Abstract
The nonlinear elastodynamic modeling and analysis of the 4-UPS-UPU spatial 5-degree-of-freedom parallel mechanism are investigated. The kinetoelastodynamics theory is used to derive the elastic dynamic equations of 4-UPS-UPU spatial parallel mechanism. In order to grasp the effect of geometric nonlinearity on dynamic behaviors, such as displacement error output, velocity error output, acceleration error output, stress of driving limbs, and natural frequencies, the variations of dynamic behaviors considering geometric nonlinearity and without considering geometric nonlinearity are discussed, respectively. The numerical simulation results show the nonlinear elastodynamic model established can reasonably reflect the dynamic behaviors of 4-UPS-UPU spatial parallel mechanism with flexible driving limbs. And geometric nonlinearity is demonstrated to have significant impact on dynamic response and dynamic characteristics of spatial parallel mechanism. The researches can provide important theoretical base for the optimal design of spatial parallel mechanism.
Highlights
The spatial parallel mechanism has a series of advantages, such as high speed, high acceleration, stronger bearing capacity, and higher ratio of stiffness and weight [1, 2]
In the high speed working conditions, the light weight driving limbs of spatial parallel mechanism are bound to have a certain degree of elastic deformation, which can cause the motion error and vibration of the mechanism and lead to the decrease of the kinematics performance and dynamics performance of mechanism [3, 4]
The dynamic equations of the 4-UPS-UPU high speed spatial parallel mechanism are built according to the following assumptions
Summary
The spatial parallel mechanism has a series of advantages, such as high speed, high acceleration, stronger bearing capacity, and higher ratio of stiffness and weight [1, 2]. Wang and Mills [5] established dynamics model of planar 3-RRR elastic inside links parallel robot by the use of finite element method and Craig-Bampton theory and analyzed the response of moving platform and vibration of inside links bottom. Based on the kinetoelastodynamics theory, the nonlinear elastodynamic model of the 4-UPS-UPU 5-DOF spatial parallel mechanism (see Figure 1), which has three translation degrees of freedom and two rotation degrees of freedom and consists of four UPS (universal joints-prismatic pairsspherical joints) driving limbs, one UPU (universal jointsprismatic pairs-universal joints) driving limb, a fixed platform, and a moving platform, is investigated; the effect of geometric nonlinearity on dynamic behaviors, such as displacement error output, velocity error output, acceleration error output, stress of driving limbs, and natural frequencies, is analyzed
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