Research On Singularity Avoidance And Performance Optimization Of A Planar Parallel Mechanism With Kinematic Redundancy

Compared with series mechanism,parallel kinematic machines(PKMS)have several advantages of high stiffness,large load-weight capacity and agility,which are regarded as a hotspot of mechanism research.However,traditional parallel kinematic machines with small workspace and inertial singularity,which seriously limited the advantage of PKMS.For solve this problem,the paper will lead kinematic redundancy into the design of PKMS to avoid singularity,enlarge the workspace and improve the performance of them.Under this background,a 3DOF planar parallel mechanism with kinematic redundancy(planar PM-KR)is used as a carrier to study the impact of kinematic redundancy to the workapce's size,avoidance of singularity and performance.Firstly,the architecture of the planar PM-KR is analysied and the inverse kinematic is established by the method of closed-loop vector analysis according to it's structure's character.And the solution of inverse kinematic can be obtained by comparing the motor's values between the virtual prototype and theoretical equations,which is unique correspondence with the initial installation configuration of the mechanismSecondly,the workspace-singularity maps of the planar PM-KR are drawn based on the Jacobian matrices,the condition of singularity and the limition of inverse kinematic.with the obtained workspace-singularity atlasmaps,the method of aisle-transition layer is proposed and three tasks are used to prove that the redundant structure can be used to expand the workspace boundary and avoid singularity.Meanwhile,the indesx of kinematic performance of manipulability,velocity minimum,velocity isotropy and dexterity are used to analyse the distributed character of each index of the planar PM-KR to prove kinematic redundancy can adjust the indesx of kinematic performance of it.Thirdly,the characters of the closed-loop of kinematic redundance are considered when the theory model of statics and dynamic are established by principle of virtual work.The numerical tasks of applying the changeable and constant load on the moving platform are designed,and the results of theory versus simulation proved that the model of statics and dynamic are correctness.In statics analysis,the driving force/moment are used as indexs and the traditional 3-RRR planar parallel kinematic machines as comparative item.The compared results proved the kinematic redundance can improve the performance of static.In dynamic analysis,fistly,a task trajectory oriented value filtering algorithm of kinematic redundance and the indexs of evaluating the area of safe working are proposed.And based on them,the maps of safe working area are drawn and the range of the values of kinematic redundance are obtained,which are satisfying the need of indexs.And then,taking the total power consumption and peak power consumption as the indexes of evaluating dynamic performance,and combination with the dynamic performance of the traditional 3-RRR planar parallel kinematic machines to choose the optimal value of kinematic redundancy,which can be used to improve the dynamic performance of the mechanism and proved that kinematic redundancy was beneficial to the improvement of the dynamic performance of the mechanism.Furthermore,taking the maximization of workspace as the optimization objective,for gain the optimal structural parameters which are meets the set requirements and optimization objectives,we apply the single objective to single variable and single objective to multi-variable discrete optimization method and the constraints such as the actual machining conditions of the mechanism to carry out the optimization.Lastly,the action strategy of driving motors of a given task path is studied.And the motion ability and performance characteristics of the mechanism are verified by making a physical prototype.