| Parallel mechanisms are widely used in various fields and reconfigurable parallel mechanisms have been developed according to the requirements of multi-task and multi-objective.In this paper,the 3-RRR planar parallel mechanism(PPM)is taken as the research object.In order to solve the problems of complex drive and control and large energy consumption,the parallelogram kinematic link is used to constrain the 3-RRR PPM as a single-driven 3-RRR PPM.The input-output(IO)equation of the mechanism is derived based on Freudenstein equation.The iterative algorithm is used to establish the numerical solution of the equation.A set of parameters is given as a numerical example.Two configurations of the mechanism,named configurations I and II,are solved.The coupler curves and orientations of configuration I and II varied with input angles are calculated.The results show that the theoretical curve is consistent with the simulation curve,which verifies the correctness of the solution method.Based on the screw theory and the power coefficient,the kinematic/force performance index formula of the single-driven 3-RRR PPM is derived.Since each limb of the mechanism is interrelated,the driving power is transferred to each limb step by step through different constraint link.Under this condition,the influence of the driver on the kinematic/force performance index of the mechanism is analyzed when the driver on different limb of the mechanism.The results of numerical examples shows that the kinematic/force input transmission index(ITI)of the single-driven 3-RRR PPM is related to the cosine of the inverse pressure angle(IPA)of each limb and link,and the ITI can be used as the local transmission index(LTI),and the kinematic/force total constraint index(TCI)is always good.The good-transmission workspace(GTW)is independent of the number of times the driving power is transmitted,so the drive position of the mechanism should be determined according to the specific calculation results to ensure that the mechanism has a wider range of GWT.Based on the physical meaning of the screw,the singularity of the singler-driven 3-RRR PPM is studied from two aspects of transmission and constraint,and two singularity configurations of two constraint linkages are obtained by observation.The mathematical formula for calculating the singularity configuration of the mechanism is established,and all the singularity configurations of the mechanism are determined by calculation.By comparing the simulation results,the correctness of the theoretical calculation is verified.The results show that there are no constrained singularities and output transfmission singularity,but there are two input transmission singularities in each limb.By changing the initial input angle of the mechanism,a reconfiguration method for the configuration of the single-driven 3-RRR PPM is proposed.The effects of the reconfigration on the coupler curves and orientations,the kinematic/force performance indexes and the singularity are calculated and analyzed by giving several reconfigration angles.The results show that the theoretical curve of the reconfigurable single-driven3-RRR PPM is consistent with the simulation curve,which verifies that the solution method is also applicable to the reconfigrable mechanism.Reconfigration can significantly change the coupler curves and orientations of configuration I and II,and the impact on the configuration II more apparent.The reconfiguration has a great influence on the motion/force TPI of the mechanism.The GTW range can be increased significantly with the appropriate reconfiguration Angle,but may lose the GTW.There is no output transmission singularity in the three limbs under any reconfigration configuration.The results of this paper have important reference value for the transformation of the multi-driven mechanism into a reconfigurable single-driven mechanism. |
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