Aimed at the real-time forward kinematics solving problem of Stewart parallel manipulator in the control course, a mixed algorithm combining immune evolutionary algorithm and numerical iterative scheme is proposed. Fi...Aimed at the real-time forward kinematics solving problem of Stewart parallel manipulator in the control course, a mixed algorithm combining immune evolutionary algorithm and numerical iterative scheme is proposed. Firstly taking advantage of simpleness of inverse kinematics, the forward kinematics is transformed to an optimal problem. Immune evolutionary algorithm is employed to find approximate solution of this optimal problem in manipulator＇s workspace. Then using above solution as iterative initialization, a speedy numerical iterative scheme is proposed to get more precise solution. In the manipulator running course, the iteration initialization can be selected as the last period position and orientation. Because the initialization is closed to correct solution, solving precision is high and speed is rapid enough to satisfy real-time requirement. This mixed forward kinematics algorithm is applied to real Stewart parallel manipulator in the real-time control course. The examination result shows that the algorithm is very efficient and practical.展开更多
In order to obtain direct solutions of parallel manipulator without divergence in real time,a modified global Newton-Raphson(MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom(DOF) p...In order to obtain direct solutions of parallel manipulator without divergence in real time,a modified global Newton-Raphson(MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom(DOF) parallel manipulator.Based on geometrical frame of parallel manipulator,the highly nonlinear equations of kinematics were derived using analytical approach.The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration.The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio.NET for implementation.The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed.Applying the MGNR algorithm,the real generalized pose of moving platform is solved by using the set of given positions of actuators.The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy(1×10-9 m in linear motion and 1×10-9 rad in angular motion),even the initial guess value is far from the root.展开更多
The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism...The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.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
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
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
利用有限元通用软件 ANSYS建立了大射电望远镜精调 Stewart 平台并联机器人的有限元模型;采用ANSYS参数化设计语言(APDL)实现了该模型的参数化设计;通过对任意位姿结构进行模态分析,计算出并联机器人在其工作空间内的固有频率分布;... 利用有限元通用软件 ANSYS建立了大射电望远镜精调 Stewart 平台并联机器人的有限元模型;采用ANSYS参数化设计语言(APDL)实现了该模型的参数化设计;通过对任意位姿结构进行模态分析,计算出并联机器人在其工作空间内的固有频率分布;根据伺服系统设计原则,确定了该并联机器人的伺服带宽。展开更多
文摘Aimed at the real-time forward kinematics solving problem of Stewart parallel manipulator in the control course, a mixed algorithm combining immune evolutionary algorithm and numerical iterative scheme is proposed. Firstly taking advantage of simpleness of inverse kinematics, the forward kinematics is transformed to an optimal problem. Immune evolutionary algorithm is employed to find approximate solution of this optimal problem in manipulator＇s workspace. Then using above solution as iterative initialization, a speedy numerical iterative scheme is proposed to get more precise solution. In the manipulator running course, the iteration initialization can be selected as the last period position and orientation. Because the initialization is closed to correct solution, solving precision is high and speed is rapid enough to satisfy real-time requirement. This mixed forward kinematics algorithm is applied to real Stewart parallel manipulator in the real-time control course. The examination result shows that the algorithm is very efficient and practical.
基金Project(HgdJG00401D04) supported by National 921 Manned Space Project Foundation of ChinaProject(SKLRS200803B) supported by the Self-Planned Task Foundation of State Key Laboratory of Robotics and System (HIT) of China+1 种基金Project(CDAZ98502211) supported by China’s "World Class University (985)" Project FoundationProject(50975055) supported by the National Natural Science Foundation of China
文摘In order to obtain direct solutions of parallel manipulator without divergence in real time,a modified global Newton-Raphson(MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom(DOF) parallel manipulator.Based on geometrical frame of parallel manipulator,the highly nonlinear equations of kinematics were derived using analytical approach.The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration.The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio.NET for implementation.The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed.Applying the MGNR algorithm,the real generalized pose of moving platform is solved by using the set of given positions of actuators.The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy(1×10-9 m in linear motion and 1×10-9 rad in angular motion),even the initial guess value is far from the root.
文摘The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.
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.
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.
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.
