Based on Hertz theory,the engagement rigidity model of the cycloid ball transmission is established,and the engagement rigidity is converted to the dimensionless form. The influence regularity of the structural parameters on the dimensionless engagement rigidity of cycloid ball engagement pairs is analyzed. The equivalent torsional rigidity formula of the planetary transmission section is deduced by using the engagement rigidity. On the basis of considering the the equivalent torsional rigidity of the input shaft,the output shaft and the planetary transmission section,the 4 freedoms torsional vibration model of the NN cycloid ball transmission is established,and the analysis of example is carried out.