Stiffness modeling is one of the most significant issues in the design of parallel kinematic machine (PKM). This paper presents a semi-analytical approach that enables the stiffness of PKM with complex machine frame geometry to be estimated effectively. This approach can be implemented by three steps: (i) decomposition of the entire system into two sub-systems associated with the parallel mechanism and the machine frame respectively; (ii) stiffness modeling of each sub-system using the analytical approach and the finite element analysis; and (iii) generation of the stiffness model of the entire system by means of linear superposition. In the modeling process of each sub-system, the virtual work princi- ple and overall deflection Jacobian are employed with special attention to the bending rigidity of the constrained passive limb and the interface stiffness of the machine frame. The stiffness distribution of a 5-DOF hybrid robot named TriVariant-B is investigated as an example to illustrate the effectiveness of this approach. The contributions of component rigidities to that of the system are evaluated using global indices. It shows that the results achieved by this approach have a good match to those obtained through finite element analysis and experiments.
WANG YouYuHUANG TianZHAO XueManMEI JiangPingDerek G CHETWYND
A novel reconfigurable 5-DOF hybrid manipulator―TriVariant-B is composed of a 2-DOF spherical parallel mechanism which is serially connected with a 3-DOF open-loop kinematic chain undergoing one translation and two rotations by a prismatic joint. The merit of this design is that a relatively large workspace/limb- stroke ratio can be achieved thanks to the decomposition of the fixed point rotation and the relative translation. In this paper, on the basis of inverse dynamic formula- tion of the 2-DOF spherical parallel mechanism, an approach is proposed for esti- mating the servomotor parameters including moment of inertia, rated speed and the maximum torque in a quick manner. The approach has been employed for the development of a prototype for frame cutting process.
We derive the non-dimensional coupling equation of two exciters,including inertia coupling,stiffness coupling and load coupling.The concept of general dynamic symmetry is proposed to physically explain the synchronisation of the two exciters,which stems from the load coupling that produces the torque of general dynamic symmetry to force the phase difference between the two exciters close to the angle of general dynamic symmetry.The condition of implementing synchronisation is that the torque of general dynamic symmetry is greater than the asymmetric torque of the two motors.A general Lyapunov function is constructed to derive the stability condition of synchronisation that the non-dimensional inertia coupling matrix is positive definite and all its elements are positive.Numeric results show that the structure of the vibrating system can guarantee the stability of synchronisation of the two exciters,and that the greater the distances between the installation positions of the two exciters and the mass centre of the vibrating system are,the stronger the ability of general dynamic symmetry is.
A study of dimensional synthesis of a 3-DOF parallel manipulator with coupling of translation and rotation is carried out.The architecture of the manipulator is composed of a moving platform attached to a fixed base through three identical PRS(prismatic-revolute-spherical) serial limbs,whose unique topology leads to the physical unit inconsistency of the conventional Jacobian matrix and the emergence of the parasitic motion.Then this paper introduces a kinetostatic performance index of the manipulator based on the condition of a dimensionally homogeneous Jacobian matrix,later,the workspace of the aforementioned manipulator is searched and the influence of the crucial design variables on the workspace is analyzed.Finally,a dimensional synthesis method of the manipulator is proposed,which may be regarded as a nonlinear programming problem with subject to the parasitic motion and other several engineering constraints.
SUN Tao1,SONG YiMin1,LI YongGang2 & LIU LinShan1 1 School of Mechanical Engineering,Tianjin University,Tianjin 300072,China
