Parallel Translation on Kahler Manifolds

In this paper, the author establishs a real-valued function on K?hler manifolds by holomorphic sectional curvature under parallel translation. The author proves if such functions are equal for two simply-connected, complete K?hler manifolds, then they are holomorphically isometric.

PERFORMANCE ANALYSIS AND KINEMATIC DESIGN OF PURE TRANSLATIONAL PARALLEL MECHANISM WITH VERTICAL GUIDE-WAYS

Performance analysis and kinematic design of the 3-PUU pure translational parallel mechanism with vertical guide-ways are investigated. Two novel performance indices, the critical slider stroke and the main section area of workspace, are defined; The expressions of two other indices, i.e. the global dexterity and global force transfer ratio are revised based on the main section of workspace. Using these indices, performance changes versus the varieties of dimensional parameters of mechanism are investigated in detail and the graphic descriptions of change tendencies of the performance indices are illustrated. By means of these obtained graphic descriptions, kinematic parameters for the 3-PUU pure translational parallel mechanism with better characteristics can be directly acquired.

Topology Search of 3-DOF Translational Parallel Manipulators with Three Identical Limbs for Leg Mechanisms

Three-degree of freedom（3-DOF） translational parallel manipulators（TPMs） have been widely studied both in industry and academia in the past decades. However, most architectures of 3-DOF TPMs are created mainly on designers＇ intuition, empirical knowledge, or associative reasoning and the topology synthesis researches of 3-DOF TPMs are still limited. In order to find out the atlas of designs for 3-DOF TPMs, a topology search is presented for enumeration of 3-DOF TPMs whose limbs can be modeled as 5-DOF serial chains. The proposed topology search of 3-DOF TPMs is aimed to overcome the sensitivities of the design solution of a 3-DOF TPM for a LARM leg mechanism in a biped robot. The topology search, which is based on the concept of generation and specialization in graph theory, is reported as a step-by-step procedure with desired specifications, principle and rules of generalization, design requirements and constraints, and algorithm of number synthesis. In order to obtain new feasible designs for a chosen example and to limit the search domain under general considerations, one topological generalized kinematic chain is chosen to be specialized. An atlas of new feasible designs is obtained and analyzed for a specific solution as leg mechanisms. The proposed methodology provides a topology search for 3-DOF TPMs for leg mechanisms, but it can be also expanded for other applications and tasks.

Type Synthesis of Fully Decoupled Three Translational Parallel Mechanism with Closed-Loop Units and High Stifness

In order to solve the problem of weak stifness of the existing fully decoupled parallel mechanism, a new synthesis method of fully decoupled three translational (3T) parallel mechanisms (PMs) with closed-loop units and high stifness is proposed based on screw theory. Firstly, a new criterion for the full decoupled of PMs is presented that the reciprocal product of the transmission wrench screw matrix and the output twist screw matrix of PMs is a diagonal matrix, and all elements on the main diagonal are nonzero constants. The forms of the transmission wrench screws are determined by the criterion. Secondly, the forms of the actuated and unactuated screws can be obtained according to their relationships with the transmission wrench screws. The basic decoupled limbs are generated by combination of the above actuated and unactuated screws. Finally, a closed-loop units construction method is investigated to apply the decoupled mechanisms in a better way on the high stifness occasion. The closed-loop units are constructed in the basic decoupled limbs to generate a high-stifness fully decoupled 3T PM. Kinematic and stifness analyses show that the Jacobian matrix is a diagonal matrix, and the stifness is obviously higher than that of the coupling mechanisms, which verifes the correctness of the proposed synthesis method. The mechanism synthesized by this method has a good application prospect in vehicle durability test platform.

Improving Parallel Corpus Quality for Chinese-Vietnamese Statistical Machine Translation

The performance of a machine translation system heavily depends on the quantity and quality of the bilingual language resource. However,getting a parallel corpus,which has a large scale and is of high quality,is a very difficult task especially for low resource languages such as Chinese-Vietnamese. Fortunately,multilingual user generated contents（ UGC）,such as bilingual movie subtitles,provide us access to automatic construction of the parallel corpus. Although the amount of UGC parallel corpora can be considerable,the original corpus is not suitable for statistical machine translation（ SMT） systems. The corpus may contain translation errors,sentence mismatching,free translations,etc. To improve the quality of the bilingual corpus for SMT systems,three filtering methods are proposed： sentence length difference,the semantic of sentence pairs,and machine learning. Experiments are conducted on the Chinese to Vietnamese translation corpus.Experimental results demonstrate that all the three methods effectively improve the corpus quality,and the machine translation performance（ BLEU score） can be improved by 1. 32.

GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD

We revisit the intrinsic differential geometry of the Wasserstein space over a Riemannian manifold,due to a series of papers by Otto,Otto-Villani,Lott,Ambrosio-Gigli-Savaré,etc.

Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine

In this paper, error modeling and analysis of a typical 3-degree of freedom translational Parallel Kine- matic Machine is presented. This mechanism provides translational motion along the Cartesian X-, Y- and Z- axes. It consists of three limbs each having an arm and forearm with prismatic-revolute-revolute-revolute joints. The moving or tool platform maintains same orientation in the entire workspace due to its joint arrangement. From inverse kinematics, the joint angles for a given position of tool platform necessary for the error modeling and analysis are obtained. Error modeling is done based on the differentiation of the inverse kinematic equations. Variation of pose errors along X, Y and Z directions for a set of dimensions of the parallel kinematic machine is presented. A non-dimensional performance index, namely, global error transformation index is used to study the influence of dimensions and its corresponding global maximum pose error is reported. An attempt is made to find the optimal dimensions of the Parallel Kinematic Machine using Genetic Algorithms in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the Parallel Kinematic Machine under study.

Design and analysis of partially decoupled translational parallel mechanisms with single-loop structures

This study presents a family of novel translational parallel mechanisms(TPMs)with single-loop topological structures.The proposed mechanism consists of only revolute and prismatic joints.The novel TPMs are simpler in structure and have fewer joints and components than the well-known Delta Robot.Four types of 2-degree of freedom driving systems are applied to different limb structures to avoid the moving actuator that causes the problem of increased moving mass.Four sample TPMs are constructed using the synthesized limbs,and one of them is investigated in terms of kinematic performance.First,a position analysis is performed and validated through numerical simulation to reveal the characteristics of partially decoupled motion,which improves the controllability of TPM.Second,singular configurations are identified,and the resulting singularity curve is obtained.Lastly,the workspace of TPM is analyzed,and the relationship between the singular configurations and the reachable workspace is explored.The workspace of the 3-CRR(C denotes the cylindrical joint and R denotes the revolute joint)translational mechanism is also presented to prove that the proposed TPM has a fairly large workspace.