Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a c...Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.展开更多
Parallel robots with SCARA(selective compliance assembly robot arm) motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parall...Parallel robots with SCARA(selective compliance assembly robot arm) motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.展开更多
A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Base...A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.展开更多
This paper focus on the accuracy enhancement of parallel kinematics machine through kinematics calibration. In the calibration processing, well-structured identification Jacobian matrix construction and end-effector p...This paper focus on the accuracy enhancement of parallel kinematics machine through kinematics calibration. In the calibration processing, well-structured identification Jacobian matrix construction and end-effector position and orientation measurement are two main difficulties. In this paper, the identification Jacobian matrix is constructed easily by numerical calculation utilizing the unit virtual velocity method. The generalized distance errors model is presented for avoiding measuring the position and orientation directly which is difficult to be measured. At last, a measurement tool is given for acquiring the data points in the calibration processing. Experimental studies confirmed the effectiveness of method. It is also shown in the paper that the proposed approach can be applied to other typed parallel manipulators.展开更多
Parallel kinematic machines (PKMs) have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attract...Parallel kinematic machines (PKMs) have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.展开更多
In order to improve the low output accuracy caused by the elastic deformations of the branch chains,a finite element-based dynamic accuracy analysis method for parallel mechanisms is proposed in this paper.First,takin...In order to improve the low output accuracy caused by the elastic deformations of the branch chains,a finite element-based dynamic accuracy analysis method for parallel mechanisms is proposed in this paper.First,taking a 5-prismatic-spherical-spherical(PSS)/universal-prismatic-universal(UPU)parallel mechanism as an example,the error model is established by a closed vector chain method,while its influence on the dynamic accuracy of the parallel mechanism is analyzed through numerical simulation.According to the structural and error characteristics of the parallel mechanism,a vector calibration algorithm is proposed to reduce the position and pose errors along the whole motion trajectory.Then,considering the elastic deformation of the rod,the rigid-flexible coupling dynamic equations of each component are established by combining the finite element method with the Lagrange method.The elastodynamic model of the whole machine is obtained based on the constraint condition of each moving part,and the correctness of the model is verified by simulation.Moreover,the effect of component flexibility on the dimensionless root mean square error of the displacement,velocity and acceleration of the moving platform is investigated by using a Newmark method,and the mapping relationship of these dimensionless root mean square errors to dynamic accuracy is further studied.The research work provides a theoretical basis for the design of the parameter size of the prototype.展开更多
To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method a...To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method and genetic algorithm are introduced for the forward kinematic solution.Based onthe inverse and forward kinematic solutions,the end-effector s error calculation procedure is developed.To solve the accuracy problem caused by the length and angular parameters' different units,a normalizationmethod is proposed based on the manufacturing tolerance.Comparison between the error analysis resultscalculated by the traditional method and the numerical method for a 4RRR PKM shows that,this numericalerror analysis method is more accurate,simpler,and can evaluate the machine s real error basedon the manufacturing tolerance.展开更多
Existing errors in the structure and kinematic parameters of multi-legged walking robots,the motion trajectory of robot will diverge from the ideal sports requirements in movement.Since the existing error compensation...Existing errors in the structure and kinematic parameters of multi-legged walking robots,the motion trajectory of robot will diverge from the ideal sports requirements in movement.Since the existing error compensation is usually used for control compensation of manipulator arm,the error compensation of multi-legged robots has seldom been explored.In order to reduce the kinematic error of robots,a motion error compensation method based on the feedforward for multi-legged mobile robots is proposed to improve motion precision of a mobile robot.The locus error of a robot body is measured,when robot moves along a given track.Error of driven joint variables is obtained by error calculation model in terms of the locus error of robot body.Error value is used to compensate driven joint variables and modify control model of robot,which can drive the robots following control model modified.The model of the relation between robot's locus errors and kinematic variables errors is set up to achieve the kinematic error compensation.On the basis of the inverse kinematics of a multi-legged walking robot,the relation between error of the motion trajectory and driven joint variables of robots is discussed.Moreover,the equation set is obtained,which expresses relation among error of driven joint variables,structure parameters and error of robot's locus.Take MiniQuad as an example,when the robot MiniQuad moves following beeline tread,motion error compensation is studied.The actual locus errors of the robot body are measured before and after compensation in the test.According to the test,variations of the actual coordinate value of the robot centroid in x-direction and z-direction are reduced more than one time.The kinematic errors of robot body are reduced effectively by the use of the motion error compensation method based on the feedforward.展开更多
This paper presents an error modeling methodology that enables the tolerance design, assembly and kinematic calibration of a class of 3-DOF parallel kinematic machines with parallelogram struts to be integrated into a...This paper presents an error modeling methodology that enables the tolerance design, assembly and kinematic calibration of a class of 3-DOF parallel kinematic machines with parallelogram struts to be integrated into a unified framework. The error mapping function is formulated to identify the source errors affecting the uncompensable pose error. The sensitivity analysis in the sense of statistics is also carried out to investigate the influences of source errors on the pose accuracy. An assembly process that can effectively minimize the uncompensable pose error is proposed as one of the results of this investigation.展开更多
This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignore...This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore,two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.展开更多
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....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.展开更多
A detailed fracture mechanics analysis of bridge-toughening in a fiber reinforced composite is presented in this paper. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for...A detailed fracture mechanics analysis of bridge-toughening in a fiber reinforced composite is presented in this paper. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite with interfacial layer is derived from the Castigliano's theorem and interface shear-lag model. A numerical result of the COD equation is obtained using the iteration solution of the second Fredholm integral equation. In order to investigate the effect of various parameters on the toughening, an approximate analytical solution of the equation is present and its error analysis is performed, which demonstrates the approximate solution to be appropriate. A parametric study of the influence of the crack length, interfacial shear modules, thickness of the interphase, fiber radius, fiber volume fraction and properties of materials on composite toughening is therefore carried out. The results are useful for experimental demonstration and toughening design including the fabrication process of the composite.展开更多
基金Supported by National Key Research and Development Program of China(Grant No.2019YFA0709001)National Natural Science Foundation of China(Grant Nos.52022056,51875334,52205031 and 52205034)National Key Research and Development Program of China(Grant No.2017YFE0111300).
文摘Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.
基金Supported by National Natural Science Foundation of China(Grant No.51305222)National Key Scientific and Technological Program of China(Grant No.2013ZX04001-021)
文摘Parallel robots with SCARA(selective compliance assembly robot arm) motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.
基金Preject 50225519 supported by the National Outstanding Youth Science Foundation of China
文摘A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.
文摘This paper focus on the accuracy enhancement of parallel kinematics machine through kinematics calibration. In the calibration processing, well-structured identification Jacobian matrix construction and end-effector position and orientation measurement are two main difficulties. In this paper, the identification Jacobian matrix is constructed easily by numerical calculation utilizing the unit virtual velocity method. The generalized distance errors model is presented for avoiding measuring the position and orientation directly which is difficult to be measured. At last, a measurement tool is given for acquiring the data points in the calibration processing. Experimental studies confirmed the effectiveness of method. It is also shown in the paper that the proposed approach can be applied to other typed parallel manipulators.
基金supported by Tianjin Research Program of Application Foundation and Advanced Technology of China (Grant No.11JCZDJC22700)National Natural Science Foundation of China (GrantNo. 51075295,Grant No. 50675151)+1 种基金National High-tech Research and Development Program of China (863 Program,Grant No.2007AA042001)PhD Programs Foundation of Ministry of Education of China (Grant No. 20060056018)
文摘Parallel kinematic machines (PKMs) have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.
基金Supported by the National Natural Science Foundation of China(Grant Nos.U21A20122,51975523 and 51905481)the Natural Science Foundation of Zhejiang Province(Grant No.LY22E050012)the Students in Zhejiang Province Science and technology Innovation Plan(Grant No.2020R403054).
文摘In order to improve the low output accuracy caused by the elastic deformations of the branch chains,a finite element-based dynamic accuracy analysis method for parallel mechanisms is proposed in this paper.First,taking a 5-prismatic-spherical-spherical(PSS)/universal-prismatic-universal(UPU)parallel mechanism as an example,the error model is established by a closed vector chain method,while its influence on the dynamic accuracy of the parallel mechanism is analyzed through numerical simulation.According to the structural and error characteristics of the parallel mechanism,a vector calibration algorithm is proposed to reduce the position and pose errors along the whole motion trajectory.Then,considering the elastic deformation of the rod,the rigid-flexible coupling dynamic equations of each component are established by combining the finite element method with the Lagrange method.The elastodynamic model of the whole machine is obtained based on the constraint condition of each moving part,and the correctness of the model is verified by simulation.Moreover,the effect of component flexibility on the dimensionless root mean square error of the displacement,velocity and acceleration of the moving platform is investigated by using a Newmark method,and the mapping relationship of these dimensionless root mean square errors to dynamic accuracy is further studied.The research work provides a theoretical basis for the design of the parameter size of the prototype.
基金Supported by the National High Technology Research and Development Programme of China ( No. 2007AA041901 )the National Natural Science Foundation of China ( No. 50775117 )+1 种基金the National S&T Major Project ( No. 2009XZ04001-025 )the Technology Innovation Fund of AVIC ( No.2009E 13224 )
文摘To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method and genetic algorithm are introduced for the forward kinematic solution.Based onthe inverse and forward kinematic solutions,the end-effector s error calculation procedure is developed.To solve the accuracy problem caused by the length and angular parameters' different units,a normalizationmethod is proposed based on the manufacturing tolerance.Comparison between the error analysis resultscalculated by the traditional method and the numerical method for a 4RRR PKM shows that,this numericalerror analysis method is more accurate,simpler,and can evaluate the machine s real error basedon the manufacturing tolerance.
基金supported by National Natural Science Foundation of China (Grant Nos. 50675079,50875246)Program for Innovative Research Team (in Science and Technology) in University of Henan Province,China
文摘Existing errors in the structure and kinematic parameters of multi-legged walking robots,the motion trajectory of robot will diverge from the ideal sports requirements in movement.Since the existing error compensation is usually used for control compensation of manipulator arm,the error compensation of multi-legged robots has seldom been explored.In order to reduce the kinematic error of robots,a motion error compensation method based on the feedforward for multi-legged mobile robots is proposed to improve motion precision of a mobile robot.The locus error of a robot body is measured,when robot moves along a given track.Error of driven joint variables is obtained by error calculation model in terms of the locus error of robot body.Error value is used to compensate driven joint variables and modify control model of robot,which can drive the robots following control model modified.The model of the relation between robot's locus errors and kinematic variables errors is set up to achieve the kinematic error compensation.On the basis of the inverse kinematics of a multi-legged walking robot,the relation between error of the motion trajectory and driven joint variables of robots is discussed.Moreover,the equation set is obtained,which expresses relation among error of driven joint variables,structure parameters and error of robot's locus.Take MiniQuad as an example,when the robot MiniQuad moves following beeline tread,motion error compensation is studied.The actual locus errors of the robot body are measured before and after compensation in the test.According to the test,variations of the actual coordinate value of the robot centroid in x-direction and z-direction are reduced more than one time.The kinematic errors of robot body are reduced effectively by the use of the motion error compensation method based on the feedforward.
基金This work was supported by the National Natural Science Foundation of China (Grant No.50075006) the Royal Society UK-China Joint Research Grant and Tianjin Scientce and Technology Commission(Grant No.003802111).
文摘This paper presents an error modeling methodology that enables the tolerance design, assembly and kinematic calibration of a class of 3-DOF parallel kinematic machines with parallelogram struts to be integrated into a unified framework. The error mapping function is formulated to identify the source errors affecting the uncompensable pose error. The sensitivity analysis in the sense of statistics is also carried out to investigate the influences of source errors on the pose accuracy. An assembly process that can effectively minimize the uncompensable pose error is proposed as one of the results of this investigation.
基金supported by the National Natural Science Foundation of China [No. 51475321]Tianjin Research Program of Application Foundation and Advanced Technology [No. 15JCZDJC38900 and 16JCYBJC19300]the International Postdoctoral Exchange Fellowship Program [No. 32 Document of OCPC, 2017]
文摘This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore,two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.
文摘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.
基金National Natural Science Foundatjon and China Postdoctoral Scjence Fbundation
文摘A detailed fracture mechanics analysis of bridge-toughening in a fiber reinforced composite is presented in this paper. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite with interfacial layer is derived from the Castigliano's theorem and interface shear-lag model. A numerical result of the COD equation is obtained using the iteration solution of the second Fredholm integral equation. In order to investigate the effect of various parameters on the toughening, an approximate analytical solution of the equation is present and its error analysis is performed, which demonstrates the approximate solution to be appropriate. A parametric study of the influence of the crack length, interfacial shear modules, thickness of the interphase, fiber radius, fiber volume fraction and properties of materials on composite toughening is therefore carried out. The results are useful for experimental demonstration and toughening design including the fabrication process of the composite.