This paper presents a novel method to make denim-fabric-polishing robots perform their primary task flexibly and efficiently within a limited workspace. Link lengths are optimized based on an adaptive fireworks algorithm to improve the comprehensive dexterity index. A forward kinematics analysis of the denim-fabric-polishing robot is conducted via the D–H method; the workspace is analyzed according to the needs at hand to determine the range of motion of each joint. To solve the movement condition number of the Jacobian matrix, the concept of low-condition-number probability is established, and a comprehensive dexterity indicator is constructed. The influence of the robot's size on the condition number and comprehensive dexterity index is determined. Finally, the adaptive fireworks algorithm is used to establish the objective optimization function by integrating the dexterity index and other performance indicators. The optimization results show that when the comprehensive dexterity index is taken as the optimization objective, the dexterity comprehensive index and other performance indices of the robot are the lowest; that is, the robot is more flexible. Compared with the traditional genetic algorithm and particle swarm algorithm, the adaptive fireworks algorithm proposed in this paper has better solving speed and solving precision. The optimized workspace of the robot meets the requirements of the polishing task. The design also yields a sufficiently flexible, efficient, and effective robot.
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