In this paper a robotic grinding system which can produce a finished workpiece that respects some product geometric specifications is proposed. It is composed of a 1 DoF active compliance actuator fixed between the grinder and the robot. The 1 DoF actuator associated to the tool can be mounted at existing robotic installations which make this solution very flexible and easy to use by the industrials. The grinding system composed of the robot and the actuator is able to apply a constant contact force between the workpiece and the grinding tool. A path planning method is also presented in this article. Using analytical calculations, the robot path is determined for surface and corner grinding of a parallelepiped workpiece with a given precision of the surface shape.