In this paper,a new type euqispeed output mechanismball slip groove output mechanism for cycloid ball transmission is presented based on approximate substitute principle and error of it is analyzed.

With teaching experience of Higher Mathematics in higher vocational college,the author explores how to reveal the higher mathematics thinking method of "Straight replace curve" in part,"approximate replace precision" as a whole by establishing and introducing of three concepts of the limit,derivative,integration,and to train the students how to analyze and solve problems.