In order to meet production requirements of small quantity and large variety for versatile market demands, industrial robots with dexterous end-effectors are usually applied to the flexible manufacturing systems. However, owing to constraints of robot¡¦s accuracy, repeatability, and resolution, assembled parts may experience collision during the insertion process. Both positional and angular errors, which cannot be easily predicted because of indeterminate collision situations, may cause failure of the assembly. One of the frequently applied strategies is to use a passive remote center compliance device. Most traditional remote center compliance (RCC) devices aim to solve insertion difficulty for round peg insertion. This dissertation is devoted to analyze the insertion behavior and develop a new remote center compliance device for square pegs, which lack of the axial symmetry property of round pegs. The presented Passive Multiple Remote Center Compliance Device (MRCC) introduces a new azimuthal compliance over traditional passive compliance mechanisms that can effectively compensate the peg¡¦s orientation deviation for polygonal assembly. Besides, a special feature of the adjustable compliance provides capability to overcome the gravity effect. Non-vertical insertions therefore become possible. A spring-supported object in space is also adopted for stability analysis of the compliant device. Actual experimental assembly processes demonstrate promising results on polygonal insertions in both traditional top-down and horizontal directions. The assembly process of a square peg consists of approach, one-point contact, two-point contact, three-point contact, four-point contact, rotation, departure from chamfer crossing, and insertion. Full analysis of the square peg mating process, using a quasi-static approach will be presented. Constraints that can avoid the jamming and wedging phenomenon for successful assembly will also be established. Furthermore, a novel geometric insertion map, which is able to predict regions of failure and success before actual insertion takes place, is developed to improve efficiency of successful assembly for square pegs.