Scale Analysis And Trajectory Planning Of A Full-Degree-of-Freedom Reconfigurable Parallel Mechanism

Industrial robots are an important part of China’s national manufacturing strategy.Parallel robots,as one of the most representative products,have the advantages of strong load-carrying capacity,high control accuracy,small cumulative error and high stiffness.They are widely used in flight simulators,parallel machine tools,precision positioning equipment,spot welding and other fields.This paper took a full-degree-of-freedom reconfigurable parallel mechanism as the research object and took the parallel machine as the engineering application background.Based on the existing research results,the kinematics,scale analysis and track planning of the reconfigurable parallel mechanism were studied.The main work of this paper is as follows:Firstly,the generalized coordinate system and the dynamic coordinate system of the reconfigurable parallel mechanism were established,and the homogeneous transformation matrix between them was obtained.On this basis,a mathematical model for the forward solution of the kinematic position of the reconfigurable parallel mechanism was established,and the inverse solution of the kinematic position of the mechanism was solved using the idea of combining numbers and figures.The feasibility and correctness of the mathematical model were verified by Newton iteration method and a specific example.At the same time,the curve of the position and position of the center of the moving platform changing with the drive value of the driver was analyzed.The direct derivation method was used to derive the time from the positive position solution equation of the parallel mechanism.The velocity Jacobian matrices of the 3-UPS and3-URS configurations were solved,and the workspace range of the parallel mechanism was analyzed.Secondly,according to the workpiece size,taking the total length of the rod as the objective function,the dexterity as the performance evaluation index,and considering the factors such as interference between the rods and the collision between the rods and the workpiece,the scale analysis of the parallel mechanism’s rod was carried out,and the optimal design method was used to analyze the scale of the parallel mechanism’s rod,and the simulation analysis was carried out with an example.The mapping relationship between workpiece size and related spray parameters and rod size of parallel mechanism was further explored,and the rule of rod size changing with related parameters was obtained,which lays a certain foundation for subsequent trajectory planning research.Finally,the workpiece-based trajectory planning analysis of the reconfigurable parallel mechanism was performed.Based on the elliptical double β distribution model,the static and dynamic spraying models on the plane and surface were constructed and solved,and the motion track when the end of the parallel mechanism moving platform can complete the spraying task was determined.The coordinates of each point on the track were determined through the combination of linear interpolation and circular interpolation.The driving values of the corresponding drivers were solved by inverse kinematic position solution of the parallel mechanism.The driving modes of 3-UPS and3-URS configuration alternating transformation were used,and then the curves of angular displacement,angular velocity and angular acceleration function of each driver were fitted by the quintic polynomial interpolation method.The simulation analysis was carried out with an example.The variation rules of the driver angular displacement,angular velocity and angular acceleration curves were analyzed when the reconfigurable parallel mechanism was in 3-UPS and3-URS configuration,and the correctness of the conclusions was further verified.This paper provides a theoretical reference for the engineering application of full-degree-of-freedom reconfigurable parallel mechanisms,which has certain scientific significance and engineering value.