The Research On Mechanism Mobility Analysis And Application Of General Linkgroup Theory

Mobility or the degree of freedom(DOF) of a mechanism is the first consideration in the mechanisms and robots analysis. In the process of applying theory to practice, “concision, fast calculation and high practicability” have been an inevitable requirement for mobility calculation.In traditional mobility calculation, the determination of over constraints is always one of the key and difficult problems. Over the past decade, based on theory of “avoiding over constraints with list intersection”, some mobility formulae emerges, which provides a new idea for fast calculation of mobility. However, these formulae are presented in the view of the mechanism as a whole. Actually, branches’ DOF can greatly reflect the constraints that the branches exert on the output mechanism, which is the premise of judging the mobility’s characteristics. And it indicates that there are still some deficiencies in the existing formulae. Towards the problem, it has been always a hot and forefront topic to seek an easier and more practical mobility theory.To start with, based on some new concepts of the “general link group” and “base point parameters”, a new formula in the calculation of the mobility is presented expressed with DOFs of the general link groups and rank of the motion parameters of base point. It is named GOM(Mobility of Groups and Output parameter) formula. Three basic issues about it are studied and demonstrated by the screw theory: a mathematical description of topology structure of mechanisms is established; analyzing the relationship between the motion parameters and dimension constraint types of link groups, and four rules to confirm motion parameters of link group are proposed; additionally analyzing the conditions of avoiding constraints for the rotation motion, “intersection rules” that can reflect the relationship between the characteristics of output member and the link groups are presented. Based on these, a relatively complete new mobility theory called “link group theory” is formed, which provides theoretical basis for the following application research of the GOM formula.The link group theory and GOM formula are applied to the mobility calculation of parallel mechanisms, which includes the general mechanisms with parasitic motion, over-constrained mechanisms, parallel mechanisms with special geometric and structural conditions, mechanisms with compound link groups, hybrid mechanisms, and multi-loops coupled mechanisms. Meanwhile, through decomposing the coupled compound link groups to several simple link groups, such as connected with each other in an intersection or union form, a method to solve the mobility calculation of multi-loops coupled mechanisms is presented. The results coincide with the prototype data, which proves the validity of the proposed formula. Also it provides a reference and new approach for the mobility analysis of more complex mechanisms.The link group theory is applied to the determination of over constraints. A new calculation formula for the number of over constraints is deduced. To determine the type of over constraints, a rule named “the validity of its vertical component” is presented which only takes parallel constraints of screw linear dependence into account in the midst of varied geometric spaces. Meanwhile eight principles of common constraint and partial constraint determination are concluded. For complicated mechanisms with multi loops, it is quite difficult to obtain its link group parameter matrix directly. To solve this problem, parameter matrixes for three closure ways of mechanisms are analyzed respectively, which are rigid closure, closure through kinematic chains and closure through kinematic pairs. Then the over constraints in mechanism can be recognized by building the parameter matrix in each closed loop. In addition, proposal of over-constraints’ judging rules in single-loop mechanism and the relationship between over constraints and partial over constraints, provide great convenience for the determination of over constraints.Type synthesis of parallel mechanism is done based on the GOM formula and the link group theory. The determination of idle freedom, passive mobility and selection of the input pairs are researched by the mobility of link group and the link group parameter matrix. With these theories, two rules for type synthesis of the rotational decoupled link groups, are established and then the method for structural synthesis of parallel mechanism is formed as well. Synthesis of one type of rotational decoupled parallel mechanisms with three limbs and two DOFs is performed. These theories can play an important role in the theory of mechanisms and robots’ design, also show far-reaching practical significance.