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The admittance of a manipulator can be used to improve robotic assembly. If properly selected, the admittance will regulate a contact force and use it to guide the parts to proper positioning. In previous work, procedures for selecting the appropriate admittance for single principal contact (PC) cases were identified. This paper extends this research for some of the two PC cases-those for which each contact occurs at a single point. The conditions obtained ensure that the motion that results from frictionless contact always instantaneously reduces part misalignment. We show that, for bounded misalignments, if an admittance satisfies the misalignment-reducing conditions at a finite number of contact configurations, then the admittance will also satisfy the conditions at all intermediate configurations.