The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invar...The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator（represented by Lie bracket）is deduced.Further,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.展开更多
Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dyna...Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.展开更多
Scissor-like element has a number of applications in deployable structures such as planar deployable structure (PDS) and ring deployable structure(RDS). However, the mobility analysis of the multi-loop deployable stru...Scissor-like element has a number of applications in deployable structures such as planar deployable structure (PDS) and ring deployable structure(RDS). However, the mobility analysis of the multi-loop deployable structures is made more difficulty by the traditional mobility formula, because the deployable structure is a very complex structure with multi-loop. Therefore, On the basis of screw theory, the calculation method of mobility of deployable structures of SLE is thoroughly discussed. In order to investigate the mobility, decomposing and composing structures(DCS) are developed, and the basic units are able to be obtained. On the basis of the deployable structures’ geometrical characteristics, there exists a closed-loop quadrilateral structure and some non-closed-loop quadrilateral structures in PDS. Also, a six legs parallel structure is present in RDS. The basic units’ mobility can be solved by both the methods of screw theory and topology constraint graphs. Then, composing the related basic units, the formula of planar deployable structures’ mobility can be built and solves the mobility of ring deployable structure. The analysis method solves the mobility analysis of the multi-loop deployable structures which is difficulty by the traditional method, and plays an important role in further research about the mobility of other complex deployable structures.展开更多
Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the st...Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.展开更多
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 sys...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.展开更多
Structural synthesis for 4-DOF parallel manipulators using screw theory issystematically studied. Motion properties and constraint conditions of 4-DOF parallel manipulatorsaccording to the relationship between screw a...Structural synthesis for 4-DOF parallel manipulators using screw theory issystematically studied. Motion properties and constraint conditions of 4-DOF parallel manipulatorsaccording to the relationship between screw and reciprocal screw are analyzed. Mathematicalexpressions for constraint screws and twist screws of moving platform are constructed, and allpossible limbs, which provide one or more force constraints, are enumerated. Finally, a parallelmanipulator with 3-rotation-DOF and 1-translation-DOF is used as an example to describe thesynthesis procedure for symmetrical and non-symmetrical 4-DOF parallel manipulators.展开更多
Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms,and the generalized analysis method and concise kinematics transfer matrix are obtained.In this study,first,acco...Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms,and the generalized analysis method and concise kinematics transfer matrix are obtained.In this study,first,according to the kinematics analysis of serial mechanisms,the basic principles of Lie groups and Lie algebras are briefly explained in dealing with the spatial switching and differential operations of screw vectors.Then,based on the standard ideas of Lie operations,the method for kinematics analysis of parallel mechanisms is derived,and Jacobian matrix and Hessian matrix are formulated recursively and in a closed form.Then,according to the mapping relationship between the parallel joints and corresponding equivalent series joints,a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are examined.A case study is performed to verify the calculated matrices wherein a humanoid hybrid robotic arm with a parallel-series-parallel configuration is considered as an example.The results of a simulation experiment indicate that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practically feasible.展开更多
First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and gene...First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and generalized inertial force according to screw theory.After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.展开更多
The lower-mobility parallel mechanism has been widely used in the engineering field due to its numerous excellent characteristics.However,little work has been devoted to the actuator selection and placement that best ...The lower-mobility parallel mechanism has been widely used in the engineering field due to its numerous excellent characteristics.However,little work has been devoted to the actuator selection and placement that best satisfy the system's functional requirements during concept design.In this study,a unified approach for synthesizing the actuation spaces of both rigid and flexure parallel mechanisms has been presented,and all possible combinations of inputs could be obtained,laying a theoretical foundation for the subsequent optimization of inputs.According to the linear independence of actuation space and constraint space of the lower-mobility parallel mechanism,a general expression of actuation spaces in the format of screw systems is deduced,a unified synthesis process for the lower-mobility parallel mechanism is derived,and the efficiency of the method is validated with two selective examples based on screw theory.This study presents a theoretical framework for the input selection problems of parallel mechanisms,aiming to help designers select and place actuators in a correct and even optimal way after the configuration design.展开更多
A humanoid robot is a complex dynamic system for its idiosyncrasy. This paper aims to provide a mathematical and theoretical foundation for the design of the configuration, kinematics analysis of a novel humanoid robo...A humanoid robot is a complex dynamic system for its idiosyncrasy. This paper aims to provide a mathematical and theoretical foundation for the design of the configuration, kinematics analysis of a novel humanoid robot. It has a simplified configuration and design for entertainment purpose. The design methods, principle and mechanism are discussed. According to the design goals of this research, there are ten degrees of freedom in the two bionic arms. Modularization, concurrent design and extension theory methods were adopted in the configuration study and screw theory was introduced into the analysis of humanoid robot kinematics. Comparisons with other methods show that: 1) only two coordinates need to be established in the kinematics analysis of humanoid robot based on screw theory; 2) the spatial manipulator Jacobian obtained by using twist and exponential product formula is succinct and legible; 3) adopting screw theory to resolve the humanoid robot arms kinematics question can avoid singularities; 4) using screw theory can solve the question of specification insufficiency.展开更多
A new method is presented to describe and analyze the spatial compliance ofcoiled springs using screw theory. After an abbreviated description for the deformation of a beamelement using screw theory, the spatial compl...A new method is presented to describe and analyze the spatial compliance ofcoiled springs using screw theory. After an abbreviated description for the deformation of a beamelement using screw theory, the spatial compliance density for a beam element is derived based onthe fundamental material theory and reasonable assumptions, and the spatial compliance of the beamwith finite length is obtained by integral. The spatial compliance of coiled springs is furtheranalyzed using the spatial compliance density of the beam element. By calculating theeigencompliance and Ball's principle screws for the whole compliance of system, the complianceproperties varying with the basic physical parameters of the system are illustrated in detail. Thebasic ideas can be used for the design and application of the coiled springs and the other compliantmechanisms with spatial compliant beam element.展开更多
The pose accuracy of parallel manipulators(PMs)is a key index to measure their performance.Establishing the grav-ity-based kinetostatic model of a parallel robot provides an important basis for its error composition a...The pose accuracy of parallel manipulators(PMs)is a key index to measure their performance.Establishing the grav-ity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement.In this paper,a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs.First,the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches.Sec-ond,the gravity model of the mechanism is established based on the screw theory and the principle of virtual work.Finally,the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained,and the influences of the external load,platform gravity,and rod gravity on the stiffness of the mechanism are decoupled.The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method.This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.展开更多
Assembly errors have great influence on assembly quality in robotic assembly systems. Error analysis is directed to the propagations and accumula-tions of various errors and their effect on assembly success.Using the ...Assembly errors have great influence on assembly quality in robotic assembly systems. Error analysis is directed to the propagations and accumula-tions of various errors and their effect on assembly success.Using the screw coordinates, assembly errors are represented as 'error twist', the extremely compact expression. According to the law of screw composition, relative position and orientation errors of mating parts are computed and the necessary condition of assembly success is concluded. A new simple method for measuring assembly errors is also proposed based on the transformation law of a screw.Because of the compact representation of error, the model presented for error analysis can be applied to various part- mating types and especially useful for error analysis of complexity assembly.展开更多
With the gradual deepening of study on the parallel mechanism,the difficulty brought by the existence of coupling to the theoretical analysis and practical application of parallel mechanisms is becoming increasingly a...With the gradual deepening of study on the parallel mechanism,the difficulty brought by the existence of coupling to the theoretical analysis and practical application of parallel mechanisms is becoming increasingly apparent.The research on the decoupled parallel mechanism is currently one of the hot fields.Though most of the rotational parallel mechanisms,which has been widely used in spatial orientation fields,are not decoupled.It is comparative difficult for the synthesis of fully decoupled rotational parallel mechanisms,and the number of the existing parallel mechanisms which can realize rotational decoupling is limited.In addition,most of the existing rotational decoupled parallel mechanism are obtained depending on the experience of the researcher,and don't possess the general theoretical significance.Based on the screw theory,this paper presents the rotational conditions of the parallel mechanism through the analysis of the relationship between the degree of freedom of the parallel mechanism and its limbs.The synthesis rule of the limbs for decoupled rotational parallel mechanism is established according to the twist screw system of the limbs,which assures the decoupling of the rotations in each limb.The selection principle of the input pairs for the rotation driven limbs is proposed,then the type synthesis method for rotational decoupled parallel mechanisms is formed.With this type synthesis method,synthesis of the rotational decoupled parallel mechanisms is performed,which can provide a reference for the development of the novel type parallel mechanisms with independent intellectual property rights.展开更多
This study presents a dynamic modeling and analysis methodology for the 3-PRS parallel mechanism.First,an improved reduced dynamic model of component substructures is proposed using the dynamic condensation technique ...This study presents a dynamic modeling and analysis methodology for the 3-PRS parallel mechanism.First,an improved reduced dynamic model of component substructures is proposed using the dynamic condensation technique and the rigid multipoint constraints at the joint/interface level,leading to a minimum set of generalized coordinates for external nodes.Next,the mapping between interface constraint stiffness and global stiffness is illustrated,resulting in an analytical stiffness model of joint substructures.Subsequently,the derived component and joint substructures are synthesized into the entire mechanism based on the Lagrange equation.Finally,a case study illustrates that the lower-order dynamic performances predicted within the proposed approach have the same trend as those obtained from a complete-order finite element model.The root mean square discrepancy of the lower-order natural frequencies between the two models is less than 5.92%,indicating the accuracy and effectiveness of the proposed model.The developed approach can highly and efficiently predict the dynamic performance distributions across the entire workspace and guide the optimal functional design under the virtual machine framework.展开更多
Modular truss space deployable antennas are key for future large aperture,high precision antennas,already proven in various in-orbit applications globally.This paper introduces a design method for a tetrahedral basic ...Modular truss space deployable antennas are key for future large aperture,high precision antennas,already proven in various in-orbit applications globally.This paper introduces a design method for a tetrahedral basic unit mechanism with dual height positioning nodes.A parametric model is established,and its DOF are analyzed to confirm the mechanism's validity.The new tetrahedral basic unit mechanism constructed by this method is a single DOF mechanism and can locate different parabolic node heights.In order to further adapt to the parabolic and large aperture requirements of the deployable antenna of the truss,a combination unit and modular unit mechanism are developed based on this tetrahedral unit.The DOF and deployment characteristics of the modular unit mechanism are analyzed and validated through simulations.Various networking methods for the modular units are proposed,followed by a comprehensive performance comparison of different modular truss deployable antenna mechanisms.A prototype model of the modular unit mechanism is also developed,with deployment experiments demonstrating the mechanism's simplicity,low DOF,and large deployment ratio.The findings of this study provide a theoretical and technical basis for the future design and development of truss deployable antenna mechanisms.展开更多
Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines(PKMs). This requires that analytical description, formulation and operation for bot...Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines(PKMs). This requires that analytical description, formulation and operation for both finite and instantaneous motions are performed by the same mathematical tool. Based upon finite and instantaneous screw theory, a unified and systematic approach for topology design and kinematic analysis of PKMs is proposed in this paper. Using the derivative mapping between finite and instantaneous screws built in the authors’ previous work, the finite and instantaneous motions of PKMs are analytically described by the simple and non?redundant screws in quasi?vector and vector forms. And topological and parametric models of PKMs are algebraically formulated and related. These related topological and parametric models are ready to do type synthesis and kinematic analysis of PKMs under the unified framework of screw theory. In order to show the validity of the proposed approach, a kind of two?translational and three?rotational(2T3R)5?axis PKMs is taken as example. Numerous new structures of the 2T3R PKMs are synthe?sized as the results of topology design, and their Jacobian matrix is obtained easily for parameter optimization and performance evaluation. Some of the synthesized PKMs have outstanding capabilities in terms of large workspaces and flexible orientations, and have great potential for industrial applications of machining and manufacture. Among them, METROM PKM is a typical example which has attracted a lot of attention from global companies and already been developed as commercial products. The approach is a general and unified approach that can be used in the innovative design of different kinds of PKMs.展开更多
A cable-driven redundant manipulator(CDRM)characterized by redundant degrees of freedom and a lightweight,slender design can perform tasks in confined and restricted spaces efficiently.However,the complex multistage c...A cable-driven redundant manipulator(CDRM)characterized by redundant degrees of freedom and a lightweight,slender design can perform tasks in confined and restricted spaces efficiently.However,the complex multistage coupling between drive cables and passive joints in CDRM leads to a challenging dynamic model with difficult parameter identification,complicating the efforts to achieve accurate modeling and control.To address these challenges,this paper proposes a dynamic modeling and adaptive control approach tailored for CDRM systems.A multilevel kinematic model of the cable-driven redundant manipulator is presented,and a screw theory is employed to represent the cable tension and cable contact forces as spatial wrenches,which are equivalently mapped to joint torque using the principle of virtual work.This approach simplifies the mapping process while maintaining the integrity of the dynamic model.A recursive method is used to compute cable tension section-by-section for enhancing the efficiency of inverse dynamics calculations and meeting the high-frequency demands of the controller,thereby avoiding large matrix operations.An adaptive control method is proposed building on this foundation,which involves the design of a dynamic parameter adaptive controller in the joint space to simplify the linearization process of the dynamic equations along with a closed-loop controller that incorporates motor parameters in the driving space.This approach improves the control accuracy and dynamic performance of the CDRM under dynamic uncertainties.The accuracy and computational efficiency of the dynamic model are validated through simulations,and the effectiveness of the proposed control method is demonstrated through control tests.This paper presents a dynamic modeling and adaptive control approach for CDRM to enhance accuracy and performance under dynamic uncertainties.展开更多
Current research on reconfigurable parallel mechanisms(RPMs)primarily focuses on achieving limited configuration changes,while mechanisms capable of extensive mode switching with distinct motion branches remain challe...Current research on reconfigurable parallel mechanisms(RPMs)primarily focuses on achieving limited configuration changes,while mechanisms capable of extensive mode switching with distinct motion branches remain challenging to design.Conventional kinematotropic chains offer limited reconfigurability,underscoring the need for novel designs that enable broader operational adaptability.In this research,a novel diamond-like chain(DLC)with metamorphic units is proposed developed from generalized diamond kinematotropic chains.By altering the axes of the metamorphic units,the DLC realizes three distinct configurations,each corresponding to one of five motion branches characterized by bifurcation and metamorphic transitions.This DLC serves as the fundamental building block for constructing a reconfigurable hybrid limb.Using screw theory,the constraint properties of the limb in its five phases are analyzed and classified into three types:unconstrained limbs,limbs applying constraint forces,and limbs applying constraint couples.Based on this analysis,a RPM consisting of three reconfigurable limbs is developed.Its reconfigurability stems from the inherent bifurcation and metamorphic capabilities of the DLC-based limbs.This research introduces a RPM capable of controlled switching among ten distinct motion modes,with mobility ranging from three to six degrees of freedom.The proposed mechanism demonstrates high versatility and practical feasibility,offering a promising solution for applications requiring variable motion characteristics and adaptive performance.展开更多
The intricate relationship between origami and mechanism underscores the fertile ground for innovation,which is particularly evident in the construction theory of thick-panel origami.Despite its potential,thick panel ...The intricate relationship between origami and mechanism underscores the fertile ground for innovation,which is particularly evident in the construction theory of thick-panel origami.Despite its potential,thick panel origami remains relatively unexplored in the context of single-loop metamorphic mechanisms.Drawing inspiration from thickpanel origami,particularly Miura origami,this study proposes a pioneering single-loop 6R multiple metamorphic mechanism.Through rigorous mathematical modeling(including the construction and resolution of the D-H closed-loop equation)and leveraging advanced analytical tools such as the screw theory and Lie theory,this study meticulously elucidates the planar,spherical,and Bennett motion branches of the mechanism.Furthermore,it delineates all the three bifurcation points between the motion branches,thereby providing a comprehensive understanding of the kinematic behavior of the mechanism.A metamorphic network can be constructed by applying several single-loop mechanisms to a symmetrical layout.Owing to its metamorphic properties,this network can act as a structural backbone for deployable antennas,aerospace shelters,and morphing wing units,thereby enabling a single mechanism to achieve multiple folding configurations.This paper not only introduces innovative metamorphic mechanisms but also suggests a promising method for uncovering and designing metamorphic mechanisms by developing new mechanisms from thick-panel origami.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51375420,51105322)
文摘The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator（represented by Lie bracket）is deduced.Further,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.
基金Supported by National Natural Science Foundation of China(Grant No.51175422)
文摘Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.
基金supported by National Natural Science Foundation of China(Grant No. 50875210)
文摘Scissor-like element has a number of applications in deployable structures such as planar deployable structure (PDS) and ring deployable structure(RDS). However, the mobility analysis of the multi-loop deployable structures is made more difficulty by the traditional mobility formula, because the deployable structure is a very complex structure with multi-loop. Therefore, On the basis of screw theory, the calculation method of mobility of deployable structures of SLE is thoroughly discussed. In order to investigate the mobility, decomposing and composing structures(DCS) are developed, and the basic units are able to be obtained. On the basis of the deployable structures’ geometrical characteristics, there exists a closed-loop quadrilateral structure and some non-closed-loop quadrilateral structures in PDS. Also, a six legs parallel structure is present in RDS. The basic units’ mobility can be solved by both the methods of screw theory and topology constraint graphs. Then, composing the related basic units, the formula of planar deployable structures’ mobility can be built and solves the mobility of ring deployable structure. The analysis method solves the mobility analysis of the multi-loop deployable structures which is difficulty by the traditional method, and plays an important role in further research about the mobility of other complex deployable structures.
基金supported by National Natural Science Foundation of China (Grant No. 50675016)
文摘Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51005195,51205339)
文摘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.
文摘Structural synthesis for 4-DOF parallel manipulators using screw theory issystematically studied. Motion properties and constraint conditions of 4-DOF parallel manipulatorsaccording to the relationship between screw and reciprocal screw are analyzed. Mathematicalexpressions for constraint screws and twist screws of moving platform are constructed, and allpossible limbs, which provide one or more force constraints, are enumerated. Finally, a parallelmanipulator with 3-rotation-DOF and 1-translation-DOF is used as an example to describe thesynthesis procedure for symmetrical and non-symmetrical 4-DOF parallel manipulators.
基金Supported by Zhejiang Province Foundation for Distinguished Young Scholars of China(Grant No.LR18E050003)National Natural Science Foundation of China(Grant Nos.51975523,51475424,51905481)Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems(Grant No.GZKF-201906).
文摘Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms,and the generalized analysis method and concise kinematics transfer matrix are obtained.In this study,first,according to the kinematics analysis of serial mechanisms,the basic principles of Lie groups and Lie algebras are briefly explained in dealing with the spatial switching and differential operations of screw vectors.Then,based on the standard ideas of Lie operations,the method for kinematics analysis of parallel mechanisms is derived,and Jacobian matrix and Hessian matrix are formulated recursively and in a closed form.Then,according to the mapping relationship between the parallel joints and corresponding equivalent series joints,a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are examined.A case study is performed to verify the calculated matrices wherein a humanoid hybrid robotic arm with a parallel-series-parallel configuration is considered as an example.The results of a simulation experiment indicate that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practically feasible.
文摘First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and generalized inertial force according to screw theory.After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.
基金Supported by National Natural Science Foundation of China(Grant No.51775475).
文摘The lower-mobility parallel mechanism has been widely used in the engineering field due to its numerous excellent characteristics.However,little work has been devoted to the actuator selection and placement that best satisfy the system's functional requirements during concept design.In this study,a unified approach for synthesizing the actuation spaces of both rigid and flexure parallel mechanisms has been presented,and all possible combinations of inputs could be obtained,laying a theoretical foundation for the subsequent optimization of inputs.According to the linear independence of actuation space and constraint space of the lower-mobility parallel mechanism,a general expression of actuation spaces in the format of screw systems is deduced,a unified synthesis process for the lower-mobility parallel mechanism is derived,and the efficiency of the method is validated with two selective examples based on screw theory.This study presents a theoretical framework for the input selection problems of parallel mechanisms,aiming to help designers select and place actuators in a correct and even optimal way after the configuration design.
基金Project 20050290011 supported by the Doctoral Program Foundation of the Ministry of Education of China
文摘A humanoid robot is a complex dynamic system for its idiosyncrasy. This paper aims to provide a mathematical and theoretical foundation for the design of the configuration, kinematics analysis of a novel humanoid robot. It has a simplified configuration and design for entertainment purpose. The design methods, principle and mechanism are discussed. According to the design goals of this research, there are ten degrees of freedom in the two bionic arms. Modularization, concurrent design and extension theory methods were adopted in the configuration study and screw theory was introduced into the analysis of humanoid robot kinematics. Comparisons with other methods show that: 1) only two coordinates need to be established in the kinematics analysis of humanoid robot based on screw theory; 2) the spatial manipulator Jacobian obtained by using twist and exponential product formula is succinct and legible; 3) adopting screw theory to resolve the humanoid robot arms kinematics question can avoid singularities; 4) using screw theory can solve the question of specification insufficiency.
基金This project is supported by National Natural Science Foundation of China(No.50075009) and SRF for ROCS, SEM.
文摘A new method is presented to describe and analyze the spatial compliance ofcoiled springs using screw theory. After an abbreviated description for the deformation of a beamelement using screw theory, the spatial compliance density for a beam element is derived based onthe fundamental material theory and reasonable assumptions, and the spatial compliance of the beamwith finite length is obtained by integral. The spatial compliance of coiled springs is furtheranalyzed using the spatial compliance density of the beam element. By calculating theeigencompliance and Ball's principle screws for the whole compliance of system, the complianceproperties varying with the basic physical parameters of the system are illustrated in detail. Thebasic ideas can be used for the design and application of the coiled springs and the other compliantmechanisms with spatial compliant beam element.
基金Supported by National Natural Science Foundation of China(Grant No.52275036)Key Research and Development Project of Jiaxing Science and Technology Bureau of China(Grant No.2022BZ10004).
文摘The pose accuracy of parallel manipulators(PMs)is a key index to measure their performance.Establishing the grav-ity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement.In this paper,a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs.First,the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches.Sec-ond,the gravity model of the mechanism is established based on the screw theory and the principle of virtual work.Finally,the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained,and the influences of the external load,platform gravity,and rod gravity on the stiffness of the mechanism are decoupled.The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method.This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.
基金This work is Supported by the National Science Foundation under Grant 863 -512 -9820-04.
文摘Assembly errors have great influence on assembly quality in robotic assembly systems. Error analysis is directed to the propagations and accumula-tions of various errors and their effect on assembly success.Using the screw coordinates, assembly errors are represented as 'error twist', the extremely compact expression. According to the law of screw composition, relative position and orientation errors of mating parts are computed and the necessary condition of assembly success is concluded. A new simple method for measuring assembly errors is also proposed based on the transformation law of a screw.Because of the compact representation of error, the model presented for error analysis can be applied to various part- mating types and especially useful for error analysis of complexity assembly.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50875227, 51005195)
文摘With the gradual deepening of study on the parallel mechanism,the difficulty brought by the existence of coupling to the theoretical analysis and practical application of parallel mechanisms is becoming increasingly apparent.The research on the decoupled parallel mechanism is currently one of the hot fields.Though most of the rotational parallel mechanisms,which has been widely used in spatial orientation fields,are not decoupled.It is comparative difficult for the synthesis of fully decoupled rotational parallel mechanisms,and the number of the existing parallel mechanisms which can realize rotational decoupling is limited.In addition,most of the existing rotational decoupled parallel mechanism are obtained depending on the experience of the researcher,and don't possess the general theoretical significance.Based on the screw theory,this paper presents the rotational conditions of the parallel mechanism through the analysis of the relationship between the degree of freedom of the parallel mechanism and its limbs.The synthesis rule of the limbs for decoupled rotational parallel mechanism is established according to the twist screw system of the limbs,which assures the decoupling of the rotations in each limb.The selection principle of the input pairs for the rotation driven limbs is proposed,then the type synthesis method for rotational decoupled parallel mechanisms is formed.With this type synthesis method,synthesis of the rotational decoupled parallel mechanisms is performed,which can provide a reference for the development of the novel type parallel mechanisms with independent intellectual property rights.
基金supported by the EU Horizon 2020 research and innovation program under the Marie Sk?odowska-Curie (Grant No.734272)the China Scholarship Council (Grant No.201908060118)。
文摘This study presents a dynamic modeling and analysis methodology for the 3-PRS parallel mechanism.First,an improved reduced dynamic model of component substructures is proposed using the dynamic condensation technique and the rigid multipoint constraints at the joint/interface level,leading to a minimum set of generalized coordinates for external nodes.Next,the mapping between interface constraint stiffness and global stiffness is illustrated,resulting in an analytical stiffness model of joint substructures.Subsequently,the derived component and joint substructures are synthesized into the entire mechanism based on the Lagrange equation.Finally,a case study illustrates that the lower-order dynamic performances predicted within the proposed approach have the same trend as those obtained from a complete-order finite element model.The root mean square discrepancy of the lower-order natural frequencies between the two models is less than 5.92%,indicating the accuracy and effectiveness of the proposed model.The developed approach can highly and efficiently predict the dynamic performance distributions across the entire workspace and guide the optimal functional design under the virtual machine framework.
基金sponsored by the National Natural Science Foundation of China(No.52075467)Hebei Province Fund Outstanding Youth Fund Project,China(No.E2024203107)。
文摘Modular truss space deployable antennas are key for future large aperture,high precision antennas,already proven in various in-orbit applications globally.This paper introduces a design method for a tetrahedral basic unit mechanism with dual height positioning nodes.A parametric model is established,and its DOF are analyzed to confirm the mechanism's validity.The new tetrahedral basic unit mechanism constructed by this method is a single DOF mechanism and can locate different parabolic node heights.In order to further adapt to the parabolic and large aperture requirements of the deployable antenna of the truss,a combination unit and modular unit mechanism are developed based on this tetrahedral unit.The DOF and deployment characteristics of the modular unit mechanism are analyzed and validated through simulations.Various networking methods for the modular units are proposed,followed by a comprehensive performance comparison of different modular truss deployable antenna mechanisms.A prototype model of the modular unit mechanism is also developed,with deployment experiments demonstrating the mechanism's simplicity,low DOF,and large deployment ratio.The findings of this study provide a theoretical and technical basis for the future design and development of truss deployable antenna mechanisms.
基金Supported by National Natural Science Foundation of China(Grant No.51675366)Tianjin Research Program of Application Foundation and Advanced Technology(Grant Nos.16JCYBJC19300,15JCZDJC38900)
文摘Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines(PKMs). This requires that analytical description, formulation and operation for both finite and instantaneous motions are performed by the same mathematical tool. Based upon finite and instantaneous screw theory, a unified and systematic approach for topology design and kinematic analysis of PKMs is proposed in this paper. Using the derivative mapping between finite and instantaneous screws built in the authors’ previous work, the finite and instantaneous motions of PKMs are analytically described by the simple and non?redundant screws in quasi?vector and vector forms. And topological and parametric models of PKMs are algebraically formulated and related. These related topological and parametric models are ready to do type synthesis and kinematic analysis of PKMs under the unified framework of screw theory. In order to show the validity of the proposed approach, a kind of two?translational and three?rotational(2T3R)5?axis PKMs is taken as example. Numerous new structures of the 2T3R PKMs are synthe?sized as the results of topology design, and their Jacobian matrix is obtained easily for parameter optimization and performance evaluation. Some of the synthesized PKMs have outstanding capabilities in terms of large workspaces and flexible orientations, and have great potential for industrial applications of machining and manufacture. Among them, METROM PKM is a typical example which has attracted a lot of attention from global companies and already been developed as commercial products. The approach is a general and unified approach that can be used in the innovative design of different kinds of PKMs.
基金Supported by National Natural Science Foundation of China(Grant No.52405040)Research Project of State Key Laboratory of Mechanical System and Vibration(Grant No.MSV202514)。
文摘A cable-driven redundant manipulator(CDRM)characterized by redundant degrees of freedom and a lightweight,slender design can perform tasks in confined and restricted spaces efficiently.However,the complex multistage coupling between drive cables and passive joints in CDRM leads to a challenging dynamic model with difficult parameter identification,complicating the efforts to achieve accurate modeling and control.To address these challenges,this paper proposes a dynamic modeling and adaptive control approach tailored for CDRM systems.A multilevel kinematic model of the cable-driven redundant manipulator is presented,and a screw theory is employed to represent the cable tension and cable contact forces as spatial wrenches,which are equivalently mapped to joint torque using the principle of virtual work.This approach simplifies the mapping process while maintaining the integrity of the dynamic model.A recursive method is used to compute cable tension section-by-section for enhancing the efficiency of inverse dynamics calculations and meeting the high-frequency demands of the controller,thereby avoiding large matrix operations.An adaptive control method is proposed building on this foundation,which involves the design of a dynamic parameter adaptive controller in the joint space to simplify the linearization process of the dynamic equations along with a closed-loop controller that incorporates motor parameters in the driving space.This approach improves the control accuracy and dynamic performance of the CDRM under dynamic uncertainties.The accuracy and computational efficiency of the dynamic model are validated through simulations,and the effectiveness of the proposed control method is demonstrated through control tests.This paper presents a dynamic modeling and adaptive control approach for CDRM to enhance accuracy and performance under dynamic uncertainties.
基金Supported by National Natural Science Foundation of China(Grant No.52175019)Beijing Municipal Natural Science Foundation(Grant Nos.L222038,20240484699)+1 种基金Joint Funds of Industry-university-research of Shanghai Academy of Spaceflight Technology(Grant No.SAST2022-017)Beijing Municipal Key Laboratory of Space-ground Interconnection and Convergence of China and Key Laboratory of IoT Monitoring and Early Warning,Ministry of Emergency Management,Project‘Vice President of Science and Technology’of Changping District,Beijing.
文摘Current research on reconfigurable parallel mechanisms(RPMs)primarily focuses on achieving limited configuration changes,while mechanisms capable of extensive mode switching with distinct motion branches remain challenging to design.Conventional kinematotropic chains offer limited reconfigurability,underscoring the need for novel designs that enable broader operational adaptability.In this research,a novel diamond-like chain(DLC)with metamorphic units is proposed developed from generalized diamond kinematotropic chains.By altering the axes of the metamorphic units,the DLC realizes three distinct configurations,each corresponding to one of five motion branches characterized by bifurcation and metamorphic transitions.This DLC serves as the fundamental building block for constructing a reconfigurable hybrid limb.Using screw theory,the constraint properties of the limb in its five phases are analyzed and classified into three types:unconstrained limbs,limbs applying constraint forces,and limbs applying constraint couples.Based on this analysis,a RPM consisting of three reconfigurable limbs is developed.Its reconfigurability stems from the inherent bifurcation and metamorphic capabilities of the DLC-based limbs.This research introduces a RPM capable of controlled switching among ten distinct motion modes,with mobility ranging from three to six degrees of freedom.The proposed mechanism demonstrates high versatility and practical feasibility,offering a promising solution for applications requiring variable motion characteristics and adaptive performance.
基金Supported by National Natural Science Foundation of China(Grant Nos.52192634,52305015,52335003)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515011268)Science and Technology Innovation Committee of Shenzhen(Grant Nos.GXWD20231129102029003,KQTD20210811090146075).
文摘The intricate relationship between origami and mechanism underscores the fertile ground for innovation,which is particularly evident in the construction theory of thick-panel origami.Despite its potential,thick panel origami remains relatively unexplored in the context of single-loop metamorphic mechanisms.Drawing inspiration from thickpanel origami,particularly Miura origami,this study proposes a pioneering single-loop 6R multiple metamorphic mechanism.Through rigorous mathematical modeling(including the construction and resolution of the D-H closed-loop equation)and leveraging advanced analytical tools such as the screw theory and Lie theory,this study meticulously elucidates the planar,spherical,and Bennett motion branches of the mechanism.Furthermore,it delineates all the three bifurcation points between the motion branches,thereby providing a comprehensive understanding of the kinematic behavior of the mechanism.A metamorphic network can be constructed by applying several single-loop mechanisms to a symmetrical layout.Owing to its metamorphic properties,this network can act as a structural backbone for deployable antennas,aerospace shelters,and morphing wing units,thereby enabling a single mechanism to achieve multiple folding configurations.This paper not only introduces innovative metamorphic mechanisms but also suggests a promising method for uncovering and designing metamorphic mechanisms by developing new mechanisms from thick-panel origami.
