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Our research aims at developing a meal-assistance robot with vision system and multi-gripper that enables frail elderly to live more independently. This paper presents a development of a chopstick-type gripper for a meal-assistance robot, which is capable of adapting its shape and contact force with the target food according to the size and the stiffness. By solely using position control of the driving motor, the above feature is enabled without relying on force sensors. The gripper was designed based on the concept of planar 2-DOF under-actuated mechanism composed of a pair of four-bar chains having a torsion spring at one of the passive joints. To clarify the gripping motion and relationship among the contact force, food's size and stiffness, and gripping position, kineto-elasto-static analysis of the mechanism was carried out. It was found from the result of the analysis that the mechanism was able to change its gripping force according to the contact position with the target object, and this mechanical characteristic was utilized in its grasp planning in which the position for the gripping the object was determined to realize a simple control system, and sensitivity of the contact force due to the error of the stiffness value was revealed. Using a three-dimensional (3D) printed prototype, an experiment to measure the gripping force by changing the contact position was conducted to validate the mechanism feature that can change its gripping force according to the size and the stiffness and the contact force from the analysis results. Finally, the gripper prototype was implemented to a 6-DOF robotic arm and an experiment to grasp real food was carried out to demonstrate the feasibility of the proposed grasp planning.