Measurement of interaction forces to an instrument tip of the surgical robot is necessary to render high-fidelity haptic feedback for the minimally invasive robotic surgery. This paper proposes a method to estimate the 3-DOF interaction forces by measuring reaction forces at connection parts, known as the trocar and the drape plate, between the instrument and the slave robot arm. Estimation of the interaction forces in the x and y directions to the instrument tip can be estimated by measuring the reaction force at the trocar support. Estimation of the interaction force in the z direction can be estimated by measuring the reaction force at the drape plate and the trocar support. It is confirmed that the interaction forces can be estimated accurately regardless of the friction and change of the $l_T$ by installing a 3-DOF force sensor at the trocar support and a 1-DOF force sensor at the drape plate support. I-shaped 3-DOF force sensor at the trocar support is designed to minimize the coupling effect, and 1-DOF force sensor at the drape plate is designed. It is possible to estimate the interaction forces in the x and y directions by using the sensor at the trocar support with average $L_2$ relative error less than 7.68 % and 3.25 %, respectively. The interaction force in the z direction is also estimated with error less than 8.26 % by using the sensors at the drape plate and the trocar support.