| Hybrid kinematics mechanisms(HKMs) can have better stiffness and precise positioning compared to parallel mechanisms, as well as larger working envelopes and better control decoupling compared to serial mechanisms, while disadvantages of both serial and parallel mechanisms are minimized, hence, HKMs have attracted great attention. However, the amount of hybrid mechanism is limited and knowledge of synthesis is shortness on one hand. On another hand, the difficulties of kinematics analysis, control and standardization brought by the existence of coupling to the theoretical analysis and practical application of parallel kinematics mechanisms(PKMs) and HKMs are becoming increasingly apparent. This paper aims at searching for an efficient synthesis method for the HKMs as well as decoupled PKMs and HKMs, based on the GF set. Main contents of this paper are as follows:Firstly, the basic concept and mathematical operation of GF set are introduced. This paper presents a method to synthesize HKMs by analyzing characteristics of structure composition of hybrid mechanisms. It is shown that structural synthesis of HKMs can be developed by the combination of elements of GF set and rotation axis transfer theorem, number synthesis formulas is set up, a detailed algorithm of type synthesis for HKMs is proposed as well. According to the approach proposed in this paper, a lot of novel topological structures of 5-DoF HKMs were designed. Meanwhile, three hybrid mechanisms are synthesized to demonstrate the applicability of the method of structural synthesis for HKMs.Secondly, to avoid the difficulties in the kinematics and dynamic analysis brought by the existence of coupling in the PKMs, a structural synthesis method is proposed on PKMs based on GF set. According to union arithmetic of GF set and rotational motion planet theorem, the selection criterion of the input kinematic pairs and type synthesis principle of decoupled branches are given. Following the type synthesis steps, specific process for structural synthesis of 5DoF decoupled PKMs which include sole and double motivation kinematic chain is finished. Constraint screw is applied to analyze kinematic characteristic of PKMs synthesized above. The expression of the Jacobian matrix is deduced which validates the decoupling feature of the mechanism according to the relationship between input and output. In addition it demonstrates the effectiveness of the novel method of structural synthesis for PKMs.Then, to obtain the structure of fully-decoupled HKMs, a simple and effective synthesis of decoupled HKMs is proposed and described in detail based on GF set. The topological structure of the hybrid mechanism is developed by the principle of elements of GF set combination formula and the synthesis equation r of hybrid mechanism. Combining with the selection criterion of the input pair and the design principle of decoupled branches, the decoupling of the HKMs is ensured. According to the type synthesis theory, the structural synthesis of the 5-DOF decoupled HKMs is finished. Moreover, the expression of position and velocity of end-effector is deduced and the Jacobian matrix is obtained. Meanwhile, the decoupling feature of the proposed HKMs is validated.Finally, in order to solve the bottleneck problem of multi 3D printing equipment, a fully-decoupled 3CPa RR&RRo HMs is presented as the actuator of 3D printing. Screw theory is applied to analyze the kinematic characteristic of mechanism and calculating the degree of freedom of 3CPa RR&RRo which is verified via the ADAMS software. The kinematic matrix of the hybrid mechanism is carried out by using the D-H convention. The expression of the forward kinematics is deduced to obtain the Jacobian matrix and velocity equation, and the analysis of singularity is carried out. Moreover, simulation model is built with ADAMS, the velocity of the end-effectors of mechanism is drawn. It is proved the validity of the theoretical analysis. |
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