On Singularity Of Several Kinds Of Spacial Parallel Manipulators

Compared with a series manipulator, a parallel manipulator is with some advantages. Parallel manipulators can fill the area which series manipulators are not applicable. The needs of the application accelerate the theoretical research of parallel manipulators. The study of the singularity is important in the theoretical research of parallel manipulators. With the complete analysis of the developments of the application and the research of parallel manipulators, especially the progresses of the singularity research of parallel manipulators international and at home, a thorough and systemic study about the root and principle of singularity and the behavior of the mechanical and movement of the parallel manipulator in singularity is gone along in this paper. Depending on the investigation of the singular characteristics of parallel manipu- lators and analyzing some references about the singularity, this paper expatiates the dis- tinctness of singularity in parallel and series manipulator based on the definition of singu- larity of manipulator. The force Jacobian matrix of lower-mobility parallel manipulator is established. Furthermore, several new methods to class the singularity, such as the method based on the causes of singularity, motion stations at singularity, linear-complex charac- teristics, and method to research singularity, are presented. This is significant to the singu- larity research. The analysis of the kinematics characteristics for spatial lower-DOF parallel manipu- lators is the most complicated in the theoretical study of parallel manipulators. In the fa- mily of the lower-DOF parallel manipulators, the 3-RPS parallel manipulator is a focus in the applications and researches. In this paper, the symplectics of the six output variables is studied firstly, then the singularity regularity of the 3-RPS parallel manipulator is presen- ted firstly and then the general singularity discriminant is obtained. The distributing chart of position singularity and the distributing chart of pose singularity are gained. The cha- racteristics of all the ten positions and orientations in the singularity are analyzed tho- roughly and the attestations to the singularity based on the line geometry are presented. 4-dof and 5-dof parallel manipulator, particularly symmetrical 4-dof and 5-dof para- llel manipulator is indispensabe in the family of lower-DOF parallel manipulators. The restricting conditions, the solutions of the forward and inverse position kinematics of two 4-dof and one 5-dof parallel manipulator are established firstly. Three expressions to dis- tinguish singularity of the three parallel manipulators are built. This is groundwork to the popular applications and the singularity study of the three parallel manipulators. 6-dof parallel manipulator is applied universally. The 6/6 and 3/6-Stewart are ty- pical among the 6-dof parallel manipulators. About 3/6-Stewart parallel manipulator, the singularity regularity in the β inclined plane is found by the geometrical condition of singularity firstly. The singularity locus is a hyperbola in the β inclined plane. Its asym- ptote and real axis and image axis are ascertained. Then with the kinematics method and the singularity transform method, the discriminants of singularity in the three dimensional space is received. By way of the corresponding numerical examples, the singularity dis- tributing in the three-dimensional space and the singularity analyzing of the 3/6-Stewart parallel manipulator at some poses are worked out. Moreover, the relation of inverse to each other of velocity Jacobian and the force Jacobian matrix of 6-dof Stewart parallel manipulator is proved. Finally, the correctness of the singularity principle and analysis is validated with tests.