The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modem parallel mechanisms. However its range of application needs to further extend to general multi-loop spatial mechanism. This kind of mechanism is not only more complex in structure but also with strong motion coupling among loops, making the mobility analysis even more complicated, and the relevant research has long been ignored. It is focused on how to apply the new principle for general spatial mechanism to those various multi-loop spatial mechanisms, and some new meaningful knowledge is further found. Several typical examples of the genera/multi-loop spatial mechanisms with motion couple even strong motion couple are considered. These spatial mechanisms include different closing way： over-constraint appearing in rigid closure, in movable closure, and in dynamic closure as well; these examples also include two different new methods to solve this kind of issue： the way to recognize over-constraints by analyzing relative movement between two connected links and by constructing a virtual loop to recognize over-constraints. In addition, over-constraint determination tabulation is brought to analyze the motion couple. The researches above are all based upon the screw theory. All these multi-loop spatial mechanisms with different kinds of structures can completely be solved by following the directions and examples, and the new mobility theory based on the screw theory is also proved to be valid. This study not only enriches and develops the theory and makes the theory more universal, but also has a special meaning for innovation in mechanical engineering.
As one of the typical less-mobility parallel mechanisms, the spherical parallel mechanism Up.s with two degrees of freedom （2-DOF） possess high order overconstraints, and the calculation of its stiffness is partly different with general parallel mechanisms owing to the bars in each branch are assumed to be arc-shaped. By means of small deformation superposition principle, the relationship between the angle displacement and line displacement of moving platform and the forces acted on the branches were derived out. Based on the results of static analysis, the relationship between the applied force, the line displacement and the angle displacement of the mechanism was set up. And then the stiffness matrix was obtained. The six principal stiffness of the mechanism and the corresponding directions were achieved by the orthogonal transformation. The numerical calculation was performed and the results showed that the principal stiffness and directions are varied with the pose-position of the mechanism, and the principal stiffness is gradually enlarged when it is far away from the anigin. In addition, the torsion stiffness is much greater and the line deformation stiffness is smaller, the difference between the two parts is huge. The research content of this paper supplies the theoretical foundation for the further engineering design and application of the spherical parallel mechanism.
With the gradual deepening of study on the parallel mechanism,the difficulty brought by the existence of coupling to the theoretical analysis and practical application of parallel mechanisms is becoming increasingly apparent.The research on the decoupled parallel mechanism is currently one of the hot fields.Though most of the rotational parallel mechanisms,which has been widely used in spatial orientation fields,are not decoupled.It is comparative difficult for the synthesis of fully decoupled rotational parallel mechanisms,and the number of the existing parallel mechanisms which can realize rotational decoupling is limited.In addition,most of the existing rotational decoupled parallel mechanism are obtained depending on the experience of the researcher,and don't possess the general theoretical significance.Based on the screw theory,this paper presents the rotational conditions of the parallel mechanism through the analysis of the relationship between the degree of freedom of the parallel mechanism and its limbs.The synthesis rule of the limbs for decoupled rotational parallel mechanism is established according to the twist screw system of the limbs,which assures the decoupling of the rotations in each limb.The selection principle of the input pairs for the rotation driven limbs is proposed,then the type synthesis method for rotational decoupled parallel mechanisms is formed.With this type synthesis method,synthesis of the rotational decoupled parallel mechanisms is performed,which can provide a reference for the development of the novel type parallel mechanisms with independent intellectual property rights.
Compared with the parallel mechanisms, the mobility analysis of the general multi-loop spatial mechanisms（GMSMs） is more difficult to obtain correct results. The reason is that its multi-loop is formed through several times of closings and there also exists motion coupling even strong coupling, where the over-constraints are concealed. However, the mobility analysis for this kind of mechanisms has been paid few attentions. A new systemic methodology for analyzing mobility is proposed for GMSMs also based on the screw theory. The key issue for mobility analysis is to recognize the over-constraint. Firstly, three theorems are given and point out： the reason and site of over-constraint occurrence, calculating the number of over-constraints by the screw theory, and how to analyze the over-constraints for a single-loop mechanism as well. Then, three closing forms for GMSMs are proposed including rigid closure, movable closure and dynamic closure, and for the three different forms the different analysis methods are also given. Especially, for the most difficult issue of GMSMs with the multi-loop Closure in many times and the inevitable motion coupling, two important methods are proposed： ＂recognizing over-constraints by analyzing relative movement＂ and ＂recognizing over-constraints by virtual loop＂. The two methods are well used to solve the issue. Above-mentioned principles are not only systematic and effective but also unified. They provide a theoretical basis for the general multi-loop spatial mechanisms.
Coupling is the significant characteristic of parallel mechanism,while it is just the coupling that brings about much difficulty for the configuration design,theoretical analysis and the development of the control system of the parallel mechanism. And recently,the research on the decoupled parallel mechanism becomes one of the research hot points in the mechanism fields. In this paper,a type synthesis method for the translational decoupled parallel mechanism( TDPM) is proposed based on the screw theory. To achieve the decoupling characteristics of the translational parallel mechanism,the translational decoupled criterion for type synthesis of the branches are presented in this paper. According to this criterion and the realization conditions of rotational degree of freedom of the mechanism proposed former,a large number of branches for the TDPM are obtained. Taking the three degrees of freedom( DOFs) TDPM as an example,the process of type synthesis is discussed in detail. Using this proposed type synthesis method,a serial of translational decoupled parallel mechanisms, including but not limited to all the existing typical 3-DOF TDPMs, are obtained, which identifies the correctness and effective of the method. The contents of this paper provide a reference and possess significant theoretical meanings for the synthesis and development of the novel decoupled parallel mechanisms.
