This work introduces an approach for automatic hair combing by a lightweight robot. For people living with limited mobility, dexterity, or chronic fatigue, combing hair is often a difficult task that negatively impacts personal routines. We propose a modular system for enabling general robot manipulators to assist with a hair-combing task. The system consists of three main components. The first component is the segmentation module, which segments the location of hair in space. The second component is the path planning module that proposes automatically-generated paths through hair based on user input. The final component creates a trajectory for the robot to execute. We quantitatively evaluate the effectiveness of the paths planned by the system with 48 users and qualitatively evaluate the system with 30 users watching videos of the robot performing a hair-combing task in the physical world. The system is shown to effectively comb different hairstyles.