In the near future, collaborative robots (cobots) are expected to play a vital role in the manufacturing and automation sectors. It is predicted that workers will work side by side in collaboration with cobots to surpass fully automated factories. In this regard, physical human-robot interaction (pHRI) aims to develop natural communication between the partners to bring speed, flexibility, and ergonomics to the execution of complex manufacturing tasks. One challenge in pHRI is to design an optimal interaction controller to balance the limitations introduced by the contradicting nature of transparency and stability requirements. In this paper, a general methodology to design an admittance controller for a pHRI system is developed by considering the stability and transparency objectives. In our approach, collaborative robot constrains the movement of human operator to help with a pHRI task while an augmented reality (AR) interface informs the operator about its phases. To this end, dynamical characterization of the collaborative robot (LBR IIWA 7 R800, KUKA Inc.) is presented first. Then, the stability and transparency analyses for our pHRI task involving collaborative drilling with this robot are reported. A range of allowable parameters for the admittance controller is determined by superimposing the stability and transparency graphs. Finally, three different sets of parameters are selected from the allowable range and the effect of admittance controllers utilizing these parameter sets on the task performance is investigated.