Analysis Of Kinematics Characteristics Of Spatial Parallel Mechanism With Kinematic Scaling Branches

There is a wide range of industrial application for the 3T1 R parallel mechanism(PM)and 3T PM.In this paper,a new type of 3T1 R PM and 3T PM were proposed by introducing the pantograph kinematic sub-chain.The following studies are mainly conducted in this paper.Combining parallelogram mechanism with parallelogram scissors mechanism,a new planar two-dimensional pantograph unit which consists of revolute joint only was proposed and corresponding two-dimensional pantograph mechanism was designed after modular combination.Firstly,according to the mechanisms and machine theory,modular principle of the pantograph mechanism for scaling two-dimensional planar graph was explained as the mechanism can be divided into three types of modules which are all derived from the two-dimensional moving unit.Secondly,the kinematic model of bottom module was established based on closed loop vector method.In accordance with the central symmetry of mechanism,the kinematic relations between two adjacent modules were deduced which can be used to establish the whole kinematic model of the planar two-dimensional pantograph mechanism consisted of multi-layer modules.On the basis of analysis of kinematics,the dynamic model of two-dimensional pantograph mechanism was established by using Lagrange method.Finally,taking the mechanism with four-layer modules as an example,the dynamics numerical calculation and virtual simulation were carried out,and meanwhile the correctness and effectiveness of the kinematics and dynamics equations were verified.A novel structural symmetry 3T(PM)with revolute joints only was proposed by introducing the pantograph kinematic sub-chain.It consists of a moving platform,a base plate and three connecting pantograph legs between moving platform and base plate.Firstly,constraint wrenches of each leg were formulated based on screw theory and the results illustrated that the moving platform is in possession of three translational degrees of freedom.Solving models with analytical solutions including forward and inverse position problems were established.Analyzing the models' characteristics,a new driving method of this PM was proposed by changing the distance between collinear equidistant points on the symmetrical connecting pantograph legs.Workspace was obtained by utilizing the model of inverse position solution and Jacobian matrix was deduced by establishing mapping relationships between input and output speed.Performance analysis were carried out by using dexterity and stiffness indexes and corresponding distributions over the workspace were sketched.The results showed that this PM can be folded in a narrow space and extended for a large workspace which is symmetric around the Y-axis,and meanwhile the distributions of performance indexes are also symmetric around the Y-axis.A 3T1 R PM with four legs was designed by taking the obtained pantograph mechanisms as sub-chains.Firstly,the structure coupling-reducing optimization design for this PM was performed,whose POC and DOF were unchanged with lower coupling degree(k=1).Secondly,the modeling method and the numerical solutions for forward and inverse position equations of the PM were established based on ordered single-open-chain(SOC)units.The working space and the rotational ability of this PM was obtained and the rotational capacity map was drawn by using the inverse position equations.Finally,according to the map,the range of workspace which can realize the full rotational capability was selected which can be treated as a theoretical basis for the design and applications for this mechanism.