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Robots are not typically used for assembly tasks in which positioning requirements exceed robot capabilities. To address this limitation, a significant amount of work has been directed toward identifying desirable mechanical behavior of a robot for force-guided assembly. Most of this work has been directed toward the `standard' peg-in-hole assembly problem. Little has been done to identify the specific behavior necessary for reliable assembly for different types of polygonal parts, and little has been done relating assembly characteristics to classes of part geometries. This paper presents the best passive admittance and associated maximum coefficient of friction for planar force-assembly of a variety of different polygonal parts, specifically pegs with rectangular, trapezoidal, triangular, and pentagonal cross sections. The results show that force-guided assembly can be reliably achieved at higher values of friction when parts are shorter and wider. For all geometries considered, force-guided assembly is ensured for any value of friction less than 0.8 when the optimal admittance is used; and, for some geometries, for any value of friction less than 15.

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