Nullspace Construction And Intersection Calculation Of Screw System And Their Applications In Mechanisms

Due to the palpable geometrical interpretation and integrated algebraic form,screw theory and screw algebra have become a popular mathematical tool which were used by many kinematicians and roboticists.This dissertation deals with the key issues relevant to nullspace construction and intersection calculation of screw system when screw theory and screw algebra are applied in mechanism analysis,and focuses on nullspace construction of screw system with dependent columns,intersection calculation of screw system and its applications in mobility analysis of parallel mechanisms and multifurcation of a reconfigurable 6R linkage.The main contents of this dissertation are summarized as follows:(1)Nullspace construction of screw system,also known as the calculation of reciprocal screw system,has great significance in kinematics,statics and dynamics of mechanisms.This dissertation aims to solve the problem that the construction law of nullspace fails to calculate the reciprocal of a screw system with two dependent columns.The linearly dependence relation among the column vectors is investigated and the cause of the problem is analyzed.Besides,an extended approach is put forward to solve the reciprocal screw system.Further,the approach is generalized to nullspace construction of a screw system with more dependent columns,and is applied to obtain the reciprocal screw systems of kinematic chains.(2)Intersection calculation of screw system is almost a blank domain at present.According to the relationship between a screw and a six-dimensional space vector,this dissertation proposes a method for obtaining screw systems intersection based on nullspace construction.A rigorous mathematical proof of the method is embedded.In addition,according to the association between the screw system intersection and the platform twist space of the parallel mechanism,the method is applicable to mobility analysis of parallel mechanisms.(3)During the process of mobility analysis of parallel mechanisms,the previous screw-based methods need to calculate the reciprocal screw systems over and over again to get the motion-screw system of the platform which is the intersection of all the limbs' motion-screw systems.Based on the proposed method of screw system intersection calculation,this dissertation analyzes the instantaneous mobility and the motion-screw system of the platforms in a general parallel mechanism,an overconstrained mechanism,a single-loop mechanism and a bifurcated parallel mechanism.These results prove the validity of the proposed method by comparing with that of the existing studies.(4)The furcation point in a mechanism is a salient feature of reconfigurable mechanisms.This dissertation presents a reconfigurable overconstrained 6R linkage inspired from a Bennett linkage.The motion screws of each joint are given.The motion branches are identified through different geometrically-constrained conditions of the joints according to closure equations.For different motion branches,the linkage has corresponding kinematic characteristics and it will be discussed using the calculation of screws in the motion-screw system of the linkage.Meanwhile,all the furcation points are obtained by discussing the relationship between joint angles.The motion of the linkage under each furcated configuration is analyzed and the motion branches transformation is shown together with kinematic curves.The outcomes of this dissertation have great theoretical significance in the development of screw theory and screw algebra,and show the potential applications in complex spatial mechanisms.