Research On Ruled Surface And Mechanism Synthesis Of Single Loop Overconstrained Mechanism

The single loop over-constrained mechanism is a special spatial linkage mechanism due to the special function constraint relationship between the joints and the links,it still has certain mobility.The sing loop over-constrained mechanism is widely used in aerospace,building structure,and other fields because of its good rigidity,simple structure,and large deformation capacity.Moreover,the over-constrained mechanism is a critical basis for the study of complex mechanisms such as reconfigurable mechanism,metamorphic mechanism,and multi-mode mechanism.Therefore,this research of the single loop over-constrained mechanisms have certain theoretical significance and practical value.In this paper,based on the kinematics of single loop over-constrained mechanism and with the help of the fundamental theory of analytic geometry,the internal relationship between the kinematics of over-constrained mechanism and the ruled surface is systematically explored.Through the derivation of the analytical model of the instantaneous mapping between two kinds of over-constrained mechanisms and ruled surfaces,the kinematic rules of the instantaneous mapping between the single loop over-constrained mechanisms and ruled surfaces is analyzed in-depth,and the correlation between the two types of over-constrained mechanisms is explored with the hyperboloid of one sheet as the bond.The research contents are mainly focused on the following three aspects.(1)The characteristics of the ruled surface and the kinematics of the Bennett mechanism are analyzed,which lays the foundation for the following research.The basic types and characteristics of ruled surfaces are analyzed,and the motion generation of two kinds of hyperboloids through generators is discussed.Based on the traditional definition of pressure angle,the analytical model of the Bennett mechanism is established.The input angle equals n?(10)?/ 2(n ?N)corresponding to the configuration of the minimum pressure angle of Bennett mechanism with arbitrary structural parameters is discovered.The physical meaning of the minimum pressure angle of the Bennett mechanism,which equals the angle between the joint axis of the output link is revealed.(2)The analytical model of the instantaneous mapping between the Bennett mechanism and the hyperboloid of one sheet is derived,and the mapping rules between the Bennett linkage’s both joint points and joint axes and the hyperboloid of one sheet are revealed.The equation of elliptic hyperboloid defined by the joint axis of the Bennett mechanism is derived,and the analytical relationship between the mechanism and the elliptic hyperboloid is established.The analytical expression of the structural parameters of the Bennett mechanism from elliptic hyperboloid is derived,and the bi-directional mapping relationship between Bennett mechanism and hyperboloid defined by its joint axis is established.Furthermore,the analytical model of the structure parameters of Bennett mechanism on the circular hyperboloid is derived,and the rules of the position variation of the Bennett mechanism on this kind of hyperboloid is analyzed.(3)The rules of instantaneous mapping between the threefold-symmetric Bricard mechanism and the circular hyperboloid are explored,and the intrinsic relations between the Bennett mechanism and the threefold-symmetric Bricard mechanism are analyzed.The analytic expression of the structural parameters of the threefold-symmetric Bricard mechanism on the circular hyperboloid is derived,and the variation rules of the mechanism on the circular hyperboloid with the same parameter are analyzed with an example.Moreover,the relationship between 4R closed-loop mechanism constructed by two threefold-symmetric Bricard mechanisms with the same parameters on circular hyperboloid and Bennett mechanism is explored,and the conclusion that the Bennett mechanism can be synthesized by the threefold-symmetric Bricard mechanism is testified.This research not only enriches the kinematics of the over-constrained mechanism,but also provides a new idea for the synthesis of the over-constrained mechanism,and also provides a reference for the construction of the deformable structure with adjustable hyperboloid parameters.