1. A system used to finish a three-dimensional surface of a part, the system comprising: a controller unit configured to generate a finishing tool control signal; a finishing tool having a finishing surface, the finishing tool being coupled to a movable arm that responds to the control signal received from the controller unit during a finishing operation; and a sensor unit configured to measure a contact force between the finishing surface of the finishing tool and the three-dimensional surface of the part during the finishing operation, wherein the controller unit dynamically adjusts a position of the finishing tool based on a variable contact force profile that specifies the contact force of the finishing surface applied along a plurality of contact surface areas along the three-dimensional surface of the part and that accommodates variations along the three-dimensional surface of the part compared to a calculated three-dimensional tool path.