Surface finishing, as the final stage in the manufacturing pipeline, is a key process in determining the quality and life span of a product. Such a task is characterized by low contact forces and minimal material removal from the object surface. Despite the advancements in machine learning and artificial intelligence, human workforce is still irreplaceable in performing such tasks due to superior dexterity and adaptability, but this is often prone to risks such as hand-arm vibration syndrome due to hand-held tools. Therefore, we propose a collaborative approach to assist the human in carrying out such tasks with the help of two case studies: Human–Robot-Collaborative edge chamfering and polishing tasks, based on an impedance controlled collaborative curve tracing technique. We propose a collaborative framework, where the robot assists an operator to guide the end-effector/tool along a pre-defined parametric curve. The algorithm is demonstrated in two scenarios. In the first case, we address a collaborative chamfering task whereas the second case focuses on a polishing application (for straight edges). For these kinds of tasks, the curve to be traced assumes the shape of a straight line along the edge. We make use of the compliant feature of a cobot, which allows the user to physically guide the robot in the task space, to generate a mathematical model for the tool path. From the end-user perspective, this is more intuitive than the classical programming-based path planning approaches. In the process of machining, to enhance the path tracking accuracy and to ensure constant tool-surface contact, we implement guidance virtual fixtures through impedance control. As a result, the machining error is reduced. Nanyang Technological University National Research Foundation (NRF) This project was conducted within the Rolls-Royce@NTU Corporate Lab with support from the National Research Foundation (NRF) Singapore under the Corp Lab@University Scheme.