Type Synthesis Of Parallel Mechanism With Four Displacement Parameters Based On Generalized Link Group

The calculation of degrees of freedom is the basis of mechanism research.It is the ultimate goal of mechanism research to synthesize new mechanism according to type synthesis methods to solve practical problems in life and engineering.In this paper,according to a fast and simple formula of Mobility of Groups and Output Parameter(GOM formula),the parallel mechanism with four displacement parameters is synthesized.The details are as follows:Firstly,the concept of the original displacement parameters of the link group is proposed.According to the relationship between the displacement parameters of the link group and the constraints of the link group,the displacement parameters of the output link are determined.Whether correctness of the displacement parameter of the output link is based on the correctness of the degree of freedom calculation.The validity of the displacement parameters of the output link is judged by using Grassmann line geometry,and the calculation formula of GOM degree of freedom is improved.The correctness of the improved degree of freedom formula is verified by several typical examples.According to the improved formula of degree of freedom calculation,type synthesis method for parallel mechanism is proposed,and the parallel mechanisms with four output displacement parameters are consisted of 1R3 T,3R1T and 2R2 T mechanism.For the parallel mechanism with 2R2 T displacement parameter,the two cases are analyzed: The output constrained force is parallel to the constrained couple;The output constrained force are not parallel to the constrained couple.In the mechanism synthesis process,the constraints of the output components of each type of mechanism are analyzed,and the corresponding link group sets are synthesized according to the link group formula.Then,according to the geometric relationship between the mechanism synthesis formula and the constraint,a single-loop parallel mechanisms with four,three,and two degrees of freedom,are synthesized.On the basis of a single loop,the multi-loop mechanisms are synthesized by using the concept of virtual pair.