Analysis Of Kinematics And Statics Of Redundant (PS+RPS+SPS)+(SP+SPR+SPS) And Inverted Mechanism

Redundant mechanisms with more higher agility and workspace enlargement,have received widespread attention from some researchers in the academia and industry field.Meanwhile,the mechanisms have wide application prospect in various fields,for example,aerospace,medical equipment and industrial automation.In this paper,a kind of redundant serial-parallel mechanisms composed of PS+RPS+SPS and SP+SPR+SPS mechanisms is used as the object of study.Through the analysis of the constraint of theoretical model of the redundant mechanism,the problem of kinematics and statics of the redundant mechanisms are discussed.The research results of redundant mechanisms not only do foreshadowing for the following theoretical research,but also are of great significance to its applications.The main contents of this paper are as follows:Firstly,a class of two-layer redundant serial-parallel mechanisms composed of PS+RPS+SPS and SP+SPR+SPS mechanisms is introduced.Based on the constraint and coupling relation of redundant mechanism,the number of independent degrees of freedom for the terminal platform is acquired.Subsequently,the forward displacement and inverse displacement of the redundant mechanism are analyzed.According to the property of the mechanism,in order to make the linear actuating limbs that have many different solutions more flexible,select manipulability as optimization function in this level,the lengthen of the linear actuating limbs are optimized,a set of optimal position solutions is acquired.Some numerical examples of the redundant mechanism are given to verify the analysis result of the displacement.The workspace of redundant mechanism is solved.Secondly,based on the constraint of the terminal platform in position level,the constraint of the terminal platform in velocity level is acquired.Subsequently,the forward velocity and inverse velocity of the mechanism are also analyzed.In order to prevent the linear actuating limbs of the mechanism from exceeding range of motion,select avoiding joint limits as optimization function in this level,and apply the gradient projection method,a set of optimal velocity solutions is acquired.Eventually,a new method that is applied to the redundant series-parallel mechanisms is acquired.Some numerical examples of the(PS+RPS+SPS)+(SP+SPR+SPS)redundant mechanism are given to verify the analysis result of the kinematics.Thirdly,based on the research results of the kinematics,the statics of the redundant serial-parallel mechanisms is given.Based on the principle of virtual work,the statics of single parallel mechanism is analyzed firstly,subsequently,the statics of the serial-parallel mechanism is analyzed and the actuating forces are optimized,the numerical example is given to verify the analysis and the optimization result.Finally,a class of two-layer redundant serial-parallel mechanisms composed of SP+SPR+SPS and PS+RPS+SPS mechanisms is introduced.Based on the research results of the(PS+RPS+SPS)+(SP+SPR+SPS)redundant mechanism,the kinematics and statics of this mechanism are analyzed.The workspace of the mechanism is solved.