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First the kinematic principle of singularity is proved, that is the intersecting point of threenormal planes of three velocities at three non-collinear points in a rigid body lying in the plane determined by the three corresponding points. It is a sufficient and necessary condition that the velocities ofthree non-collinear points in a rigid body can determine a screw motion of the body Based on thisprinciple, a simple and direct new method to distinguish the singularity of the parallel manipulator islered. Wth this new kinematic method, the 3-RPS parallel manipulator is studied. Its singularity lociare obtained for some orietations for the first time and verified with Grassmann line geometry andscrew theory and the force Jacobian matrix.
First the kinematic principle of singularity is proven, that is the intersecting point of threenormal planes of three velocities at three non-collinear points in a rigid body lying in the plane determined by the three corresponding points. It is a sufficient and necessary condition that the velocities ofthree non-collinear points in a rigid body can determine a screw motion of the body Based on thisprinciple, a simple and direct new method to distinguish the singularity of the parallel manipulator islered. Wth this new kinematic method, the 3-RPS parallel manipulator is studied. Its singularity lociare obtained for some orietations for the first time and verified with Grassmann line geometry andscrew theory and the force Jacobian matrix.