This work considers a disc cam mechanism with an upright installed negative radius translating roller follower. Accurate descriptions, as well as the basic concept and steps, are given for the shape, basic/overall size, and size synthesis of the new mechanism. A size coordinate system O – r₀R and size domain (r₀, R) are established, which are given discrete-meshing (grid) treatment. In addition, four constraints are proposed for the calculation formula. The traversal technique is used to achieve visual mapping under single/merged constraints, which gives the corresponding boundary and solution domain. Then, a combination of multiobjective planning and visual mapping reveals important principles such as the non-inferior region (1), ridge point Pj*/ridge line p*, and bottom ridge point P**/double optimal point Pb*, as well as the existence of the global optimal solution. We have therefore obtained instructive and important conclusions for the size synthesis of the new mechanism.