Constrained motion is essential for varying robotics tasks, especially in surgical robotics, for instance, the case of minimally invasive interventions. This article proposes generic formulations of the classical bilateral constrained motion (i.e., when the incision hole has almost the same diameter as that of the tool) as well as unilaterally constrained motion (i.e., when the hole incision has a larger diameter compared to the tool diameter). One of the latter constraints is combined with another surgical task such as incision/ablation or suturing a wound (modeled here by 3D geometric paths). The developed control methods based on the hierarchical task approach are able to manage simultaneously the constrained motion (depending on the configuration case, i.e., bilateral or unilateral constraint) and a 3D path following. In addition, the proposed methods can operate with both straight or curved surgical tools. The proposed methods were successfully validated in various scenarios. Foremost, a simulation framework was proposed to access the performances of each proposed controller. Thereafter, several experimental validations were carried out. Both the simulation and experimental results have demonstrated the relevance of the proposed approach, as well as promising performances in terms of behavior as well as accuracy.