Studies On Mobility Calculation And Dynamic Analysis Methods Of Bennett Unit Depolyable Mechanisms

During the unfolding or folding processes,deployable mechanism shows the motion characteristics of the mechanism,while it presents the stability of the structure in its configuration keeping stages.Therefore,deployable mechanism can be called as the deployable structure.Due to small folding dimension,convenient for store and transportation,large unfolding configuration,convenient for application and maintaining configuration,deployable mechanism has been widely used in the aeronautic,astronautic and building fields.Bennett linkage is a typical spatial overconstraint mechanism,which can bear lager load than other regular unit linkages on the premise of guaranteeing kinematic accuracy.As a unit mechnism,Bennett linkage can be used to compose large deployable mechanism by the array,overlapping method and so on,and this kind of deployable mechanisms are called as Bennett unit deployable mechanisms.Bennett linkage can be used to build deployable antennas,deployable masts,shelters and so on,and their application prospects are broad.This paper studied the configuration design methods and mobility calculation methods of Bennett unit deployable mechanism.This paper also built the kinematic,dynamic and joint clearance dynamic characteristic analysis methods of Bennett linkage and Bennett unit deployable mechanism.These methods are testified by comparing the theory results with the experimental results.The main research works and novel points are as follows:(1)Based on the screw theory,the kinematic and dynamic analysis models of Bennett Linkage are built,and its kinematic and dynamic characteristics are analyzed.Firstly,based on the kinematic pair dismantling method,Bennett linkage is treated as a spatial open series mechanism,and the screw theory combining with virtual work principle are applied to deduce the kinematic and dynamic analysis equations of the open chain series mechanism by composing of revolute pairs.Secondly,the transformation relationships between the global coordinate system and the local coordinate system in Bennett linkage are analyzed,and the kinematic and dynamic models of Bennett linkage are built by using the characteristic of spatial open series mechanism.Thirdly,the improved solution method of reciprocal screw is proposed based on the existing method,which is applied to solve the kinematic pair constraint forces of Bennett linkage.This novel method can be used not only to solve the kinematic pair constraint forces of other linkages but also to combine with traditional method to solve static forces and dynamic analysis.Finally,the kinematic and dynamic characteristics of Bennett linkage are analyzed by the method proposed in this paper.(2)The configuration designs of the multi-bar linkages based on Bennett linkage and Bennett unit deployable mechanisms are carried out,and their mobility calculation formulas are built.Firstly,the constituting geometrical condition of the multi-bar linkages based on Bennett linkage and Bennett unit deployable mechanism are studied,and their configuration designs are accomplished.Secondly,with the help of adding virtual bars combining with unit overconstraint overlapping method,the overconstraint solution procedures of the multi-bar linkage based on Bennett linkage are simplified,and their degrees of freedom are calculated by the Modified G-K formula.Then,Bennett unit deployable mechanisms are classified,and their overconstraints and degrees of freedom are solved by the overlapping method and the Modified G-K formula respectively.Finally,the adjacent link fixing method is used to control the mobility of Bennett unit deployable mechanism,and some novel Bennett unit deployable mechanisms are constructed.(3)According to the multi-closed loop and overconstraint characteristics of Bennett unit deployable mechanism,the kinematic and dynamic analysis model and solution method of Bennett unit deployable mechanism are proposed.Firstly,the coordinate transformation matrices between the adjacent units of Bennett unit deployable mechanism are deduced.Secondly,the Jacobian matrices and Hessian matrices for the mass centroid of all links and kinematic pairs of Bennett unit deployable mechanism are obtained by the kinematic analysis method of the spatial open chain series mechanism proposed in this paper and through combining with screw theory and the coordinate transformation method,and then its kinematic analysis model was built.Finally,the virtual work principle is used to build the dynamic analysis model of this mechanism,and then its dynamic characteristics was analyzed.(4)A joint clearance in mechanism is described using an equivalent joint clearance link.The joint clearance dynamic analysis models of Bennett linkage and Bennett unit deployable mechanism are built,which are used to study the effect of joint clearance on their dynamic characteristics.Firstly,the kinematic parameters of the equivalent joint clearance link are decided by constraint forces of Bennett unit linkage.The vector loop equations of Bennett linkage are built,and then on this basis the dynamic analysis model with joint clearance of Bennett linkage is proposed.Secondly,according to the characteristics of Bennett unit deployable mechanism,a novel idea to solve joint clearance dynamics of complex deployable mechanisms is proposed.In the new method,the complex deployable mechanisms are divided into many unit mechanisms.The influence of the clearance of the motion pair on the unit mechanism is studied.Finally,according to the geometrical relationships between unit mechanisms,effects on kinematics and dynamics of the whole deployable mechanism with joint clearance are studied.(5)In order to testify the correctness of the model and method in this paper,the dynamic characteristic experimental researches of Bennett unit deployable mechanism are carried out.Firstly,the experimental elements of Bennett linkage and Bennett unit deployable mechanism are designed and manufactured.A dynamic performance experiment table of Bennett unit deployable mechanism is constructed,and the experiments of the deployable mechanism dynamics and the joint clearance dynamics are carried out.And then,the mass centroid vibration accelerations of relevant links of Bennett linkage and Bennett unit deployable mechanism under the ideal condition and considering joint clearances are tested.Finally,the tested values are contrasted to the theoretic values,and the results testified the validity of the joint clearance dynamic analysis model and analysis method.This paper studied the kinematics,dynamics and joint clearance dynamics of Bennett linkage and Bennett unit deployable mechanism,and the configuration design and mobility calculation of Bennett unit deployable mechanism.The research can deepen the cognition of Bennett linkage and Bennett unit deployable mechanism to some extent.This benefits their promotions and applications in the engineering fields.Meanwhile,it can provide references for the kinematics,dynamics,joint clearance dynamics,mobility calculation and configuration designs of other unit deployable mechanisms.