In this article, we developed a new grip force measurement concept that allows for embedding tactile stimulation mechanisms in a gripper. This concept is based on a single force sensor to measure the force applied on each side of the gripper, and substantially reduces tactor motion artifacts on force measurement. To test the feasibility of this new concept, we built a device that measures control of grip force in response to a tactile stimulation from a moving tactor. We calibrated and validated our device with a testing setup with a second force sensor over a range of 0 to 20 N without movement of the tactors. We tested the effect of tactor movement on the measured grip force, and measured artifacts of 1% of the measured force. We demonstrated that during the application of dynamically changing grip forces, the average errors were 2.9% and 3.7% for the left and right sides of the gripper, respectively. We characterized the bandwidth, backlash, and noise of our tactile stimulation mechanism. Finally, we conducted a user study and found that in response to tactor movement, participants increased their grip force, the increase was larger for a smaller target force, and depended on the amount of tactile stimulation.