Dynamic Modeling Method of Spatial Passive Over-constrained Parallel Mechanism Based on Newton Euler Method

doi:10.3901/JME.2020.11.048

Abstract

Abstract: The 4-RPTR four-degree-of-freedom space passive over-constrained (redundant constrained) parallel mechanism is taken as the research object, and the Newton Euler method combined with the complementary deformation coordination equation is used to analyze the dynamics. The number of dynamic equations based on Newton’s Euler method is 78, but due to the existence of passive over-constraints of the mechanism, the unknown variables of the required solutions are 80. When the eight deformation coordination equations are added according to the method of planar over-constrained mechanism, it will be linearly related to the 78 equations built, resulting in the equations being unable to solve. Based on this, when proposing the dynamics modeling of passive over-constrained parallel mechanism, the reason for the passive over-constraint of the mechanism should be analyzed firstly. On this basis, adding the deformation of the member caused by the redundant constrained force (torque) and the position and posture error of the terminal platform as a complementary equation ensures that the equations are linearly independent and can be solved. To this end, the relationship between the deformation of the rod and the position and posture error of the terminal platform caused by the rotational joint restraining torque directly causing the redundant constraint is introduced, and eight deformation coordination equations are added, and six unknown variables are introduced, thereby obtaining 86 equations. Containing 86 unknowns, and the equations are linearly independent, the dynamic solution model of the mechanism is obtained. Based on matlab and adams software, the dynamics simulation of the mechanism is carried out. When the same motion trajectory is given at the terminal of the platform, the correctness of the dynamic model can be seen by comparing the driving force variation curves of the two methods. It provides a new idea for dynamic modeling of this type of space passive over-constrained mechanism.

Key words: parallel mechanism, over-constraint, dynamics, deformation coordination analysis

CLC Number:

TH113

LI Yongquan, GUO Yu, ZHANG Yang, ZHANG Lijie. Dynamic Modeling Method of Spatial Passive Over-constrained Parallel Mechanism Based on Newton Euler Method[J]. Journal of Mechanical Engineering, 2020, 56(11): 48-57.

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