The optimization of cam mechanisms with translating flat-face followers, upon consideration of curvature constraints, is discussed here. When minimizing the size of the cam disk, cam profiles with cusps, i.e., profiles with curvature discontinuities, can appear. On the other hand, cusps are undesirable because they give rise to inadmissibly large contact stresses and hence, should be prevented from occurring. Conditions under which these discontinuities appear, although available in the literature, are not readily applicable to a specific problem. However, if the synthesis of the follower-displacement program is based on spline functions, then readily applicable design formulas, leading to unconstrained optimum designs, are derived. In the presence of curvature constraints, design charts are derived that produce the cusp-free, minimum-size profile for a given displacement program. The same problem for oscillating flat-face followers is addressed in an accompanying paper.

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