Certain aspects relate to systems and techniques for medical robotic systems that leverage a versatile, open kinematic chain together with a set of medical-procedure-specific software-controlled actuation constraints in order to perform a variety of medical procedures. The robotic system can be operated in a first mode by identifying a remote center and constraining the actuation of motorized joints to maintain intersection of at least an insertion axis with the remote center. The robotic system can be operated in a second mode by identifying a virtual rail position and constraining the actuation of motorized joints to maintain alignment of the insertion axis along the virtual rail.