Kinematic Position Analysis of a 7R Double Loops Spherical Mechanism without Resultant Elimination
A method for kinematic analysis of a 7R double loops spherical mechanism is proposed.Taking the direction vector of the spherical 4R linkage as an intermediate variable,a set of linear equations about it is established.Without resultant elimination,the motion equations of input and output are directly obtained.The displacement analysis results are consistent with the data in the existing literature.The advantage of this method is that it does not need to introduce intermediate joint variables into the kinematic equation,which simplifies the process of mechanism displacement analysis.This method is used to analyze the motion of a multi-mode 7R double loops spherical mechanism.By factoring the kinematic equation,the two motion modes and their common positions of the mechanism are determined,and the rotating workspace of the mechanism is analyzed.The results show that the 7R double loops spherical mechanism has two motion modes that are belong to one dimensional rotational displacement subgroup and one dimensional rotational displacement manifold.This method has certain theoretical application value in analyzing the influence of structural parameters on the motion mode of 7R double loops spherical mechanism.
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