| A dynamic analysis method of parallel mechanism based on sub-kinematic chain was studied in this paper.Then,a kind of plane punching mechanism with zero coupling degree,a spatial 2T1 R parallel mechanism with zero coupling degree and a spatial 2T1 R PM with one coupling degree were proposed for dynamic modeling,solving and analysis.The solution analysis of the above three mechanisms showed the effectiveness and applicability of the research method.Firstly,three kinds of mechanisms with different degrees of freedom,coupling degrees and their topological characteristics were introduced,which lay the foundation for the kinematic and dynamic analysis of the mechanism.According to the principle and design method for structure coupling-reducing of PM,a plane punching mechanism with symbolic solution of position and zero coupling degree(described as mechanism 1)was designed.At the same time,according to the topology design method of the PM based on the position,orientation and characteristic(POC)equation,a new type of spatial2T1 R PM,which was composed of rotating pairs,and had zero coupling degree and partially decoupled motion(described as mechanism 2),was improved and designed.And its topological characteristic parameters were analyzed,such as POC,DOF,coupling degree,etc.This paper also introduced the topological characteristics of a spatial 2T1 R PM with one coupling degree(described as mechanism 3),proposed by the author’s team.Secondly,the basic idea of the ordered single open chains method based on the Newton-Euler(abbreviation: N-E)principle was introduced.The inverse dynamic modeling of mechanism 1 was established through this method,and compared with the Lagrange method,which showed that the accuracy of the former is higher.At the same time,the ordered single open chains method based on the principle of virtual work was introduced,and the inverse dynamic modelings of mechanism 2 and mechanism 3 were established respectively through this method.Compared with the traditional method of virtual work principle,it showed that the ordered single open chains method based on the principle of virtual work had the advantages of clear modeling ideas,and the ability to obtain the reaction force of the kinematic pair at the joint of the sub-kinematic chain.Finally,on the basis of the foregoing topological structure analysis and kinematics analysis,using the ordered single open chains method based on the principle of virtual work,two types of dynamic response equation(positive and negative)were introduced and their solution ideas were solved.At the same time,taking the above-mentioned mechanisms 1,2,and 3 as the research objects,the matrix coefficients of acceleration(angular acceleration)and the function of the force(moment)on the component with respect to the generalized acceleration were solved respectively.Furthermore,the response equations were numerically solved,and the motion ways of the three mechanisms were obtained.Compared with the dynamic simulation of ADAMS,the correctness of the above dynamic response equations were verified. |
