Modeling and analysis of the equivalent convex mandrel of the three-dimensional braiding carbon fiber composite robotic arm

The third robotic arm (drive housing) of a six-axis industrial robot often has a vertical inwardly concave surface to facilitate the installation of spatially vertical drive motors. With the inwardly concave surface of the robotic arm it is difficult to realize three-dimensional (3D) braiding directly, and based on this problem, an equivalent convex mandrel is added to the concave mandrel. The mathematical model of the concave mandrel is established, and the mathematical expression of the concave mandrel is obtained. In any cross-section perpendicular to the x-axis, the equivalent outwardly convex cross-sectional line is obtained according to the condition that the length of the outwardly convex and concave mandrel cross-sectional line is equal. All outwardly convex cross-sectional lines form a smooth surface of the equivalent convex mandrel. By the numerical calculation method, the braiding trajectory and the downward pressure trajectory are predicted for various take-up speeds. The length error of the braiding trajectory and the downward pressure trajectory are within 5%, which verifies the accuracy of the convex mandrel. The variation pattern of the braiding angle is smooth, verifying the braidability of the convex mandrel. The experimental results show that the outwardly convex carbon fiber fabric can be pressed down to fit the surface of the concave mandrel. Therefore, a carbon fiber composite arm with an inwardly concave surface can be manufactured by 3D braiding with the addition of an equivalent convex mandrel.