For assembly tasks, it is essential to fix target parts firmly and accurately estimate their poses. Several rigid jigs for individual parts are frequently used in assembly factories to achieve a precise and time-efficient product assembly. However, providing customized jigs is time-consuming. In this study, to address the lack of versatility in the shapes for which jigs can be used, we developed a flexible jig with a soft membrane including transparent beads and oil with a tuned refractive index. The bead-based jamming transition was accomplished by discharging only the oil, enabling the part to be firmly fixed. Because the two cameras under the jig can capture membrane shape changes, we proposed a sensing method to estimate the orientation of the part based on the behaviors of markers created on the jig's inner surface. Through estimation experiments, the proposed system can estimate the orientation of a cylindrical object with a diameter larger than 50 mm and an RMSE of less than 3°.