An important extension about second synthesis task of disc cam mechanism with floating roller push rod is carried out. According to the output parameter travel angle β,m, of cam- linkage combination mechanism of a high speed printing machine,the existence of a amplitude（β,m,）,max,which is the maximum value,and the corresponding "β,m, solution domain"-( 0,（ β,m,）,max,〗are found and revealed. The preceding study found that,regardless of digging the potential of existing mechanisms or scalable coverage,all has important theoretical value and practical engineering significance.