Analysis And Type Synthesis Of Lower-mobility Parallel Mechanims Based On Constraint And Its Errors

Lower-mobility parallel mechanisms rely on strictly geometrical constraints of axis of pairs in and between limbs to obtain the reduced number of DOF. In practice however these constraints will never been perfectly fulfilled due to the inevitability of errors, and hence produce series bad effects and problems.In this paper,the constraint system and overconstraint characteristics of lower mobility parallel mechanisms were analysed systematically based on screw theory and set theory.And then the statically determinate and statically indeterminate nature of the mechanisms in the reduced DOF space were obtained.Using structural mechanics theory,effects of geometrical constraints errors on lower-mobility parallel mechanisms were studied via virtual open kinematic chain method.The results revealed the sensitivity with respect to geometrical conditions of overconstrainted mobility,and provided an insight into the effects of constraint errors and overconstraints on parallel mechanisms.Due to the inherent shortcomings of overconstraint mechanisms,the design method of non-overconstrained structure were presented systematically in order to improve the self-adaptive and dynamic performance.The main work and achievement of this paper is as follows:â‘ Using screw theory and set theory as mathematical tools,the DOF and constraint system of pairs,open kinematic chains,single loop mechanisms,were systematically summarized and in-depth studied.The constraint and overconstraint characteristics of lower-mobility parallel mechanisms were studied via the union of limb constraints and the coupling of loop overconstraint.A symbol method to describe the constraint mode were built.The quantity relationship of overconstraints between basic loops and whole mechanism had been obtained.A system approach for overconstraint quatity calculation,overconstrained loop identification,overconstraint distribution in loop,have been established.The concepts of all-loop overconstraint,multi loop overconstraint, and single-loop overconstraint ,have been provided.This builds a concrete basis for analysis and design of lower-mobility parallel mechanisms.â‘¡Based upon the exponential matrix and exponential products of modern screw theory for the rigid body transformation,the pose error of kinematic pair axis were treated as the result of equivalent screw motion,and an error model of open kinematic chain was built by using the products of exponentials formula.Meanwhile,the position and orientation errors of tool tip were represented as virtual prismatic and revolute pair's screw motion respectivly,and its calculation formula is presented.A software package for screw calculation was developed under Matlab enviroment.Using this package,the error simulation of two typical open kinematic mechanisms were performed via Matlab programming.Furthermore,Adams's simulation were used in verifying the established model.The results indicate that the simulation method is effective and correct,the modeling process is simple and intuitive.â‘¢Based on overconstraint analysis, and using the virtual open kinematic chain mehod of loop,the effects of geometric constraint erros of pairs'axis on lower-mobiliy parallel mechanism, were studied.Using matrix force method,the internal force and deformations of links were caculated,and parasitic motions of moving platform were analysised.Moreover,the strain energy fluctuations were investigated.Simulation results provide an insight into the effects of constraint errors and overconstraints on parallel mechanisms.â‘£Based upon wrench system and set theory, the structural conditions of non-overconstrained lower-mobility parallel mechanisms and its synthesis method were proposed.The detailed synthesis procedure of 3-DOF parallel mechanisms were discussed and a series novel symmetrical structures had been found.Finally, the difference between overconstrained and non-overconstrained structure was compared. This provides a new point of view and approach for the structural synthesis of lower-mobility parallel robots and a new way to eliminate the sensitivity of overconstraint with respect to geometrical erros of the kinematic pairs.The above research results provided an insight into the principal of interaction between limb constraint,and overconstraint coupling in different loops.Furthermore it revealed the sensitivity with respect to the geometrical conditions of overconstrained lower-mobility parallel mechanisms and its impact on the performance of the mechanism.This provided a new idea for mechanism analysis.The systematic design procedure of non-overconstrained structure provided a comprehensive new way and innovative approaches to eliminate the effects of overconstraint and geometrical conditions erros.The achievement of this paper enriched the analysis theory and methods of lower-mobility parallel mechanisms.It also given a new way and opened up a new field for the applications of non-overconstrained mechanisms.The results have important theoretical and practical engineering value.