The paper presents an analytical approach for designing grooved cam mechanisms with a modified arrangement of the common translating follower. That is, an intermediate link having three rollers is added between the cam and the common follower. On the basis of an existing cam mechanism with a common roller follower, an intermediate link that has three rollers is added between the cam and the common follower. Such a cam mechanism has two set of profile and can create multiple contact points between the cam and the follower at any instant. The two sets of profiles of such a cam mechanism can serve as the grooved types. Since the follower has three rollers that can simultaneously contact the cam at any instant, it can be positive driven along the guided groove of cam contour. The contact forces and contact stresses of such cam mechanisms are analyzed to illustrate the advantage of spreading force transmission and reducing contact stress of this uncommon follower. The obtained results indicate that the contact stress at the surface of the cam and the follower for such a cam mechanism can be reduced by 30% to 47% in comparison to those of cam mechanism with a common translating roller follower. In conclusion, the cam mechanism with a translating follower having an added ternary-roller intermediate link can be a preferable choice for the applications that follower is against heavy loads or move at high speed.