Cam mechanisms featuring negative-radius roller-followers are highly valued for their load-bearing capacity, simplicity, and compactness. Despite these advantages, severe undercutting poses a significant design challenge. This paper introduces an innovative analytical approach to cam contour design by utilizing the camshaft's axis position and the roller radius as the primary design parameters. By revealing the quantitative relationship between the curvature radii of the cam pitch curve and the cam contour, a novel no-undercutting criterion is established. Based on this criterion, two distinct regions for camshaft axis positioning are quantitatively identified: Type I (the inevitable-undercutting region) and Type II (the possible-undercutting region). Furthermore, a spatial model integrating the camshaft position and roller radius is constructed to intuitively visualize both the underlying causes of undercutting and the global motion fidelity solution space. This proposed approach not only simplifies the determination of the minimum cam contour size but also aligns more closely with practical engineering scenarios where the follower's position is predetermined.
Hu et al. (2026) studied this question.