Dynamic Optimization Design Of High-speed Parallel Robot Mechanism With Four-degree-of-freedom Double-action Platform

In this paper,a novel 4-DOF high-speed parallel mechanism and its dynamic comprehensive optimization design were researched in response to the requirements of automated production line(handling,sorting,packaging assembling and so on)in industries such as electronics,food,medicine and military.Firstly,a new type 4-DOF high-speed parallel mechanism with double platform was proposed,and its motion characteristics(three translations and one rotation)were verified through simulation.The forward and inverse kinematics model of the mechanism was established.Then the velocity,acceleration and Jacobian matrix of the moving platform can be solved by deriving the kinematics equation.The singularities of the mechanism were also analyzed in detail.Secondly,the Lagrangian equation and the virtual work principle were used to establish the complete and simplified rigid-body dynamic model of the mechanism,respectively.The effectiveness of the simplified rigid-body dynamics model was verified by cases.Based on the simplified model,three rigid-body dynamic performance indexes(singular value of dynamic matrix,maximum torque per unit acceleration,and maximum equivalent moment of inertia)were constructed.Combined with the constraints such as transmission angle and spherical joint,the rigid-body dynamics dimensional synthesis was carried out.Thirdly,a spatial elastic beam element model was established using the finite element method,then the element dynamics equations and branch chain elastic dynamic equations can be derived.According to the kinematic and dynamic constraints between the rigid body and the elastic body,the elastic dynamic equation of the mechanism can be obtained from the deformation coordination relationship of the branch chain elastic dynamic equation.The dynamic characteristics of the mechanism were analyzed using the modified linear acceleration method.On this basis,the ratio of the low-order natural frequency to the mass of the system was taken as the performance index and the optimization of elastic dynamics was completed by combining constraints such as mass,thickness and frequency fluctuation.Fourthly,based on the simplified rigid-body dynamics model and the elastic dynamics model of the system,a hierarchical optimization strategy was adopted,and the kinematic and dynamic parameters of the 4-DOF high-speed parallel mechanism can be optimized by numerical iteration.Finally,a virtual prototype of the 4-DOF high-speed parallel robot with double platform was constructed,and the typical gate-shaped motion trajectory of the end effector was planned using a 3-4-5 order subpolynomial motion law.The calculation formula of the path interpolation point coordinates of the end effector in any working plane was derived,and the input speed,acceleration and torque of the active arms were solved.