bonding or can be arrested in an intra-molecularly H-bonded monomeric state (M) depending on the sample preparation method. Living supramoleular polymerization of M can be initiated by a seed, generated from P.

Computer Aided Synthesis of Rational Motion Under Kinematic Constraints of Spatial SS Open Chains

2008 ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Numerical Algorithm ◽  
Smooth Curve ◽  
Dual Quaternion ◽  
Open Chain ◽  
End Effector ◽  
Kinematic Constraints ◽  
Constraint Manifold ◽  
Computer Aided ◽  
Quaternion Representation ◽  
Iterative Numerical Algorithm

In this paper, we study the problem of rational motion interpolation under kinematic constraints of spatial SS open chains. The objective is to synthesize a smooth rational motion that interpolates a given set of end effector positions and satisfies the kinematic constraints imposed by spatial SS open chains. The kinematic constraints under consideration define a constraint manifold representing all the positions available to the end effector. By choosing dual quaternion representation for the displacement of the end effector, the problem is reduced to designing a smooth curve in the space of dual quaternions that is constrained to lie inside the constraint manifold of the spatial SS open chain. An iterative numerical algorithm is presented that solves this problem effectively. The results presented in this paper are extension of our previous work on the synthesis of piecewise rational planar and spherical motions for open and closed chains under kinematic constraints.

scholarly journals On the Modelling of Tethered Mobile Robots as Redundant Manipulators

Robotics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 81
Author(s):  
Matteo Caruso ◽  
Paolo Gallina ◽  
Stefano Seriani
Keyword(s):  
Mobile Robots ◽  
Robotic Arm ◽  
Redundant Manipulators ◽  
Simulation Environment ◽  
Kinematic Redundancy ◽  
Open Chain ◽  
Secondary Tasks ◽  
Cluttered Environments ◽  
A Chain ◽  
Manipulator Control

Controlling a chain of tethered mobile robots (TMRs) can be a challenging task. This kind of system can be considered kinematically as an open-chain robotic arm where the mobile robots are considered as a revolute joint and the tether is considered as a variable length link, using a prismatic joint. Thus, the TMRs problem is decoupled into two parallel problems: the equivalent robotic manipulator control and the tether shape computation. Kinematic redundancy is exploited in order to coordinate the motion of all mobile robots forming the chain, expressing the constraints acting on the mobile robots as secondary tasks for the equivalent robotic arm. Implementation in the Gazebo simulation environment shows that the methodology is capable of controlling the chain of TMRs in cluttered environments.

Workspace Analysis and Dimensional Synthesis on a Delta Parallel Mechanism with Branch Chain Offset

2012 ◽  
Vol 152-154 ◽  
pp. 1526-1532
Author(s):  
Chen Chen Huang ◽  
Lin Yong Shen ◽  
Jin Wu Qian ◽  
Yan An Zhang
Keyword(s):  
Cross Section ◽  
Inverse Kinematics ◽  
Force Feedback ◽  
Dimensional Synthesis ◽  
Open Chain ◽  
Vector Method ◽  
Workspace Analysis ◽  
Matrix Condition Number ◽  
A Chain ◽  
Matrix Condition

In this paper, we intend to design a force-feedback device that meets the requirements in workspace. First, based on the modified Delta mechanism, we introduced a chain offset angle that is defined as alpha. We established the positive and inverse kinematics model by the vector method. According to the inverse kinematics formula, envelope body equation of single-open-chain subspace was deduced. We drew the geometric shape of the subspace under three situations while L1 was more than or equal to or less than L2. Then the influence of alpha on the whole workspace and mechanism size is deeply discussed. The cross section view of the space was also plotted by MATLAB. Finally, we gave an example using the Jacobin matrix condition number as the mechanism performance index for dimensional synthesis. The results show that the workspace meets the requirements well.

The Cartan structure equations

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Riemannian Manifold ◽  
Riemann Tensor ◽  
Structure Equation ◽  
Exterior Derivative ◽  
Schwarzschild Metric ◽  
Civita Connection ◽  
Structure Equations ◽  
Levi Civita Connection

This chapter focuses on Cartan structure equations. It first introduces a 1-form and its exterior derivative, before turning to a study of the connection and torsion forms, thereby expressing the torsion as a function of the connection forms and establishing the torsion differential 2-forms. It then turns to the curvature forms drawn from Chapter 23 and Cartan’s second structure equation, along with the curvature 2-forms. It also studies the Levi-Civita connection. The components of the Riemann tensor are then studied, with a Riemannian manifold, or a metric manifold with a torsion-less connection. The Riemann tensor of the Schwarzschild metric are finally discussed.

An Interactive Approach to Designing Planar Parallel Manipulators Using Image Space Representation

2012 ◽  
Author(s):  
Anurag Purwar ◽  
Sagar Anantwar ◽  
Ping Zhao
Keyword(s):  
Software Tool ◽  
Parallel Manipulators ◽  
Image Space ◽  
Space Representation ◽  
Dimensional Synthesis ◽  
Interactive Approach ◽  
Constraint Manifold ◽  
Closed Chain ◽  
Planar Parallel Manipulator ◽  
Structure Equations

Structure equations of mechanisms are well-known to give rise to algebraic constraint manifolds that describe the space of poses available to a certain link (usually, end-effector or coupler) of open chains or mechanisms. In this paper, by using planar quaternion representation for planar displacements, we obtain constraint manifold of such manipulators and show that the task of dimensional synthesis of a planar parallel manipulator (PPM) is reduced to simple geometric manipulation of the manifold in the Image Space. Earlier, this approach has been shown to work for planar 6R closed chain mechanisms as well as for RRR- and RPR-type leg topologies of a PPM. Here, we complete the extension to other five leg topologies and provide a developer version software tool for dimensional synthesis of a PPM.

TELOMERIC ASSOCIATIONS OF GAMETIC AND SOMATIC CHROMOSOMES IN DIPLOID AND AUTOTETRAPLOID ORNITHOGALUM VIRENS

1974 ◽  
Vol 16 (1) ◽  
pp. 61-76 ◽  
Author(s):  
Terry Ashley ◽  
E. B. Wagenaar
Keyword(s):  
Meiotic Prophase ◽  
Pollen Grain ◽  
Root Tip ◽  
Open Chain ◽  
Homologous Chromosomes ◽  
End To End ◽  
A Chain ◽  
Diploid Cells ◽  
Ornithogalum Virens ◽  
Haploid Pollen

In acetocarmine root-tip squashes, diploid cells of Ornithogalum virens in prophase exhibit configurations resulting from end-to-end associations of the six chromosomes. Homologues lie opposite one another in a ring. Prophase chromosomes of the autotretraploid cells likewise associate end-to-end; however, four homogues instead of two generally lie adjacent to one another and four (or eight) ends are often connected instead of the two (or four) found in diploid cells. Prophase chromosomes in a haploid pollen grain of a diploid form an open chain of three chromosomes, whereas in pollen from the autotetraploid balanced gametes form a configuration in which homologous pairs lie adjacent to one another and are attached end-to-end to other homologous pairs of nonhomologous chromosomes to form a chain. These observations are discussed in terms of the role telomeric associations may play in recognition and pairing of homologous chromosomes during meiotic prophase. This recognition of homologues may occur as early as syngamy.

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