By analysis of the driving-point admittance, it is shown how time delays and discrete control can create instabilities for a simple position controller in contact with the environment. The lowest frequency of contact instability due to time delay or sampling is determined analytically. It is shown how mechanical compliance between the motor and point of contact can eliminate these instabilities. To achieve the best relative stability when contacting arbitrary environments, the mechanical/control design of manipulators should maintain a critical relationship between the frequency of the compliant mode and a frequency associated with contact instability. >