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A drillbit-rock vibro-impact system with a linear rock contact law is considered in this paper. This system is a simplified model to study the drillbit oscillation in a percussive drilling system. The main purpose of this work is to explore the optimized vibration condition of the drillbit to improve the drilling efficiency in practical drilling applications. In order to eliminate the influences of drilling progression on the dynamic analysis of drillbit oscillation, the drillbit oscillation is separated from its drift via oscillation reconstruction. The obtained bounded mathematical model is analyzed by numerical integration and numerical continuation. Based on the codimension-one bifurcations detected by TC-HAT during one-parameter continuation, the two-parameter bifurcation curves are traced by two-parameter continuation. These explored two-parameter bifurcation curves constitute the parameter boundaries for the period-one one-impact oscillation of drillbit, which is verified as the optimal oscillation with the highest drilling efficiency. [ABSTRACT FROM AUTHOR]