Analysis of Terminal Constraints and DOF of(2-UPU+SPR)+(2-UPU+RPS)Asymmetric Hybrid Manipulator
The previous research on hybrid mechanisms has not conducted in-depth analysis on their low degree of freedom(DOF)characteristics,and there is still insufficient understanding of their terminal constraints and DOF forms.The terminal constraints and DOF problems of a novel(2-UPU+SPR)+(2-UPU+RPS)mechanism are investigated.By establishing an analytical model for solving the intersection of two sub-constrained screw systems,the terminal constraint of this hybrid mechanism is solved.The DOF composition principle of the mechanism is analyzed,and the terminal constraint problem is transformed into the intersection of the two sub-constrained screw systems.Based on the distribution characteristics of the terminal constraints in the two sub-mechanisms,the terminal constraints and DOF properties of the hybrid mechanism under different geometric conditions are discussed.The analytical expressions for the distribution surface and straight generatrix of the terminal constraints for the sub-mechanisms are established,and the axis equations corresponding to the terminal constraints of the hybrid mechanism under general and special cases are obtained.A numerical example is given for solving the terminal constraint of the hybrid manipulator,and the intuitive distribution of the terminal constraints of the mechanism in general and special cases are given.The research results indicate that in general case,the terminal constraint of the mechanism is a constraint screw.In special case,the terminal constraint is either a pure constraint or a constraint couple.This study provides a reference for solving the terminal constraints of the hybrid manipulators,lays a certain foundation for depth study of the hybrid manipulators,and also provides a new idea for solving the intersection of screw systems.
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