In constant-breadth cam mechanisms closure of the higher kinematic pairs formed by the bilateral cam-follower contact is guaranteed by the geometry of both cam and follower. A study of the cam profile by means of its radius of curvature and the sliding velocities in the upper pair enables us to predict the correct functioning of the mechanism. This work presents the equations for calculating cam breadth when the translating follower is eccentric with an inclination, the radius of curvature of its profile and the sliding velocities of constant-breadth cam mechanisms with translating and oscillating followers. This study also analyses the influence of the angle of inclination and the offset of the flat-faced translating followers on the size of the cam and the kinematics of the mechanism. Numerical examples are given of constant-breadth cams obtained for distinct values of the mentioned parameters. Additionally, this paper describes the redesign of a cam of a conventional sewing machine and the new cam prototype, with a continuity of an order higher than the original profile, is included. (C) 2014 Elsevier Ltd. All rights reserved.