Synthesis with GF Sets and Kinematics Analysis Based on BP Neural Network of Serial-Parallel Hybrid Mechanisms
摘要
Hybrid mechanisms are widely used in manufacturing, medical, military and some other fields. The research on hybrid mechanism has been a hot topic in the field of mechanism in recent years. The configuration of the hybrid mechanism is generally complex and changeable, and it is difficult to determine a unified rule and method of synthesis, design and analysis. Based on the topology synthesis for parallel mechanisms (PMs), the GF sets theory, this paper studies a class of serial-parallel hybrid mechanisms. Then the type synthesis method of such hybrid mechanisms based on the intersection and union rule in GF sets is proposed, and this kind of serial-parallel hybrid mechanism is classified into type A and type B for design and analysis. On this basis, a unified kinematics solution method based on the pose allocation strategy with parasitic motion is proposed for the A-type serial-parallel hybrid mechanism. In addition, this paper focuses on the kinematics analysis of the more complex and more coupled B-type hybrid mechanism. For this kind of inverse kinematics problem which is difficult to obtain analytical solutions because of the coupling of sub-PMs, a new method based on the iterative algorithm with the Jacobian matrix and the BP neural network training is proposed in this paper, and a (3-PRS)-(3-PRS) hybrid mechanism is introduced in detail as an example. The relevant verification and simulation analysis prove that the high-coupling B-type serial-parallel hybrid mechanism proposed in this paper can obtain the inverse solution accuracy of about \(10^{ - 9}\) mm and \(10^{ - 10}\) μrad under the given target pose, and its iteration steps and calculation time are greatly reduced compared with the conventional numerical iteration algorithm. The results show that the method proposed in this paper can generally and efficiently get the kinematics solutions of such hybrid mechanisms under any given continuous or large-range discrete poses, thus providing a basis for real-time motion control and planning. The research in this paper can provide some reference for the design and analysis of related hybrid mechanisms.