A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and ...A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and effective accuracy analysis method for parallel manipulator is still needed. In order to enhance solution efficiency, an interval analysis method（lA method） is introduced to solve the terminal error bound of the Stewart platform with detailed solution path. Taking a terminal pose of the Stewart platform in FAST as an example, the terminal error is solved by the Monte Carlo method（MC method） by 4 980 s, the stochastic mathematical method（SM method） by 0.078 s, and the IA method by 2.203 s. Compared with MC method, the terminal error by SM method leads a 20% underestimate while the IA method can envelop the real error bound of the Stewart platform. This indicates that the IA method outperforms the other two methods by providing quick calculations and enveloping the real error bound of the Stewart platform. According to the given structural error of the dimension parameters of the Stewart platform, the IA method gives a maximum position error of 19.91 mm and maximum orientation error of 0.534°, which suggests that the IA method can be used for accuracy design of the Stewart platfbnn in FAST. The 1A method presented is a rapid and effective accuracy analysis method for Stewart platform.展开更多
2015年7月,英国上诉法院布里格斯大法官接受首席大法官和案卷主事官的委托,为司法部"法院与裁判所事务局"(HMCTS)推行法院改革提供支持。布里格斯大法官组建研究团队,包括斯图尔特法官(Mr Justice Stephen Stewart)、伯德法官...2015年7月,英国上诉法院布里格斯大法官接受首席大法官和案卷主事官的委托,为司法部"法院与裁判所事务局"(HMCTS)推行法院改革提供支持。布里格斯大法官组建研究团队,包括斯图尔特法官(Mr Justice Stephen Stewart)、伯德法官(HH Judge Nigel Bird)、莱瑟姆法官(District Judge Christopher Lethem)、古德曼先生(Richard Goodman),于2015年12月发布《民事法院结构改革中期报告》,公开征集各方意见;并在此基础之上,于2016年7月发布《民事法院结构改革最终报告》。《最终报告》的第六部分"在线法院"既是整篇报告的亮点,也是司法改革的热点。法院现代化建设是英国政府自1873年以来一次性投入资金最多的司法改革项目。在线法院作为其中的核心工程,既是英国追求数字时代司法公正的必然选择,也承载了复兴英国司法的梦想:在线法律服务将会成为英国经济的增长点,将会成为英国竞争的软实力。英国民事法院改革的整体理念就是要建立一个公正、适当、便捷的法院——传承历史的辉煌,继续引领世界潮流。英国人一边忧心忡忡地盘算着,在线法院这么"烧钱",世界上又没有成功的先例可供模仿,这场改革简直就是"摸着石头过河"!一边又对新建在线法院摩拳擦掌,跃跃欲试。作风一向沉稳的布里格斯大法官也变得矛盾起来:他一方面精打细算、谨小慎微;一方面又豪爽大气、敢为天下先。他的态度明确而坚决,因为他认为:传统法院是工业化时代的结果,而在线法院是互联网时代的产物;传统法院必将衰落,在线法院必将崛起。为了实现建立在线法院的目标,即便付出的时间、金钱和努力都付诸东流也在所不惜!在线法院将是这个时代里最具革命性、最具颠覆性的新型法院;在线法院将改变法院生产正义的方式以及当事人实现正义的途径。这才是在线法院开创的新时代;这才是我们期待�展开更多
There is proposed an adaptive sliding controller in task space on the base of the linear Newton-Euler dynamic equation of motion platform in a six-DOF flight simulator. The uncertain parameters are divided into two gr...There is proposed an adaptive sliding controller in task space on the base of the linear Newton-Euler dynamic equation of motion platform in a six-DOF flight simulator. The uncertain parameters are divided into two groups： the constant and the time-varying. The controller identifies constant uncertain parameters using nonlinear adaptive controller associated with elimination of the influences of time-varying uncertain parameters and compensation of the external disturbance using sliding control. The results of numerical simulation attest to the capability of this control scheme not only to, with deadly accuracy, identify parameters of motion platform such as load, inertia moments and mass center, but also effectively improve the robustness of the system.展开更多
A ground-based hardware-in-the-loop （HIL） simulation system with hydraulically driven Stewart platform for spacecraft docking simulation is presented. The system is used for simulating docking process of the on-orbi...A ground-based hardware-in-the-loop （HIL） simulation system with hydraulically driven Stewart platform for spacecraft docking simulation is presented. The system is used for simulating docking process of the on-orbit spacecraft. Principle and structure of the six-degree-of-freedom simulation system are introduced. The docking process dynamic of the vehicles is modeled. Experiment results and mathematical simulation data are compared to validating the simulation system. The comparisons of the results prove that the simulation system proposed can effectively simulate the on-orbit docking process of the spacecraft.展开更多
The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially ...The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially for Stewart platform.Recently,several scholars make their great contribution to the effective solution of this problem,but neither of them find the right answer.This paper gives a brief analysis of the kinematics of the Stewart platform and derives the Jacobian matrices of the system through the velocity equation.On the basis of the traditional classification of singularities,the second type of singularity is investigated.An assumption of any three of the six variables of the Stewart platform as constant is made,then the analytical expression of singularity locus equation of the second type singularity which contains another three pose variables is obtained.The singularity locus is represented in the three-dimensional space through the derived equation.The correctness and validity of the proposed method are verified through examples.Finally,the singularity analysis of an electric Stewart platform in its desired workspace and reachable workspace is implemented.Thus,one can easily identify whether singularity exists in a given workspace of a Stewart platform and determine whether the existed singularity can be avoided through the proposed method.The proposed method also provides theoretical principle for the design and application of the Stewart platform and has great significance for the trajectory planning and control.展开更多
The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensive...The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra（CGA）. The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.展开更多
A safety mechanism capable of moving at will within the range of its whole link lengths is designed based on the link space. Sixteen extreme poses are obtained in a Stewart platform. The singular points of the extreme...A safety mechanism capable of moving at will within the range of its whole link lengths is designed based on the link space. Sixteen extreme poses are obtained in a Stewart platform. The singular points of the extreme poses are solved by using homotopy method as well as the judgment condition of singular points, and thereby the maximum link lengths are achieved. The rotation angles of joints and the distances between two neighboring links are analyzed in a calculation example in which that the mechanism moves among the extreme poses is assumed. Then an algorithm to test the safety mechanism is presented taking the constraint conditions into account. A safety mechanism having optimal properties of global movement is worked out by optimizing all structural parameters through minimizing the average condition number of extreme poses.展开更多
The kinematic design issue of Gough-Stewart platforms is investigated. Based upon a full understanding of the geometrical characteristics of workspace boundary, a spherically-shaped prescribed workspace having a given...The kinematic design issue of Gough-Stewart platforms is investigated. Based upon a full understanding of the geometrical characteristics of workspace boundary, a spherically-shaped prescribed workspace having a given orientation capability is defined for the synthesis of a well behaved workspace. Two performance measures are presented, i.e. the local dexterity and workspace radius ratio. The dimensions of the platform are determined with a prior knowledge of how the design parameters affect the dexterity and workspace radius ratio, resulting in an optimal design in terms of these performance indices. An example of application to the kinematic design of a hexapod machine tool is given to illustrate the effectiveness of this approach.展开更多
Optimum design is a key approach to make full use of potential advantages of a parallel manipulator. The optimum design of multi-parameter parallel manipulators（more than three design parameters）, such as Stewart ma...Optimum design is a key approach to make full use of potential advantages of a parallel manipulator. The optimum design of multi-parameter parallel manipulators（more than three design parameters）, such as Stewart manipulator, relies on analysis based and algorithm based optimum design methods, which fall to be accurate or intuitive. To solve this problem and achieve both accurate and intuition, atlas based optimum design of a general Stewart parallel manipulator is established, with rational selection of design parameters. Based on the defined spherical usable workspace（SUW）, primary kinematic performance indices of the Stewart manipulator involving workspace and condition number are introduced and analyzed. Then, corresponding performance atlases are drawn with the established non-dimensional design space, and impact of joint distribution angles on the manipulator performance is analyzed and illustrated. At last, an example on atlas based optimum design of the Stewart manipulator is accomplished to illustrate the optimum design process, considering the end-effector posture. Deduced atlases can be flexibly applied to both quantitative and qualitative analysis to get the desired optimal design for the Stewart manipulator with respect to related performance requirements. Besides, the established optimum design method can be further applied to other multi-parameter parallel manipulators.展开更多
Active vibration control is needed for future space telescopes, space laser communication and other precision sensitive payloads which require ultra-quiet environments. A Stewart platform based hybrid isolator with 6 ...Active vibration control is needed for future space telescopes, space laser communication and other precision sensitive payloads which require ultra-quiet environments. A Stewart platform based hybrid isolator with 6 hybrid struts is the effective system for active/passive vibration isolation over 5-250 Hz band. Using an identification transfer matrix of the Stewart platform, the coupling analysis of six channels is provided. A dynamics model is derived, and the rigid mode is removed to keep the signal of pointing control. Multi objective robust H∞ and μ synthesis strategies, based on singular values and structured singular values respectively, are presented, which simultaneously satisfy the low frequency pointing and high frequency disturbance rejection requirements and take account of the model uncertainty, parametric uncertainty and sensor noise. Then, by performing robust stability test, it is shown that the two controllers are robust to the uncertainties, the robust stability margin of H, controller is less than that of μ controller, but the order of μ controller is higher than that of H, controller, so the balanced controller reduction is provided. Additionally, the μ controller is compared with a PI controller. The time domain simulation of the μ controller indicates that the two robust control strategies are effective for keeping the pointing command and isolating the harmonic and stochastic disturbances.展开更多
A novel methodology is presented for the workspace analysis of Stewart parallel manipulators. The workspace is defined that enables a description to be made in a unified framework of both the position and orientation ...A novel methodology is presented for the workspace analysis of Stewart parallel manipulators. The workspace is defined that enables a description to be made in a unified framework of both the position and orientation capabilities of the mobile platform. Given the orientation capability of the mobile platform, the piecewise closed solution to the workspace boundary is formulated. It is indicated for the first time that the workspace boundary is in fact the cap of twelve envelope surfaces, each of which is generated by a family of spherical surfaces having the movable center located on a two\|branch closed spherical curve. Two examples are given to illustrate the effectiveness of this approach.展开更多
Despite small workspace, parallel manipulators have some advantages over their serial counterparts in terms of higher speed, acceleration, rigidity, accuracy, manufacturing cost and payload. Accordingly, this type of ...Despite small workspace, parallel manipulators have some advantages over their serial counterparts in terms of higher speed, acceleration, rigidity, accuracy, manufacturing cost and payload. Accordingly, this type of manipulators can be used in many applications such as in high-speed machine tools, tuning machine for feeding, sensitive cutting, assembly and packaging. This paper presents a special type of planar parallel manipulator with three degrees of freedom. It is constructed as a variable geometry truss generally known planar Stewart platform. The reachable and orientation workspaces are obtained for this manipulator. The inverse kinematic analysis is solved for the trajectory tracking according to the redundancy and joint limit avoidance. Then, the dynamics model of the manipulator is established by using Virtual Work method. The simulations are performed to follow the given planar trajectories by using the dynamic equations of the variable geometry truss manipulator and computed force control method. In computed force control method, the feedback gain matrices for PD control are tuned with fixed matrices by trail end error and variable ones by means of optimization with genetic algorithm.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10973023,11103046,11203048)
文摘A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and effective accuracy analysis method for parallel manipulator is still needed. In order to enhance solution efficiency, an interval analysis method（lA method） is introduced to solve the terminal error bound of the Stewart platform with detailed solution path. Taking a terminal pose of the Stewart platform in FAST as an example, the terminal error is solved by the Monte Carlo method（MC method） by 4 980 s, the stochastic mathematical method（SM method） by 0.078 s, and the IA method by 2.203 s. Compared with MC method, the terminal error by SM method leads a 20% underestimate while the IA method can envelop the real error bound of the Stewart platform. This indicates that the IA method outperforms the other two methods by providing quick calculations and enveloping the real error bound of the Stewart platform. According to the given structural error of the dimension parameters of the Stewart platform, the IA method gives a maximum position error of 19.91 mm and maximum orientation error of 0.534°, which suggests that the IA method can be used for accuracy design of the Stewart platfbnn in FAST. The 1A method presented is a rapid and effective accuracy analysis method for Stewart platform.
文摘There is proposed an adaptive sliding controller in task space on the base of the linear Newton-Euler dynamic equation of motion platform in a six-DOF flight simulator. The uncertain parameters are divided into two groups： the constant and the time-varying. The controller identifies constant uncertain parameters using nonlinear adaptive controller associated with elimination of the influences of time-varying uncertain parameters and compensation of the external disturbance using sliding control. The results of numerical simulation attest to the capability of this control scheme not only to, with deadly accuracy, identify parameters of motion platform such as load, inertia moments and mass center, but also effectively improve the robustness of the system.
文摘A ground-based hardware-in-the-loop （HIL） simulation system with hydraulically driven Stewart platform for spacecraft docking simulation is presented. The system is used for simulating docking process of the on-orbit spacecraft. Principle and structure of the six-degree-of-freedom simulation system are introduced. The docking process dynamic of the vehicles is modeled. Experiment results and mathematical simulation data are compared to validating the simulation system. The comparisons of the results prove that the simulation system proposed can effectively simulate the on-orbit docking process of the spacecraft.
基金supported by Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No.NCET-04-0325)
文摘The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially for Stewart platform.Recently,several scholars make their great contribution to the effective solution of this problem,but neither of them find the right answer.This paper gives a brief analysis of the kinematics of the Stewart platform and derives the Jacobian matrices of the system through the velocity equation.On the basis of the traditional classification of singularities,the second type of singularity is investigated.An assumption of any three of the six variables of the Stewart platform as constant is made,then the analytical expression of singularity locus equation of the second type singularity which contains another three pose variables is obtained.The singularity locus is represented in the three-dimensional space through the derived equation.The correctness and validity of the proposed method are verified through examples.Finally,the singularity analysis of an electric Stewart platform in its desired workspace and reachable workspace is implemented.Thus,one can easily identify whether singularity exists in a given workspace of a Stewart platform and determine whether the existed singularity can be avoided through the proposed method.The proposed method also provides theoretical principle for the design and application of the Stewart platform and has great significance for the trajectory planning and control.
基金Supported by National Natural Science Foundation of China(Grant No.51375059)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA040203)+1 种基金Special Fund for Agro-scientific Research in the Public Interest of China(Grant No.201313009-06)National Key Technology R&D Program of the Ministry of Science and Technology of China(Grant No.2013BAD17B06)
文摘The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra（CGA）. The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.
文摘A safety mechanism capable of moving at will within the range of its whole link lengths is designed based on the link space. Sixteen extreme poses are obtained in a Stewart platform. The singular points of the extreme poses are solved by using homotopy method as well as the judgment condition of singular points, and thereby the maximum link lengths are achieved. The rotation angles of joints and the distances between two neighboring links are analyzed in a calculation example in which that the mechanism moves among the extreme poses is assumed. Then an algorithm to test the safety mechanism is presented taking the constraint conditions into account. A safety mechanism having optimal properties of global movement is worked out by optimizing all structural parameters through minimizing the average condition number of extreme poses.
基金Project supported by the National Natural Science Foundation of China (Grant No. 59775006) other financial sources.
文摘The kinematic design issue of Gough-Stewart platforms is investigated. Based upon a full understanding of the geometrical characteristics of workspace boundary, a spherically-shaped prescribed workspace having a given orientation capability is defined for the synthesis of a well behaved workspace. Two performance measures are presented, i.e. the local dexterity and workspace radius ratio. The dimensions of the platform are determined with a prior knowledge of how the design parameters affect the dexterity and workspace radius ratio, resulting in an optimal design in terms of these performance indices. An example of application to the kinematic design of a hexapod machine tool is given to illustrate the effectiveness of this approach.
基金Supported by National Natural Science Foundation of China(Grant Nos.51205224,51475252)National Outstanding Youth Science Foundation of China(Grant No.51225503)
文摘Optimum design is a key approach to make full use of potential advantages of a parallel manipulator. The optimum design of multi-parameter parallel manipulators（more than three design parameters）, such as Stewart manipulator, relies on analysis based and algorithm based optimum design methods, which fall to be accurate or intuitive. To solve this problem and achieve both accurate and intuition, atlas based optimum design of a general Stewart parallel manipulator is established, with rational selection of design parameters. Based on the defined spherical usable workspace（SUW）, primary kinematic performance indices of the Stewart manipulator involving workspace and condition number are introduced and analyzed. Then, corresponding performance atlases are drawn with the established non-dimensional design space, and impact of joint distribution angles on the manipulator performance is analyzed and illustrated. At last, an example on atlas based optimum design of the Stewart manipulator is accomplished to illustrate the optimum design process, considering the end-effector posture. Deduced atlases can be flexibly applied to both quantitative and qualitative analysis to get the desired optimal design for the Stewart manipulator with respect to related performance requirements. Besides, the established optimum design method can be further applied to other multi-parameter parallel manipulators.
文摘Active vibration control is needed for future space telescopes, space laser communication and other precision sensitive payloads which require ultra-quiet environments. A Stewart platform based hybrid isolator with 6 hybrid struts is the effective system for active/passive vibration isolation over 5-250 Hz band. Using an identification transfer matrix of the Stewart platform, the coupling analysis of six channels is provided. A dynamics model is derived, and the rigid mode is removed to keep the signal of pointing control. Multi objective robust H∞ and μ synthesis strategies, based on singular values and structured singular values respectively, are presented, which simultaneously satisfy the low frequency pointing and high frequency disturbance rejection requirements and take account of the model uncertainty, parametric uncertainty and sensor noise. Then, by performing robust stability test, it is shown that the two controllers are robust to the uncertainties, the robust stability margin of H, controller is less than that of μ controller, but the order of μ controller is higher than that of H, controller, so the balanced controller reduction is provided. Additionally, the μ controller is compared with a PI controller. The time domain simulation of the μ controller indicates that the two robust control strategies are effective for keeping the pointing command and isolating the harmonic and stochastic disturbances.
文摘A novel methodology is presented for the workspace analysis of Stewart parallel manipulators. The workspace is defined that enables a description to be made in a unified framework of both the position and orientation capabilities of the mobile platform. Given the orientation capability of the mobile platform, the piecewise closed solution to the workspace boundary is formulated. It is indicated for the first time that the workspace boundary is in fact the cap of twelve envelope surfaces, each of which is generated by a family of spherical surfaces having the movable center located on a two\|branch closed spherical curve. Two examples are given to illustrate the effectiveness of this approach.
文摘Despite small workspace, parallel manipulators have some advantages over their serial counterparts in terms of higher speed, acceleration, rigidity, accuracy, manufacturing cost and payload. Accordingly, this type of manipulators can be used in many applications such as in high-speed machine tools, tuning machine for feeding, sensitive cutting, assembly and packaging. This paper presents a special type of planar parallel manipulator with three degrees of freedom. It is constructed as a variable geometry truss generally known planar Stewart platform. The reachable and orientation workspaces are obtained for this manipulator. The inverse kinematic analysis is solved for the trajectory tracking according to the redundancy and joint limit avoidance. Then, the dynamics model of the manipulator is established by using Virtual Work method. The simulations are performed to follow the given planar trajectories by using the dynamic equations of the variable geometry truss manipulator and computed force control method. In computed force control method, the feedback gain matrices for PD control are tuned with fixed matrices by trail end error and variable ones by means of optimization with genetic algorithm.
