Dynamics Modeling And Control Of A Class Of Redundantly-Actuated Parallel Mechanisms

The modeling,analysis,optimization,and control of redundantly actuated parallel mechanisms(RAPMs)are investigated.Parallel mechanisms(PMs)have the advantages of high load,high precision and low inertia.Therefore,those PMs with reduced degrees of freedom(dof)are regularly used as plug-and-play spindle heads to build hybrid machine tools,which can achieve both high precision and high speed in machining of large and complex curved parts,such as aerospace components,nuclear power blades and gas turbines.On the other hand,PMs have disadvantages of reduced workspace and singularities,which limit further application in the industry.An effective solution is introducing actuation redundancy(AR).AR can not only overcome the above shortcomings,but also improve the stiffness and load.Redundant actuation,however,poses challenges to dynamics modeling and controller designing regarding internal force distribution and optimization.In order to solve the above problems,a systematic approach in modeling,optimization,actuation,and control is pivotal to the application and industrialization of RAPMs.In order to optimize the designing and modeling of RAPM,two reduced dof spatial RAPM,2PUR-2RPU and 2UPR-2RPU,are studied thoroughly,from kinematics and dynamics to torque optimization and control.The contents are as follows:(1)Taking the 2PUR-2RPU RAPM as an example,the kinematics and dexterity are analyzed comprehensively.A global optimization method and algorithm based on the condition number is proposed to optimize system parameters.A brief kinematic analysis of the 2UPR-2RPU RAPMs is included as well.By resorting to the static force analysis,the mapping between the external forces of the moving platform and the driving forces is revealed,and the stiffness model is obtained.Finally,the comparison with the non-redundant counterpart is presented,of both the 2PUR-2RPU and the2UPR-2RPU RAPMs,which confirms the superior stiffness of redundantly actuated ones.(2)Based on the screw theory,a dynamics modeling approach,that is simple in practice and systematic in theory,is proposed by means of the natural orthogonal complement method(NOC).The driving forces(and or torques)are optimized by Euclidean norm,and an explicit algorithm to calculate the right Moore-Penrose generalized inverse of the coefficient matrix is proposed by QR decomposition.Then,the above-mentioned three RAPMs are used as examples to illustrate the modeling procedures of the NOC methodology.(3)Several approaches for optimal distribution of redundant forces(torques)are compared.Integrating the Euclidean-norm and the infinite-norm solutions,a redundant solution based on the high-value p-norm is firstly proposed and then applied to the RAPMs under study.Furthermore,a geometrical based minimum-actuation method is expanded to efficiently and effectively optimize redundant forces.(4)The differences between Cartesian space and joint space in controlling RAPM are analyzed and compared.To balance actuator-force and track trajectory,a synchronous optimization method is proposed and integrated into two controllers,one revised Force/Position Hybrid control law and the other hybrid reaching-law integral SMC,followed by simulation and comparison for the the 2PUR-2RPU robot.(5)Finally,an experimental study of a 2UPR-2RPU RAPM prototype is included as verification of the proposed control laws.The purpose of this thesis is to provide some theoretical guidance for the design,analysis,optimization and control of RAPMs,and to lay the foundation for the system modeling and engineering applications of such mechanisms.