Novel Reconfigurable Goldberg 6R Linkages And Their Isomerizations

Reconfigurable mechanisms,having various configurations and mobilities,can perform different motions to meet the needs of one machine with multiple functions.Based on the constructions of Goldberg 6R linkages,by adding some link conditions to the linkages to lead to the linkages with symmetric geometric parameters,this paper proposed four novel reconfigurable 6R linkages,and analyzed the motion branches and bifurcations.Based on the construction of variant series Goldberg 6R linkage,utilizing the same Bennett linkages left and right,a line-symmetric Goldberg-Bricard 6R linkage was obtained.There was one Goldberg 6R branch,two line-symmetric Bricard 6R branches and one Bennett 4R branch.Based on the construction of L-shape Goldberg 6R linkage,a plane-symmetric Goldberg-Bricard 6R linkage was constructed by using on equilateral Bennett linkage in the middle and two Bennett linkages with opposite twist in the up and right.There was a plane-symmetric Bricard 6R branch,a Bennett 4R branch and a series branch.Based on the construction of Wolhart’s double-Goldberg linkage,a reconfigurable double-Goldberg 6R linkage was constructed by using two special Goldberg 5R linkages.There were two Goldberg 6R branches and two isomeric line-symmetric 6R branches.Based on the construction of variant L-shape Goldberg6 R linkage,a reconfigurable variant L-shape Goldberg 6R linkage with one Goldberg6 R branch and one series branch was constructed by three equilateral Bennett linkages.Based on the new reconfigurable linkages and the isomerizations proposed by Wolhart,the isomeric linkages of these new reconfigurable mechanisms were derived.Based on the numerical method of singular value decomposition,the branch characteristics and bifurcations of eight new reconfigurable linkages were analyzed.Based on the above,the functions of isomerizations were summarized.Isomerizations do not change the numbers of motion branches and bifurcation points.However,the forms of motion branches are altered,which is represented by the change of movable joint numbers and the change of symmetries.Through the bifurcations of the linkages,reconfigurations,the same effect of reassembly of line-symmetric Bricard linkages were realized.The relationships between Bennett-based family and Bricard-related family was discussed preliminarily.The Goldberg-Bricard 6R linkages can bifurcate between Bennett-based and Bricard-related families.In this paper,the method of constructing Goldberg 6R linkages by equilateral Bennett linkages was proposed,and the possibility was verified by an example of the reconfigurable variant L-shape Goldberg 6R linkage.