Collaborative robots are a promising alternative to traditional haptic displays due to their expansive workspaces, ability to generate substantial forces, and cost-effectiveness. However, they have higher levels of friction compared to conventional haptic displays, which negatively impact the precise movement and accuracy of haptic feedback, potentially causing operator fatigue. This article proposes a novel model-free, energy-based approach for estimating and compensating the friction coefficient. Our approach calculates the time-varying impact of frictional forces during an energy cycle, defined as the period between two consecutive zero crossings of the system's kinetic energy, based on the energy dissipated by friction. This approach directly estimates the friction coefficients, based on the chosen friction model, without requiring any prior system model information or tuning parameters. The effectiveness of our approach is demonstrated through single and multi-degree-of-freedom human interaction experiments using a Franka Emika Panda robot. The results indicate that the proposed approach outperforms state-of-the-art friction compensation methods.