Motion/Force Transmissibility Evaluation And Optimum Design For Redundantly Actuated Parallel Manipulators

This paper proposes new indices for optimal design and analysis of redundantly actuated parallel manipulators by evaluating their motion/force transmissibility.The main contents cover the following aspects:(1)This method is based on the screw theory,and the motion/force transmission in the parallel manipulator is discussed.(2)A method for evaluating the motion/force transmissibility of redundantly actuated parallel manipulators is presented,and novel global indices is proposed for optimal design.First,we proposed a method to extract a multi-DOF(degrees of freedom)redundantly actuated PM into several subsidiary 1-DOF PMs with two or more actuators by locking some actuators in an ergodic manner.Then,a new index of output transmission performance is proposed by investigating the mean value of the instantaneous power produced by the multiple actuation wrenches and one twist of the moving platform of 1-DOF PMs.A local transmission index(LTI)is defined as the minimum value of the index of output and input transmission performance.A global transmission index(GTI)is then established based on the LTI.The proposed LTI and GTI are coordinate-free and have clear physical interpretation.The validity and universality of the new indices are demonstrated by analysis of a class of redundantly actuated lower-mobility PMs with extra articulated limbs.(3)Friction stir welding(FSW)has been widely applied in many fields as an alternative to traditional fusion welding.Though a serial robot can provide the orientation ability required to weld along a curved surface,it can barely support the huge axial downward force that FSW generates.A redundantly actuated 2UPR-2RPU parallel robot for FSW is proposed to overcome this limitation,where U denotes a universal joint,R a revolute joint and P a prismatic pair.First,mobility analysis of the 2UPR-2RPU parallel mechanism is presented using screw theory.The mechanism has one translational and two rotational degrees of freedom,which satisfies the orientation demands in FSW.Second,forward and inverse position solutions to the mechanism are obtained.After obtaining the Jacobian matrix from the velocity equations,singularity of the mechanism is discussed.It is shown that actuation redundancy decreases singularity in this parallel robot.(4)The Jacobian matrix of the 2UPR-2RPU parallel mechanism is homogenized using the characteristic length.The reciprocal of the condition number of the homogenous Jacobian matrix is used to evaluate the kinematic performance of the parallel mechanism.Finally,a set of optimal link parameters are selected from the performance atlases of global conditioning index of the proposed parallel robot.(5)The motion/force transmission evaluation is applied to the 2UPR-2RPU parallel manipulator,and GTI is used for the optimal design.The result shows great improvement of motion/force transmission for the manipulator,and is compared to that of GTI method.The research of this paper enriches the theory of parallel robot,and is helpful to the industrial applications of robotic technology.