This paper presents a classification on the workspaces of planar serial three-link manipulators, that is, position workspace and orientation angle workspace. Position workspace indicates the region reached by the refe...This paper presents a classification on the workspaces of planar serial three-link manipulators, that is, position workspace and orientation angle workspace. Position workspace indicates the region reached by the reference point on the end-effector. Orientation angle workspace indicates a set of angle ranges by which the end-effector can reach with certain orientation for every point in the reachable position workspace. By introducing a virtual equivalent mechanism, reachable position workspace can be di- vided into several Grashof intervals and non-Grashof intervals. The calculation equations of orientation angle workspace are deduced in three situations according to the relationships among four link lengths in the virtual four-bar chain. Three examples are given for three kinds of relationship of link lengths. The orientation angle workspace of extended groups, that is, two of the three link lengths equal, and the orientation angle workspace when the reference point on the end-effector moves along a non-radial direction are also discussed. A program is developed to calculate orientation angle workspaces and output variation curves of orientation angle workspace and key data within the position workspace. The approach and program in this paper can be used for fast calculation and identification of the variation rule of the orientation angle workspace of any given planar serial three-link manipulator on the basis of its link parameters, and for the design of a highly dexterous serial manipulator with proposed link rela- tions.展开更多
This paper presents a new method of analyzing the orientation angle rotatability of a planar serial n-link manipulator by examining the rotatability of its virtual equivalent mechanism.Workspace orientation boundary r...This paper presents a new method of analyzing the orientation angle rotatability of a planar serial n-link manipulator by examining the rotatability of its virtual equivalent mechanism.Workspace orientation boundary region decomposition is proposed based on the polynomial discriminant derived from a serial three-link manipulator.Orientation angle workspace indicates a set of angle ranges by which the end-effector can reach with certain orientation for every point in the reachable position workspace.By introducing a virtual equivalent mechanism,the open-chain kinematic problem is converted into a close-chain mechanism,and the Grashof-type condition is used to examine the rotatability of the end-effector link.The reachable position workspace can be divided into several Grashof intervals and non-Grashof intervals based on the extreme positions and singular configurations of a manipulator.The derived equations in this paper can be used to calculate the variation rule of the orientation angle workspace of any given planar serial n-link manipulator on the basis of its link parameters.The orientation angle rotatability of a seven-link serial manipulator is solved by the proposed method and graphical representations of the orientation angle workspaces are mapped onto a three-dimensional coordinate system.The theoretical approach has practical significance for the design of a highly dexterous serial n-link manipulator with proposed link relations.展开更多
基金Supported by the Natural Science Foundation of Shanxi Province (Grant No. 20041070)
文摘This paper presents a classification on the workspaces of planar serial three-link manipulators, that is, position workspace and orientation angle workspace. Position workspace indicates the region reached by the reference point on the end-effector. Orientation angle workspace indicates a set of angle ranges by which the end-effector can reach with certain orientation for every point in the reachable position workspace. By introducing a virtual equivalent mechanism, reachable position workspace can be di- vided into several Grashof intervals and non-Grashof intervals. The calculation equations of orientation angle workspace are deduced in three situations according to the relationships among four link lengths in the virtual four-bar chain. Three examples are given for three kinds of relationship of link lengths. The orientation angle workspace of extended groups, that is, two of the three link lengths equal, and the orientation angle workspace when the reference point on the end-effector moves along a non-radial direction are also discussed. A program is developed to calculate orientation angle workspaces and output variation curves of orientation angle workspace and key data within the position workspace. The approach and program in this paper can be used for fast calculation and identification of the variation rule of the orientation angle workspace of any given planar serial three-link manipulator on the basis of its link parameters, and for the design of a highly dexterous serial manipulator with proposed link rela- tions.
基金supported by the Natural Science Foundation of Shanxi Province of China (Grant No.2010011036-1)
文摘This paper presents a new method of analyzing the orientation angle rotatability of a planar serial n-link manipulator by examining the rotatability of its virtual equivalent mechanism.Workspace orientation boundary region decomposition is proposed based on the polynomial discriminant derived from a serial three-link manipulator.Orientation angle workspace indicates a set of angle ranges by which the end-effector can reach with certain orientation for every point in the reachable position workspace.By introducing a virtual equivalent mechanism,the open-chain kinematic problem is converted into a close-chain mechanism,and the Grashof-type condition is used to examine the rotatability of the end-effector link.The reachable position workspace can be divided into several Grashof intervals and non-Grashof intervals based on the extreme positions and singular configurations of a manipulator.The derived equations in this paper can be used to calculate the variation rule of the orientation angle workspace of any given planar serial n-link manipulator on the basis of its link parameters.The orientation angle rotatability of a seven-link serial manipulator is solved by the proposed method and graphical representations of the orientation angle workspaces are mapped onto a three-dimensional coordinate system.The theoretical approach has practical significance for the design of a highly dexterous serial n-link manipulator with proposed link relations.
