Type Synthesis of 4-DOF Parallel Kinematic Mechanisms Based on Grassmann Line Geometry and Atlas Method

Many methods are proposed to deal with the type synthesis of parallel kinematic mechanisms（PKMs）, but most of them are less intuitive to some extent. Thus, to propose a concise and intuitive type synthesis method for engineering application is a very challenging issue, which should be further studied in the field. Grassmann line geometry, which can investigate the dimensions of spatial line-clusters in a concise way, is taken as the mathematic foundation. Atlas method is introduced to visually describe the degrees of freedom（DOFs） and constraints of a mechanism, and the dual rule is brought in to realize the mutual conversion of the freedom-space and constraint-space. Consequently, a systematic method based on Grassmann line geometry and Atlas method is generated and the entire type synthesis process is presented. Three type 4-DOF PKMs, i.e., 1T3R, 2T2R and 3T1R（T： translational DOF; R： rotational DOF）, are classified according to the different combinations of the translational DOFs and rotational DOFs. The type synthesis of 4-DOF PKMs is carried out and the possible configurations are thoroughly investigated. Some new PKMs with useful functions are generated during this procedure. The type synthesis method based on Grassmann line geometry and Atlas method is intuitive and concise, and can reduce the complexity of the PKMs＇ type synthesis. Moreover, this method can provide theoretical guidance for other PKMs＇ type synthesis and engineering application. A novel type synthesis method is proposed, which solves the existing methods＇ problems in terms of complicated, not intuitive and unsuitable for practical application.

Type Synthesis of Walking Robot Legs

Walking robots use leg structures to overcome obstacles or move on complicated terrains. Most robots of current researches are equipped with legs of simple structure. The specific design method of walking robot legs is seldom studied. Based on the generalized-function(GF) set theory, a systematic type synthesis process of designing robot legs is introduced. The specific mobility of robot legs is analyzed to obtain two main leg types as the goal of design.Number synthesis problem is decomposed into two stages, actuation and constraint synthesis by name,corresponding to the combinatorics results of linear Diophantine equations. Additional restrictions are discussed to narrow the search range to propose practical limb expressions and kinematic-pair designs. Finally, all the fifty-one leg structures of four subtypes are carried out, some of which are chosen to make up robot prototypes, demonstrating the validity of the method. This paper proposed a novel type synthesis methodology, which could be used to systematically design various practical robot legs and the derived robots.

Type Synthesis Method for the Translational Decoupled Parallel Mechanism Based on Screw Theory

Coupling is the significant characteristic of parallel mechanism,while it is just the coupling that brings about much difficulty for the configuration design,theoretical analysis and the development of the control system of the parallel mechanism. And recently,the research on the decoupled parallel mechanism becomes one of the research hot points in the mechanism fields. In this paper,a type synthesis method for the translational decoupled parallel mechanism( TDPM) is proposed based on the screw theory. To achieve the decoupling characteristics of the translational parallel mechanism,the translational decoupled criterion for type synthesis of the branches are presented in this paper. According to this criterion and the realization conditions of rotational degree of freedom of the mechanism proposed former,a large number of branches for the TDPM are obtained. Taking the three degrees of freedom( DOFs) TDPM as an example,the process of type synthesis is discussed in detail. Using this proposed type synthesis method,a serial of translational decoupled parallel mechanisms, including but not limited to all the existing typical 3-DOF TDPMs, are obtained, which identifies the correctness and effective of the method. The contents of this paper provide a reference and possess significant theoretical meanings for the synthesis and development of the novel decoupled parallel mechanisms.

Type Synthesis for 4-DOF Parallel Press Mechanism Using G_F Set Theory

Parallel mechanisms is used in the large capacity servo press to avoid the over-constraint of the traditional redundant actuation. Currently, the researches mainly focus on the performance analysis for some specific parallel press mechanisms. However, the type synthesis and evaluation of parallel press mechanisms is seldom studied, especially for the four degrees of freedom（DOF） press mechanisms. The type synthesis of 4-DOF parallel press mechanisms is carried out based on the generalized function（GF） set theory. Five design criteria of 4-DOF parallel press mechanisms are firstly proposed. The general procedure of type synthesis of parallel press mechanisms is obtained, which includes number synthesis, symmetrical synthesis of constraint GF sets, decomposition of motion GF sets and design of limbs. Nine combinations of constraint GF sets of 4-DOF parallel press mechanisms, ten combinations of GF sets of active limbs, and eleven combinations of GF sets of passive limbs are synthesized. Thirty-eight kinds of press mechanisms are presented and then different structures of kinematic limbs are designed. Finally, the geometrical constraint complexity（GCC）, kinematic pair complexity（KPC）, and type complexity（TC） are proposed to evaluate the press types and the optimal press type is achieved. The general methodologies of type synthesis and evaluation for parallel press mechanism are suggested.

Type Synthesis of Two-Degrees-of-Freedom Rotational Parallel Mechanism with Two Continuous Rotational Axes

The two-rotational-degrees-of-freedom（2R） parallel mechanism（PM） with two continuous rotational axes（CRAs） has a simple kinematic model.It is therefore easy to implement trajectory planning,parameter calibration,and motion control,which allows for a variety of application prospects.However,no systematic analysis on structural constraints of the 2R-PM with two CRAs has been performed,and there are only a few types of 2R-PM with two CRAs.Thus,a theory regarding the type synthesis of the 2R-PM with two CRAs is systematically established.First,combining the theories of reciprocal screw and space geometry,the spatial arrangement relationships of the constraint forces applied to the moving platform by the branches are explored,which give the 2R-PM two CRAs.The different distributions of the constraint forces in each branch are also studied.On the basis of the obtained structural constraints of branches,and considering the geometric relationships of constraint forces in each branch,the appropriate kinematic chains are constructed.Through the reasonable configuration of branch kinematic chains corresponding to every structural constraint,a series of new 2R-PMs with two CRAs are finally obtained.

A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms,or using screw theory to perform multiple getting intersection and union to complete type synthesis.The number of redundant parallel mechanisms obtained by these two methods is limited.In this paper,based on Grassmann line geometry and Atlas method,a novel and effective method for type synthesis of redundant actuated parallel mechanisms(PMs)with closed-loop units is proposed.Firstly,the degree of freedom(DOF)and constraint line graph of the moving platform are determined successively,and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph,and a branch constraint allocation scheme is formulated based on the allocation criteria.Secondly,a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units.Finally,the branch chains that meet the requirements of branch chains configuration criteria and F&C(degree of freedom&constraint)line graph are assembled.In this paper,two types of 2 rotational and 1 translational(2R1T)redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational(2T1R)redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples,and 238,92 and 15 new configurations were synthesized.All the mechanisms contain closed-loop units,and the mechanisms and the actuators both have good symmetry.Therefore,all the mechanisms have excellent comprehensive performance,in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled.The instantaneous analysis shows that all mechanisms are not instantaneous,which proves the feasibility and practicability of the method.

Type Synthesis of fully-Decoupled 2T2R Parallel Mechanisms Based on Driven - Chain Principle

Based on the screw theory and the driven-chain principle,a methodology of structural synthesis for fully-decoupled two-translational(2T) and two-rotational(2R) parallel mechanism is proposed by analyzing the characteristics of the input-output relations for fully-decoupled parallel mechanisms.Firstly,according to the desired kinematic characteristics of fully-decoupled parallel mechanisms,a method is proposed by virtue of screw theory to synthesize the desired forms for both the direct and the inverse Jacobian matrices.Secondly,according to the feature of the direct and the inverse Jacobian matrices,the effective screws,the actuated screws and the mobile un-actuated screws of each leg are established based on the reciprocal screw theory and all possible topology structures fulfilling the requirements are obtained.Finally,the desired fully-decoupled parallel mechanisms can be synthesized by using the structural synthesis rule and structural synthesis of fullydecoupled 2T2R parallel mechanisms can be obtained exploiting the abovementioned methodology.In particular,the direct Jacobian matrix of each synthesized fully-decoupled 2T2R parallel mechanism is a non-zero diagonal matrix throughout the entire workspace.Motors are mounted on each leg and each one of them actuates one degree-of-freedom(Do F) of the fully-decoupled parallel mechanism through a one-to-one velocity relation.

A Novel Method for Type Synthesis of Parallel Mechanism Without Parasitic Motion Based on 2R1T Parallel Mechanism with Rotational Bifurcation

The parasitic motion has been widely recognized as the major drawback of the parallel mechanism.Therefore a class of 2R1T PMs(parallel mechanism)without parasitic motion has been synthesized.However,these PMs can only rotate around two axes in sequential order.It decreases the performance of the balancing adjustment of the end-efector.In this paper,a family of 2R1T PMs without parasitic motion was reconstructed by using a novel method based on the remarkable properties of rotational bifurcation mechanisms,which can rotate in sequential order.Furthermore,some PMs rotating around two continuous axes in an arbitrary order are established by adding single joints.Taking the practicability of these structures into consideration,the workspace of 3-PRPS PM was analyzed as an example.Moreover,this study explores the practical application of the PMs without parasitic motion in developing balance mechanisms in rough-terrain fre-fghting robots.During the climbing process,the tank is adjusted to be parallel to the horizontal plane in real-time.It is proved that this kind of structure realizes continuous rotation around two rotation axes on the premise of no parasitic motion.

Type Synthesis of Fully-Decoupled 3R2T Parallel Mechanisms Based on Driven-Chain Principle

To avoid the existence of nonlinear and strong coupling in parallel mechanisms,it is necessary to address special care to the type synthesis of mechanisms,especially for the type synthesis of fully-decoupled parallel mechanisms. Based on the screw theory and the driven-chain principle,a methodology of structural synthesis for fully-decoupled three-rotational( 3R) and two-translational( 2T)parallel mechanisms was proposed by analyzing the characteristics of the input-output relations for fully-decoupled parallel mechanisms.Firstly,according to the desired kinematic characteristics of fullydecoupled parallel mechanisms,a method was presented by virtue of screw theory to synthesize the desired forms for both the direct and the inverse Jacobian matrices. Secondly,according to the feature of the direct and the inverse Jacobian matrices,the effective screws,the actuated screws and the mobile un-actuated screws of each leg were established based on the reciprocal screw theory and all possible topology structures fulfilling the requirements were obtained.Finally,the desired fully-decoupled parallel mechanisms could be synthesized by using the structural synthesis rule and structural synthesis of fully-decoupled 3R2 T parallel mechanisms could be obtained exploiting the abovementioned methodology. Furthermore,the Jacobian matrix of a synthesized 3R2 T parallel mechanism was deduced to demonstrate the decoupling feature of the parallel mechanism,which also validated the correctness of the methodology of the type synthesis for fully-decoupled 3R2 T parallel mechanisms.

Type Synthesis of Spatial Straight Line Mechanisms with only Revolute Joints

Spatial straight line mechanisms are a class of spatial mechanisms whose end-effectors generate the trajectory with the form of exact straight lines, which have potential applications in many industrial sectors. This study aims to synthesis the spatial straight line mechanisms with only revolute joints, meaning that no prismatic joints are included. According to the generalized function sets and the law of one dimensional rotation, the type of compositions of characteristic and the corresponding conditions are derived. Furthermore, some novel symmetrical and asymmetrical spatial straight line mechanisms are synthesized through assembling specific kinematic chains under the corresponding conditions. Finally, several synthesized spatial straight line mechanisms are illustrated to show the effectiveness of the synthesis methodology.

Type Synthesis of Self-Alignment Parallel Ankle Rehabilitation Robot with Suitable Passive Degrees of Freedom

The current parallel ankle rehabilitation robot(ARR)suffers from the problem of difficult real-time alignment of the human-robot joint center of rotation,which may lead to secondary injuries to the patient.This study investigates type synthesis of a parallel self-alignment ankle rehabilitation robot(PSAARR)based on the kinematic characteristics of ankle joint rotation center drift from the perspective of introducing"suitable passive degrees of freedom(DOF)"with a suitable number and form.First,the self-alignment principle of parallel ARR was proposed by deriving conditions for transforming a human-robot closed chain(HRCC)formed by an ARR and human body into a kinematic suitable constrained system and introducing conditions of"decoupled"and"less limb".Second,the relationship between the self-alignment principle and actuation wrenches(twists)of PSAARR was analyzed with the velocity Jacobian matrix as a"bridge".Subsequently,the type synthesis conditions of PSAARR were proposed.Third,a PSAARR synthesis method was proposed based on the screw theory and type of PSAARR synthesis conducted.Finally,an HRCC kinematic model was established to verify the self-alignment capability of the PSAARR.In this study,93 types of PSAARR limb structures were synthesized and the self-alignment capability of a human-robot joint axis was verified through kinematic analysis,which provides a theoretical basis for the design of such an ARR.

Type Synthesis for Bionic Quadruped Walking Robots

Regarding walking robots, biomimetic design has attracted a great deal of attention. Currently, studies have focused mainly on performance analysis and the design of some specific biomimetic walking robots. However, the systematic type synthesis of bionic quadruped robots has seldom been studied. In this paper, a new approach to type synthesis for quadruped walking robots is proposed based on the generalized fimction （Ge） set theory. The current types of typical walking robots are analyzed using the Ge set theory. The research status and existing problems are investigated. The skeletal systems of quadruped mammals are analyzed. The motion characteristics of all joints of quadruped mammals are denoted by 6;F sets. A process of conversion from biological types to serial, parallel and hybrid types is proposed. Limb types in serial, parallel and hybrid topology are synthe- sized. Finally the quadruped robots with serial, parallel and hybrid topology are produced. Two of these types have been suc- cessfully used for the design of walking rescue robots that is suitable for responding to nuclear accidents.

Type synthesis of deployable mechanisms for ring truss antenna based on constraint-synthesis method

Space deployable antenna is the key equipment in realizing the communication and data transmission between the spacecraft and the earth.In order to enrich the configurations of deployable antennas,the type synthesis of deployable mechanisms for ring truss antenna is conducted in this study.First,the principle of the constraint-synthesis method based on screw theory is briefly described,the structure of the ring truss deployable antenna and its folding principle are analyzed,and the ring truss mechanism is divided into upper edges,lower edges and linkages.Then,based on the constraint-synthesis method,the type synthesis of the basic unit edges is carried out,a series of basic unit mechanisms are obtained from combining the basic unit edge mechanisms,and five mechanism units with fewer joints and simple structures are selected.Furthermore,simulation models of the five ring truss deployable mechanisms are built in Solidworks and Matlab software,and the deploying process is verified by the movement simulation.Finally,mechanism characteristics of the five mechanisms are analyzed and discussed,and a prototype is manufactured,verifying the analysis in this paper.This research provides a new way for the type synthesis of spatial deployable mechanisms,and the ring truss deployable mechanisms obtained in this study can be well applied in the field of aerospace.

Type Synthesis and Dynamics Performance Evaluation of a Class of 5-DOF Redundantly Actuated Parallel Mechanisms

This paper presents a five degree of freedom(5-DOF)redundantly actuated parallel mechanism(PM)for the parallel machining head of a machine tool.A 5-DOF single kinematic chain is evolved into a secondary kinematic chain based on Lie group theory and a configuration evolution method.The evolutional chain and four 6-DOF kinematic chain SPS(S represents spherical joint and P represents prismatic joint)or UPS(U represents universal joint)can be combined into four classes of 5-DOF redundantly actuated parallel mechanisms.That SPS-(2UPR)R(R represents revolute joint)redundantly actuated parallel mechanism is selected and is applied to the parallel machining head of the machine tool.All formulas of the 4SPS-(2UPR)R mechanism are deduced.The dynamic model of the mechanism is shown to be correct by Matlab and automatic dynamic analysis of mechanical systems(ADAMS)under no-load conditions.The dynamic performance evaluation indexes including energy transmission efficiency and acceleration performance evaluation are analyzed.The results show that the 4SPS-(2UPR)R mechanism can be applied to a parallel machining head and have good dynamic performance.

Synthesis of Schiff Base Type Macrocycles Containing Naphthalene Ring

A series of new Schiff base type macrocyclic crown ethers containing naphthalene ring were synthesized from 2,2'-di(o-formylnaphthoxy) ethyl ether or 1,2-di(o-formylnaphthoxy) ethane and four appropriate diamines. The chemical structures of the new compounds were characterized by elemental analysis, infrared spectra, nuclear magnetic resonance spectra and mass spectrometry.

STUDY ON THE SYNTHESIS OF A NEW TYPE OF PHOSPHORUS HETEROCYCLIC COMPOUNDS-PYRAZOLO[3,4-d]-1,3,2-DIAZAPHOSPHORIN-6-ONE

1-substituted-5-benzoylamino-4-pyrazolecarboxamides(2)were prepared by the reaction of 1-substituted pyrazolo[3,4-d]-oxazinone(1) with amines in benzene.The compound 2 was refluxed with excess LiAlH_4 in a mixture of THF and ether,one of the two carbamoyl groups in the molecule 2 was reduced selectively.As the results,1-substituted-5- benzylamino-4-pyrazolecarboxamides(3)were obtained.Compounds 3 reacted with Cl_2PPh-X,or P(NET_2)_3,producing the title compounds(4). The conditions of the reactions were studied.

SYNTHESIS OF A NEW TYPE OF SCOPOLAMINE ANALOGUES

A series of compounds,which are structurally analogous to scopolamine and also in accordance with the general formula of neuroleptic benzamides,were synthesized and tested for their potential antipsychotic activity.

The First Total Synthesis of Five Elegan Type Natural Products

The first total synthesis of five linear diterpenes: eleganolone (1), eleganolone acetate (2), elegandiol (3), eleganonal (4) and epoxyeleganolone (5), was achieved from (E,E)-farnesol (6) via 4 to 6 steps. The key step was the alkylation reaction of silyl cyanide with allylic iodide.

SYNTHESIS AND CHARACTERIZATION OF FOUR NOVEL TYPES OF MICROPOROUS BERYLLOPHOSPHATE(Ⅱ)

Four new types of microporous beryllophosphates were hydrothermally synthesized using BeO - P_2O_5- R - MCl (or MCl_2) - H_20, R being HMDA (1, b-hexanediamine), EDA (ethylenediamine), or TBAOH (tetrabutytamine hydroxide), M alkali or alkali earth cation. By means of X-ray diffraction patterns (XRD), infrared (IR), TG-DT and elemental analyses we show that the crystalline beryllopbospbates have novel, unique framework structures, composed from basic units of tetrahedral P0_4 and Be0_4. These materials exhibit zeolite-like adsorption and ion-exchange properties.

Type Design and Behavior Control for Six Legged Robots

The research on legged robots attracted much attention both from the academia and industry. Legged robots are multi-input multi-output with multiple end-e ector systems. Therefore,the mechanical design and control framework are challenging issues. This paper reviews the development of type synthesis and behavior control on legged robots; introduces the hexapod robots developed in our research group based on the proposed type synthesis method. The control framework for legged robots includes data driven layer,robot behavior layer and robot execution layer. Each layer consists several components which are explained in details. Finally,various experiments were conducted on several hexapod robots. The summarization of the type synthesis and behavior control design constructed in this paper would provide a unified platform for communications and references for future advancement for legged robots.