Robot grippers and hands are commonly used to grasp various objects. However, for multi-link fingers, it is challenging to cover the joints with tactile sensors, which limits the safety and sensitivity of such fingers. In the current paper we use a remote center of motion (RCM) mechanism for the joints, which enables us to cover also the joints completely with soft and thick tactile sensors, in particular distributed 3-axis sensors. The RCM joints are implemented as 6-bars, and we evaluate their robustness in simulation. A real implementation of the gripper is tested by grasping various objects, and the resulting tactile sensor readings are presented.