As a new type of specially defined pluralized vector model,the ternary number has the naturally intuitive geometric significance and it is especially helps to the three-dimensional modeling for a spatial problem. Based on the original concept of a ternary number,starts from the definition of the rotated projection product of a ternary number,the meaning of the ternary number is extended at first,the differential features of a ternary complex variable is analyzed,and then the conclusion on the differential properties of a ternary complex variable is obtained. The differential operation to a ternary complex variable can be transformed as the operating of the rotated projection product of a ternary number. As this result,it provides a new path for the analytic solution of the spatial motion analysis of the some mechanism. The checkout of the endpoint velocity and acceleration for a three-joint simple robot is carried out by this means. Both their size and direction are obtained in the only calculation process at same time. Finally,the analysis of the position is carried out for the 3-RPS type of the 3-DOF parallel robot. From another point of view,above mentioned facts show and verify that it is possible and feasible for the analytic solution of the motion analysis of the three-dimensional spatial mechanism by means of the modeling tool of a ternary number.