<p>The thin-walled workpiece with non-equal thickness and closed section, such as a blade, constantly suffers from vibration and deformation in the Machining process. Supporting the workpiece during Machining to improve its local stiffness is an effective solution to this problem. Therefore, an asymmetrical support machining strategy by collaboration of a 6-DOF robot and a machine tool is proposed in this paper. In order to implement this collaborative machining strategy, several unconventional issues need to be solved: (1) The end-supporter path of the robot should be harmonized with the machining path of the machine tool strictly; (2) In the process of collaborative machining, the motion of the workpiece and the multi-DOF structure of the robot will lead to dynamically varying interference between the links and the workpiece, so it is essential to schedule the interference-free joint path of the robot inside the time-varying feasible regions. Aiming at these two problems, this paper proposes a robot path scheduling method with variable interference avoiding for collaborative machining. First, a method based on neutral-surface mapping is presented to schedule the end-supporter path of the robot. Then, the variable feasible space without interference is transformed to the path feasible domain of the interference-avoiding joints using the conformal geometric algebraic theory. Finally, a digraph model is established to obtain the optimal variable-interference-free joint path of the robot. The verification test shows that the scheduled end-supporter and joint paths can effectively harmonize the machining path during collaborative machining.</p>