Study On Singularity Law Of A Kind Of 2R1T Parallel Mechanism

The singular characteristics of parallel mechanisms are extremely important for their application.When the mechanism is in a singular configuration,the kinematic and mechanical properties of the mechanism will undergo sudden changes.At this time,the mechanism is in an unstable state,which is prone to accidents.Therefore,it is necessary to avoid the occurrence of singular configurations during the movement of the mechanism.Therefore,it is particularly important to master the singularity change law of the mechanism.The 2R1T type mechanism in the three degree of freedom parallel mechanism is suitable for various application scenarios in daily life,and the understanding of its singularity laws restricts its application.This article focuses on the singularity of this type of mechanism.Firstly,the corresponding mathematical models of 3-RRS,3-PRS and 3-PPS parallel mechanisms are established.The improved G-K method based on the calculation of degrees of freedom calculates their degrees of freedom,compiles programs to calculate their workspace,establishes constraint relations in the motion branch plane,and gives the kinematics inverse equations of the corresponding mechanisms.Then,according to the screw theory,the branch motion screw system,constraint screw and drive screw are established,and the full Jacobian matrix of the mechanism is constructed.The singularity discriminant is obtained by using the properties of the mechanism in the singular configuration,and the singular distribution surface is given.Then,the properties of the obtained singular surfaces were identified.Through research,it was found that the singular surfaces of the 3-RRS mechanism contain some parabolic surfaces,while the properties of the remaining singular surfaces are the same as those of the3-RPS mechanism;The 3-PRS mechanism does not contain spatial singular points under the current branch layout.The singular configuration of the mechanism is verified by using the singular kinematics principle,and a theoretical explanation is given;The singular surface of the 3-PPS mechanism includes a conical surface and a parabolic cylindrical surface that intersect in space.The single variable method was used to study the influence of 3-RRS mechanism parameters on the variation of singular surfaces.By comparing singular surfaces between similar mechanisms,the regularity of singular changes was explored from the similarities and differences of the mechanisms themselves,and it was found that the differences in branch structures led to different results of singular surfaces.Finally,the correctness of the theoretical research was verified by constructing a prototype model of the aforementioned mechanism and collecting pose data of the moving platform for experiments.