An end-effector such as a gripper or multi-fingered hand is essential to enable robots to grasp and manipulate objects of various size and shape. Soft skin increases the grasp stability and can provide space for tactile sensors. However, covering the joints with skin is challenging, typically causing a considerable surface area of multi-segment robot fingers not to be covered by skin. This also creates the risk that objects get pinched in the joints when flexing the fingers. The current paper suggests using a remote center motion (RCM) mechanism to move the center of joint rotation to the surface of a thick skin layer. In particular, a 6-bar mechanism is used. Thereby, a thick soft skin layer with a continuous surface can be realized. Furthermore, adaptive joint coupling with linkages is implemented. In the current paper a 2-fingered gripper is realized, and objects of various size and shape are grasped (from thin paper to objects of 135 mm diameter). The current gripper was manufactured with 3D-printed material to enable rapid prototyping, therefore the payload was limited to only 1 kg for this version. Overall, this paper shows the feasibility of an RCM for a robot finger and discusses the benefits and limitations of such a mechanism.